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[
"Making a \"circular\" hex grid"
] |
[
"math"
] |
[
"gcai2"
] |
[
34
] |
[
""
] |
[
true
] |
[
false
] |
[
0.87
] |
As part of a "just in my spare time" programming project, I'm trying to make a hex grid that is stretched such that the center of each hex is the same distance from the center as the other hexes in its ring. I made up a quick example in SketchUp to show what I mean: Does anyone know of such a system having been used before? More importantly, how would I mathematically determine the coordinates of the corners of each tile?
|
Off the top of my head, the easiest way would be to plot the centres of the hexes where you want them to be, then apply Fortune's algorithm to generate the hexagon boundaries.
|
I'm kind of curious why you can't just use an ordinary hex grid? In a circular grid, the same constraint applies if you measure distance in # of jumps. Each hex in a ring is the same number of jumps from the center as its neighbors.
|
2D Voronoi is n log n, and you only do it once anyway. I doubt you'll get anything much more efficient than that, and if you do, it probably will be a pain in the ass to program.
|
That algorithm should do the trick. (I hadn't seen it before. That's pretty cool.) However, it seems a little unnecessary as it is meant for an arbitrary set of points. This is a pattern, not an arbitrary set. It seems like there should be a much more efficient way of doing it. (In case it wasn't clear, I don't just want to do this once to get the coordinates - I want to write code to dynamically generate the coordinates each time)
|
There is a use for these sorts of algorithms. Bees brood their eggs in hexagon plains. Currently a generic one sized hexagon sheet is given as a base for the bees brood. This means all the bees produced are of one size unlike in nature where they vary. This means that the mite that attacks the brood has a monoculture to adapt to. If instead we made a hexagon plain with varying sized hexagons we could improve bee health. Bee health is important to agriculture.
|
[
"Suggestions for a UG numerical analysis course"
] |
[
"math"
] |
[
"gbshr"
] |
[
4
] |
[
""
] |
[
true
] |
[
false
] |
[
0.83
] |
I'm about to teach undergraduate numerical analysis for the first time and was curious if anybody had any suggestions/advice to relate. For those of you who have taught NA before: do you have a preferred textbook and, if so, why do you prefer it? Are there any freely available textbooks/lecture notes that you feel are worthwhile (i.e., as a reference for students)? How do you like to balance the course between theory and application? Any other suggestions or advice? For students who took a great NA course as an undergraduate: What made the class remarkable for you? Thanks for the input!
|
I never took them, but my undergrad advisor taught some numerical analysis courses. He used the book by Cleve Moler, available for free here . Link to course description, homework, and other resources . He also taught a lower-level introductory course called Introduction to Mathematical Computation .
|
I was curious to see if anybody thought highly of Moler's book. The sample homeworks/tests will be very helpful. Thanks!
|
We are using parts of Cleve Moler's book in an undergraduate numerical analysis course, specifically chapters 1, 2 and 4. I think it's a pretty good book. It offers interesting exercises and good explanations. You can see for yourself if you like it. Personally I am not a fan of MATLAB though, being nonfree. Depending on the scope of the course you may be able to use free software such as GNU Octave , which I think would be a big plus for students.
|
I share your feelings about Matlab, but the free alternatives (I was considering Scilab as well) would seem to be problematic for students wanting to work on projects using on-campus resources. Of course, sticking with Matlab prevents them from completing assignments at home without purchasing a student license so it's a toss-up. I suppose I could accept assignments created using either without too much hassle. Thanks for the feedback on Moler's book. I have looked over it, but it's always nice to get an opinion from somebody who's spent more than a couple of hours with it.
|
This might be more advanced than what you have in mind, but when I was an undergrad I took 6.336 and thought it was totally great. The great part was building (vaguely) useful simulators for circuits and structures and fluid flow and stuff in matlab. Realizing I could actually build something useful out of all this math.
|
[
"Preparing for an undergrad in math"
] |
[
"math"
] |
[
"gco3k"
] |
[
7
] |
[
""
] |
[
true
] |
[
false
] |
[
0.69
] |
A week ago I was accepted to the University of Toronto's department of mathematical and physical sciences, and barring some unforeseen circumstances I'll be starting my undergrad as a math major in the fall. The for math majors uses Calculus by Spivak as a textbook, and I've heard that nearly half of the people taking it end up dropping it by the end of the year. I'm planning on getting myself a copy of the textbook and starting to go through it now in the hopes that it will prepare me well enough to get a relatively good mark. Does anyone have another suggestion for how I could prepare for such a class? Does anyone with first hand experience in this course have any advice? Thanks!
|
Eat lots of fruits and vegetables, and eat more vegetables after that. Eat red meat at least once a week. Find a brand of pencil you like (wood or mechanical), and get a lot of them. I like regular old yellow Ticonderogas and the Pentel GraphGear 500. Get some erasers while you're at it. Buy some nice notebooks. Go ahead and splurge on some leather-bound ones if the paper quality is good. I'm also happy with those big three-subject wirebound ones. I seriously recommend you buy yourself a whiteboard and a bunch of fine tip dry-erase pens (Expo brand is the best). I can't emphasize enough how useful it will be. I use mine every damn day and I absolutely love it. I have a couple small ones (about the size of a piece of paper) and two larger 4'x3' ones for when I need to do some serious mathing. Try to find textbooks online first to save some money, but be wary of eye strain since reading on a computer monitor can be harsh. If you would like physical copies of books, check AbeBooks for an international edition or something. I buy tons of books from places in India and China for a tiny fraction of their North American list price. I definitely prefer physical books over digital ones. If you're not from Toronto, check out the Toronto subreddit . There are regular meetups if you're into that kind of thing but I generally just use it to find out about interesting stuff to do around the city. Get a bike so you can stay fit. Also get a monthly metropass thing (forgot what they're called) to make your life easier. And don't forget to read a regular, non-math book every once in a while.
|
When writing up any kind of proof, make sure to separate solving the problem from writing up the answer. Not only will it spare whoever is grading from navigating all the false starts and bad approaches you try along the way, your proofs will be much, much better for having time to stew.
|
As someone who is finishing his master's in math and a teacher as well, when studying a math text book, always ask yourself the question, "What significance does this particular idea have for the overall framework of the course." Studying math is all about understanding the minute details all the while keeping the big picture in the forefront of the topic. It's a delicate balancing act. If you master this concept, you'll do well. That and tons of practice. Also pay attention to you first proofs course. Take that course as seriously as possible. It took me until grad school to understand how to properly construct a proof. Good proof writing is an art form. Enjoy the next 4 years of hell.... BWAHAHAHAHAHAHA!!!!... cough cough ...
|
This isn't related to your question, but while in your undergrad you should try and learn a programming language (or a few). It makes you much more employable when you actually look for a job. Also do as much summer research as you possibly can. Applying for NSERCs will really help.
|
I'm assuming there are not nearly as many handouts in uni as there are in high school? Depends on the professor but usually there won't be more than a few. Anyways, you don't happen to be studying at U of T, do you? Nah I'm just living in the city temporarily. Did my undergrad in California. Anyway, preparation definitely can't hurt you, but don't kill yourself worrying. Just review your algebra and trig and such. It'll help if you're not still rusty from summer when the class starts. Oh and I can totally understand your love for pens. I always have a giant supply of Pilot G2s around in case of emergency.
|
[
"Is wikipedia right about Legendre polynomials?"
] |
[
"math"
] |
[
"gc71q"
] |
[
2
] |
[
""
] |
[
true
] |
[
false
] |
[
0.62
] |
I did the first few by hand using Gram-Schmidt orthogonalization and ended up with them being 1, x, x - 1/3, x - (3/5)x. What's going on?
|
You agree with Wikipedia, up to a scalar factor. The scalar factor doesn't affect the orthogonality property - it's just a matter of picking what L norm you want the polynomials to have. The wiki article has <P_n, P_n> = 2/(2n+1) .
|
Other people don't.
|
Other people don't.
|
FTFY: http://en.wikipedia.org/wiki/Legendre_polynomials Wolfram agrees with Wikipedia: http://mathworld.wolfram.com/LegendrePolynomial.html
|
The Legendre polynomials as expressed on Wikipedia and Wolfram Alpha are normalized so they equal 1 at x=1. But as kfgauss says they are correct up to a scalar factor.
|
[
"If f(x) is continuous on [a, b] and f'(x) exists everywhere on (a, b), can f'(x) have discontinuities on (a, b)?"
] |
[
"math"
] |
[
"gcaax"
] |
[
33
] |
[
""
] |
[
true
] |
[
false
] |
[
0.79
] |
Hey guys, I am teaching AP calc and I was going through a practice test and I got one question wrong that I don't understand. I feel there is something fundamental that I am missing and I think I've boiled my deeper misunderstanding down to the question I posed in the title.
|
Yes. This is a classic question and the typical answer is f(x) = x sin(1/x) if x != 0 f(x) = 0 if x = 0 The proof that f is continuous, and f' exists but is not continuous is left as an exercise for the reader. :-) The book Counterexamples in Analysis has this and more. Having this book handy will do wonders for you and your class and I highly recommend it. Thank god Dover got hold of the copyright and re-printed it, it is a great book and the original is hard to find.
|
f'(x) exists everywhere on (a, b)
|
There are essentially two kinds of discontinuities for real-valued functions: jump discontinuities and oscillating ones. Jump discontinuities, gaps in the graph, won't happen with derivatives. This can be proved using the mean-value-theorem. Oscillating ones are possible and the standard example has been provided. So if a derivative has bounded variation, it will be continuous.
|
Yes. Use the formal definition. Take the limit as h goes to zero of (f(h) - f(0)) / h which is just h sin(1/h) which goes to zero (sine is bounded). But the derivative function itself is not continuous at zero, because its limit does not exist (the derivative is 2x sin(1/x) - cos(1/x), which doesn't approach any value [because of the cosine term] as x goes to zero).
|
I found this book occasionally useful for my Real Analysis class, most of the counterexamples are more applicable to that class than an AP Calculus class.
|
[
"Mental Math Tips?"
] |
[
"math"
] |
[
"gchou"
] |
[
119
] |
[
""
] |
[
true
] |
[
false
] |
[
0.88
] |
Hello I was wondering if any of you could share some simple mental math tips. If you want to multiply two numbers that are one off, square the middle number and subtract 1. 6 * 4 = 5 - 1 19 * 21 = 20 - 1
|
A related method which I often use is the sum-of-products method. For example: 37 * 13 = 37 * 10 + 37 * 3 = 370 + 30 * 3 + 7 * 3 = 370 + 90 + 21 = 460 + 21 = 481
|
A related method which I often use is the sum-of-products method. For example: 37 * 13 = 37 * 10 + 37 * 3 = 370 + 30 * 3 + 7 * 3 = 370 + 90 + 21 = 460 + 21 = 481
|
This can be shown as a sum of squares x = 20 y = 1 21² = (20+1)(20+1) = x²+2xy + y²
|
This can be shown as a sum of squares x = 20 y = 1 21² = (20+1)(20+1) = x²+2xy + y²
|
wikipedia's got you covered: http://en.wikipedia.org/wiki/Mental_calculation http://en.wikipedia.org/wiki/Trachtenberg_system
|
[
"Math and the Royal We"
] |
[
"math"
] |
[
"gc4cm"
] |
[
40
] |
[
""
] |
[
true
] |
[
false
] |
[
0.79
] |
I noticed while writing out an explanation in my homework today that I, as well as many others in mathematics, habitually use the pronoun "we" -- as in, "To find the limit, must apply l'hopital's rule." In most other sciences, it is customary to use the passive voice -- "The dish incubated at 30 C for 8 hours, after which the contents examined." I also notice "we" in my Physics textbook -- "In this case, can ignore relativistic effects because the speeds are relatively small." My question is, then, to my fellow Reddit mathematicians: Why, when we write about math, do we use "we?" Is it friendly and inclusive, or presumptuous and conceited, or neither? What's your take?
|
When you read a <biology/chemistry/physics/etc> paper, you don't have access to the materials used, thus you will be reading about something someone else was doing. Since the authors would then disinclined to be inclusive of their audience, they naturally use the passive voice which further puts the focus on the subject matter and processes rather than the scientists performing the processes. Math, however, can be replicated immediately by the audience; it's more immediately reproducible and can be followed along. It makes sense to include the audience in this case. Another way to look at it is that math is non-physical -- it's arguably more about operations than components -- so passive voice is more difficult to pull off consistently. For your examples, a "dish" and its "contents" are physically real, but L'Hopital's rule is entirely in the mind. On the other hand, maybe it's just the authors' preference, learned from reading the previous generation's work. Just a thought; who knows the real reason.
|
One aspect of expository style that frequently bothers beginning authors is the use of the editorial "we", as opposed to the singular "I", or the neutral "one". ... There is nothing wrong with the editorial "we", but if you like it, do not misuse it. Let "we" mean "the author and the reader" (or "the lecturer and the audience"). Thus, it is fine to say "Using Lemma 2 we can generalize Theorem 1", or "Lemma 3 gives us a technique for proving Theorem 4". It is not good to say "Our work on this resuit was done in 1969" (unless the voice is that of two authors, or more, speaking in unison), and "We thank our wife for her help with the typing" is always bad. The use of "I", and especially its overuse, sometimes has a repellent effect, as arrogance or ex-cathedra preaching, and, for that reason, I like to avoid it whenever possible. In short notes, obviously in personal historical remarks, and, perhaps, in essays such as this, it has its place. Paul Halmos,
|
I take it as inviting. When I write like that, I feel in some way that I'm including the reader in my arguments. I write as though I'm telling someone how to understand the proof if they were next to me.
|
It isn't the royal we, it's the editorial we.
|
I'm somewhat tempted now to "troll" (if that is the correct word) the grader: "First, the QR factorization of A was taken. Then the transpose of both sides was taken, which resulted in A being written as the product of a lower-triangular matrix and an orthogonal matrix. The textbook was then closed and ice cream was enjoyed."
|
[
"I can't math. How many trips to the moon would it take to equal the distance to the sun?"
] |
[
"math"
] |
[
"fzalb"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.25
] | null |
366
|
The moon is roughly 250,000 miles from the earth. Actually, on average it's 238,857 miles . The sun is roughly 93 million miles from the earth (more or less depending on time of year). Trips to the moon and back would be approximately 477,714 miles so 93000000 / 477714 = ~186 trips. Also: google.
|
Division dude.
|
off the top of my head, a bit under 400. The moon's about a quarter of a million miles, the sun's a bit under a hundred million miles (about 7% less). 100/(1/4) = 400. More accurately, adjusting for the 7% less makes it about 372-ish one way trips to the moon = a single one way trip to the sun. More accurately still, the average distance to the moon is a tiny bit less than a quarter of a million miles, but that will change it by less than 1%. If you want it more accurate than that, look up the distances and use a calculator
|
Thank you all. I figured near 400 given the moons average distance.
|
[
"35 years on and I still can't solve it..."
] |
[
"math"
] |
[
"fy6iu"
] |
[
286
] |
[
""
] |
[
true
] |
[
false
] |
[
0.9
] | null |
He said "I think you should be doing your school homework without cheating" and promptly switched off the computer. What an ignorant asshole.
|
I tried it again. This time I measured the apparent parallax movement of my thumb to an object twelve feet away. Extrapolating from that ratio in arcseconds, I calculated that the opposite wall is 0 AU away. X = 0 AU.
|
My dad posed this problem for me when I was around 12 years old, and I still have no clue as to how to solve it. Two ladders rest in opposite sides of a room. One is 10 feet long, while the other is 12 feet long. They each touch both walls, and cross over five feet from the floor. How wide is the room? I am in no way maths/trig inclined (Being an electrical engineer only requires you to remember two equations :) I remember writing a BASIC program to iterate through the room width until they met. Not having a computer, I kept the listing written on a tatty piece of paper in my pocket until I could visit a Tandy store in the Big City, whereupon I painstakingly entered it into their demo TRS80. At that point, a salesman came up and asked me what I was doing. I explained that I was entering a program to solve trig problem I was working on. He said "I think you should be doing your school homework without cheating" and promptly switched off the computer. To this day, I have never seen this problem posed anywhere, and have no idea as to how to go about solving it. Any takers?
|
Two ladders rest in opposite sides of a room. One is 10 feet long, while the other is 12 feet long. You should have clarified that. The way you drew the diagram, it looks like you mean the segments from the crossover point to the wall are 10 and 12 feet, not that the entire line from the walls to the corners are 10 and 12 feet.
|
You can do it by translating the problem onto the 2D plane with, say, the bottom-left corner as (0,0). Then write two equation for the two lines (representing ladders), which are: y = x * sqrt(12 - X /X y = (1 - x/X) * sqrt(10 - X where X is the width of the room. Rearrange for x and equate the two, and set y=5. This gives you an equation purely for X. PS: The resulting equation is quite messy. PPS: According to wolfram alpha, the answer is [SPOILER] 4.297 feet.
|
[
"A couple of years on, and I'm not even going to try"
] |
[
"math"
] |
[
"fymf8"
] |
[
229
] |
[
""
] |
[
true
] |
[
false
] |
[
0.91
] | null |
The proof is left to the reader as an exercise.
|
The proof is and left as an exercise for the reader.
|
You're forgetting that every mathematical theorem is either trivial or unproven. I guess if it's unproven then it's not a theorem, but you get the idea.
|
The =42 is implied.
|
They always say it's trivial...but I think the writers of our maths books forget that we are still learning the material and (unlike the authors) are not masters on the topic. Or as I frequently tell one of my maths professors
|
[
"Euler's Identity explained in 5 minutes"
] |
[
"math"
] |
[
"fxcpo"
] |
[
82
] |
[
""
] |
[
true
] |
[
false
] |
[
0.85
] |
[deleted]
|
Cool, but I would rather have had a 10 minute explanation at half his talking speed. FUCK
|
I liked his dig at string theorists
|
I never knew Seth Rogan was so smart.
|
I've also found extremely irritating. Don't know why this guy has to talk like sheldon or even say PI until 300 decimal places. It's not funny, quite the opposite, smug and embarrassing... However, i've found that was quite a good explanation (if you have a somewhat solid foundation of the mentioned concepts).
|
The derivative of e is still equal to e and taylor series can be defined the same way for complex functions. Is that sufficiently suitable? You can show that the derivative of e exists by noting that e = e cos y + i e sin y, so the partial derivatives exist everywhere and the Cauchy-Riemann equations are satified, so you can just use the difference quotient of a limit to find it like you do with real numbers.
|
[
"variablekitten (comic)"
] |
[
"math"
] |
[
"fwctu"
] |
[
3
] |
[
""
] |
[
true
] |
[
false
] |
[
0.57
] | null |
I did that once for a physics exam. Had already used so many variable names, I ended up drawing a square and a circle and a triangle for some integration constants (forgive me, it was at the end of a four-hour exam). My prof wasn't too happy.
|
Well it was a physics problem, so many variables already had an implied signification beforehand. TBH I was a bit tired so there were probably letters I hadn't already used.
|
You went through the greeks as well? Damn. I don't think I could effectively keep track of that many variables in a meaningful manner.
|
Hmm, that's true.
|
I like the alt text for this one
|
[
"Just to prove you are a human, please answer the following math challenge. (mandatory)"
] |
[
"math"
] |
[
"fxaf6"
] |
[
250
] |
[
""
] |
[
true
] |
[
false
] |
[
0.92
] | null |
It asked me for a proof of Fermat's last theorem but the field isn't large enough to accomodate, WTF?
|
Can you fit it in the margin?
|
Yes, yes it appears we do :)
|
Seems a bit too easy to OCR and feed into WolframAlpha.
|
Hello, I'm here to collect your Nerd Card on behalf of Maths.
|
[
"This is horrible, but I love this footnote"
] |
[
"math"
] |
[
"fw6pr"
] |
[
288
] |
[
""
] |
[
true
] |
[
false
] |
[
0.94
] | null |
For those who don't get it, that guy is better known for being the Unabomber.
|
It's also rare to see the name "Kaczynski" in such close proximity to the phrase "nice correspondence."
|
According to someone I know who worked with some of his contemporaries at Berkeley "he was considered one of the more normal ones".
|
Hey, Gerry, In the 1960s there was a young man that graduated from the University of Michigan. Did some brilliant work in mathematics. Specifically bounded harmonic functions. Then he went on to Berkeley. He was assistant professor. Showed amazing potential. Then he moved to Montana, and blew the competition away.
|
Pythagoras forbade his followers from eating beans because they reminded him of testicles.
|
[
"When was your \"shit just got real\" moment in math?"
] |
[
"math"
] |
[
"fwdqf"
] |
[
1
] |
[
""
] |
[
true
] |
[
false
] |
[
0.53
] | null |
............... ...............
|
When I bought the book that cost 190 bucks. Besides that Laplace Transforms... everything about them makes me sick.
|
When I multiplied by a complex conjugate.
|
Euler's solution to the Basel problem
|
The realization that questions about homeomorphisms between manifolds can be asked (and answered) in terms of group homomorphisms. That's when I "got" the "why" for algebraic topology.
|
[
"pure mathematics"
] |
[
"math"
] |
[
"fwekj"
] |
[
11
] |
[
""
] |
[
true
] |
[
false
] |
[
0.69
] | null |
Definition of the Killing Vector Field edit:
|
Not exactly. That symbol is the Covariant Derivative . It also uses the 'del' or 'nabla', but has a lower index to indicate the direction in which the covariant derivative is to be taken. It's also apparent given the context of the paper, which appears to be Riemannian differential geometry. edit: Found the equation - if X is a Killing Vector Field then [; {\cal{L}}_{X} g = <\nabla_{Y} X, Z> + <\nabla_{Z} X, Y> = g(\nabla_{Y} X, Z) + g(\nabla_{Z} X, Y) = 0;] for all Y, Z. It's the definition of the Killing Vector Field.
|
S'alright, bro. Somebody here appreciates the revelation!
|
I didn't quite get the last equation, what is it?
|
Thanks dopplerdog for the correction :)
|
[
"Doodling in Math Class: Stars"
] |
[
"math"
] |
[
"fwraf"
] |
[
165
] |
[
""
] |
[
true
] |
[
false
] |
[
0.89
] | null |
But nowhere near as cool as her cousin Emacs Hart
|
Source
|
Vi Hart is totally badass.
|
How lost you are.
|
Yes, but it doesn't follow the Q=n as was described in the video - where you count the number of "n spaced dots" over from your current pencil mark and draw the line there.
|
[
"The 86 Conjecture - no powers of two higher than 2^86 do not contain zero."
] |
[
"math"
] |
[
"fwr5m"
] |
[
37
] |
[
""
] |
[
true
] |
[
false
] |
[
0.84
] | null |
Version with double negative removed: All powers of 2 higher than 2 have at least one zero.
|
Fun.
|
You've gotten the 'Math is fun' answer, so here is another take. What is the value of being able to lift a 40 lb dumbell above your chest? Achieving that goal is not itself useful, but rather it's an indicator that you've reached a new plateau of strength. The other answer is that we just don't know how it may be useful. An optimist might tell you that it could be useful for something in particular, such as cryptography. I would tell you that it is valuable to uncover these kinds of universal truths about the way the universe must be. The truth is useful.
|
Actually the digits are randomly distributed because log(2) is irrational. If you read about this dynamical system, you will learn that the orbit of the map x -> x + lambda (modulo 1) fills the interval uniformly densely iff lambda is irrational. You can use this fact to calculate all sort of interesting probabilities and perform this author's argument more rigorously.
|
Actually the digits are randomly distributed because log(2) is irrational. If you read about this dynamical system, you will learn that the orbit of the map x -> x + lambda (modulo 1) fills the interval uniformly densely iff lambda is irrational. You can use this fact to calculate all sort of interesting probabilities and perform this author's argument more rigorously.
|
[
"It's March 1st, 11:42 my time. I need to accomplish something this month, so I need an equation to start with. Thanks!"
] |
[
"math"
] |
[
"fvlmc"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.44
] |
[deleted]
|
Consider the \sum (1/n) For what values s is this zero?
|
A common misconception is that 1/0 = infinity. It really is what the calculator says, undefined.
|
Take a look at the polynomial solutions of Lamé's differential equation .
|
Solve the Rayleigh-Plesset equation in its simplest form. [; \ddot{R}R+3/2\dot{R}^2=K((\frac{R_{o}}{R})^3-1) ;] Overdot is time derivative. Initial conditions R(0)=Ro*(1+epsilon) will yield a sinusoid with frequency sqrt(3K/Ro).
|
...er skywalker? But seriously, here's one for you. Consider chain of 2x2 diamonds which add up to N and which satisfy a left to right geq relation. For example, 3 2 0 4 2 1 0 2 1 1 is a length 3 chain for 16. Find the generating function for the number of such partitions with chains of length R. This has been done, btw. My masters advisor wants me to extend this result to m by n diamonds before we start work together. =)
|
[
"This is what they teach in middle school now... completely true story."
] |
[
"math"
] |
[
"fw601"
] |
[
327
] |
[
""
] |
[
true
] |
[
false
] |
[
0.83
] | null |
ARGH THIS MATH IS NOT PURE ENOUGH
|
They teach infinity to middle schoolers? Holy shit things have changed.
|
I don't really get what's so bad about this... It's nice of the teacher to give the kids an easy way to remember what taking the absolute value does. I don't think it impedes their understanding of what it means.
|
Fuck, the equation was actually |x|+|y|=10. My bad.
|
"In mathematics you don't understand things. You just get used to them." - John von Neumann There is nothing to "understand" conceptually about the absolute value function. When we restrict ourselves to the reals, the function does exactly this -- turns any number positive. Any deeper understanding you feel you have about absolute values is something you've gained not from being told a definition but from experience. It wouldn't really make sense to teach anything else than this definition to a middle schooler. To call the absolute value of a number the distance from the origin to that number isn't so enlightening if you haven't seen complex numbers or vectors before, it seems like a very roundabout way of saying that you get the number but turned positive. But, if you let the kids play a bit with absolute values, maybe look at the triangle inequality, they will understand absolute values as a distance. Basically, my point is that the way the teacher phrases it isn't nearly as important as the kids' own experience solving problems using it. Also, you can't argue that the simple "positive version of the number" definition is never useful; I feel like I use it a lot. Imagine yourself teaching introductory trigonometry. How would you teach students how to remember which function is the sine and which is the cosine? There is no way but simple memorization. I still think to myself "the simpler one is the one without the 'co', and that's the one that passes through the origin". You need mnemonic aids, and if this one works for middle schoolers, then it's good that they're teaching it.
|
[
"What are the best math undergrad programs in Canada?"
] |
[
"math"
] |
[
"fvh0c"
] |
[
14
] |
[
""
] |
[
true
] |
[
false
] |
[
0.74
] | null |
How about the University of Waterloo? It's the only school in Canada with a math FACULTY.
|
I can't speak for other universities but UWaterloo has a very strong mathematics programme. We have one of the few faculties of mathematics in North America (only one in Canada I believe) which allows for a very diverse offering of courses. By this I mean we have both applied mathematics and pure mathematics so you take a number of courses (analysis, algebra, and so on) at two completely different levels. Additionally have a whole faculty allows for a much larger breadth of courses available. There is a whole department dedicated to statistics, combinatorics and optimisation for example. Most universities cannot offer this simply due to size. However I don't know how it compares to others and I am just going on what I've heard and experienced. EDIT: To clarify a point, at Waterloo if you are in mathematics or computer science (one of the departments) you get a BMath. Not a BSc or a BA.
|
I can. The answer is it really depends. This year the number of NSERC in pure mathematics was lower then normal and same with applied mathematics, thus the competition was fierce. I know many very strong people (who have held NSERCs in the past) get denied. Pure mathematics (I can only speak about friends who have won NSERCs in pure mathematics so my information is based on talking with them) is notoriously competitive given that we have a department of pure mathematics and it has very strong analysis and number theory groups so it attracts very bright people in those areas. Additionally, I think it's more difficult to do good quality research in something like pure mathematics as it is much more academically demanding then, say, experimental physics (not to knock that!). Since the field is very small you get the best and brightest applying. However given that we have such a large faculty this does mean there are more NSERCs to go around. Each department has multiple (I think about 5-6 but it varies depending on funding plus you can get funding other ways) NSERCs so there are simply more to go around. Additionally, depending on what you like, there are places like the IQC which pulls people from chemistry, engineering, physics, computer science, applied mathematics, and pure mathematics so there is a lot of opportunity there. It really comes down to what you want to do.
|
I'm not from there, but by reputation alone, the math specialist program at UofT appears to be excellent. One of the really great things (or terrible things, depending on perspective) about UofT is that the department is , which means that there are lots of profs, courses, grad students, seminars, etc. Also, the nearby Fields Institute brings in a lot of active researching mathematicians to the area providing more opportunity for upper level students to hear such people give talks. Waterloo, of course, also appears to be excellent. I was there for CUMC last year, and felt that the place had a lot of really intelligent undergraduate students.
|
I'm currently studying at McGill in the Joint Honours in Mathematics and Physics program. This program is extremely demanding, as we are basically expected to undertand everything from the honours math program and everything from the honours physics program (as the name would suggest). The program is very well suited for those interested in mathematical physics, but is also comprehensive enough for those interested in further studies in pure math or theoretical or experimental physics. If physics is not your thing, the regular honours math program here is also great (I can attest to this because we share many of the same classes). McGill also offers a joint program in math and computer science.
|
[
"MATH. Not even once."
] |
[
"math"
] |
[
"fvjuw"
] |
[
536
] |
[
""
] |
[
true
] |
[
false
] |
[
0.89
] | null |
What is an anagram of Banach-Tarski? Banach-Tarski Banach-Tarski.
|
Some of us are pro-choice.
|
There are equally many numbers between [0,2] as there are between [0,1]. Math. Not even once.
|
Sorry, I don't accept the axiom of choice in it's strongest form. Take that, Banach-Tarski paradox!
|
1+2+3+4+.... = -1/12 -Math, not even once. (ramanujan summation)
|
[
"Fucking Concrete Abstract Algebra"
] |
[
"math"
] |
[
"fupl8"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.36
] | null |
Excessive swearing does not make mathematics better. If I didn't already know what a group was, I would be hard-pressed to understand what this guy is saying. This would be quite funny if the title was "Fucking Concrete Abstract Algebra" and there was no further swearing (or no excessive swearing) but this is kind of stupid.
|
It's also in the scribd archive which makes it even kinds of stupid. (Insert cardinality of the infinities joke here.)
|
It's also in the scribd archive which makes it even kinds of stupid. (Insert cardinality of the infinities joke here.)
|
I've read several things on the scribd archive which were good (ranging from quantum books to harmonic analysis texts to specific papers). But admittedly, I was looking for those things in particular so I have no idea how good scribd is overall.
|
The problem is, someone posts something to scribd, and then after a while scribd starts charging for download access to it. I'm not sure what the time period is, but it's kind of annoying. (Basically, scribd found out they couldn't make money off of ads, so they're charging for downloads of materials that others contributed.)
|
[
"We're fucked."
] |
[
"math"
] |
[
"fupwp"
] |
[
28
] |
[
""
] |
[
true
] |
[
false
] |
[
0.71
] | null |
A more tongue-in-cheek treatment: "How many zombies do you know?" Using indirect survey methods to measure alien attacks and outbreaks of the undead
|
Yeah. One of my committee members told me I need to get on that Latex band wagon. But I still use sheepskin.
|
Yeah. One of my committee members told me I need to get on that Latex band wagon. But I still use sheepskin.
|
OMG! THAT'S MY PROFESSOR! Robert Smith? (Yes his last name actually has a ? in it) He is awesome!
|
I thought one couldn't get more tongue in cheek than the OP. I was wrong, and upvoted you accordingly.
|
[
"I set up a little something for PI day! Call (253)243-2504!"
] |
[
"math"
] |
[
"g3cbx"
] |
[
16
] |
[
""
] |
[
true
] |
[
false
] |
[
0.73
] | null |
Christopher Poole ...moot?
|
Nope, a different one :/ He's richer!
|
Sneaks up on you! I've been looking forward to pi day since I set this up a couple months ago. I wasn't sure if I dared post this. I have no clue how my little server will fare against the internets!
|
I kept waiting to order key lime.
|
Pi day is tomorrow! Didn't even realize!
|
[
"A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles (pdf)"
] |
[
"math"
] |
[
"fv5mc"
] |
[
32
] |
[
""
] |
[
true
] |
[
false
] |
[
0.84
] | null |
So it's not really an algorithm for completely solving it? Just how to do it efficiently? I thought this was the way most people ended up solving them..
|
I started reading and I was like "Isn't this the way I do it already?" Though apparently not, because I never seem to finish them
|
For those who might not want to spend the time: if you can already do Sudoku's that are ranked fairly difficult, you probably already use some form of the method described in this paper, without the mathematical terminology.
|
Why don't you use a Sharpie?
|
Brainbashers has a really good list of sudoku techniques here . The advanced levels get pretty hairy to keep track of in your head, but they let you dissect really tough puzzles, and that's sort of the point of sudoku to me anyway. None of these methods require guessing.
|
[
"Hitler Learns Topology"
] |
[
"math"
] |
[
"fus25"
] |
[
482
] |
[
""
] |
[
true
] |
[
false
] |
[
0.88
] | null |
Watch out guys. Coming are spaces which are connected but not path-connected, and non-compact spaces which, when made , become compact. [EDIT: had my 'path' in the wrong place]
|
This reminds me: Munkres' Topology contains the most awful, terrible, no-good joke I have ever seen, either math-related or not: An answer to the mathematician's riddle:"How is a set different from a door?" should be:"A door must be either open or closed, and cannot be both, while a set can be open, or closed, or both, or neither!"
|
Actually, Hitler would have dismissed Topology as "Juden Mathematicks" and been done with it. Hausdorff studied at the University of Leipzig, obtaining his Ph.D. in 1891. He taught mathematics in Leipzig until 1910, when he became professor of mathematics at the University of Bonn. He was professor at the University of Greifswald from 1913 to 1921. He then returned to Bonn. When the Nazis came to power, Hausdorff, who was Jewish, felt that as a respected university professor he would be spared from persecution. However, his abstract mathematics was denounced as "Jewish", useless, and "un-German"[citation needed] and he lost his position in 1935. -- Wikipedia
|
I loved topology, but the vocabulary was terrible. Half the difficulty of the class was trying to form intuitive ideas for concepts what they were named. This is one of the most well-done Hitler memes I've ever seen. The conversation flow was perfect and the lines well-timed to the video. An excellent production.
|
Soapbox time. You are making an error here. You're mapping everyday concepts like "dart", "line", and "dartboard" onto mathematical concepts like "point", "line", and "unit disc". (For example, we can easily model dart impact areas as small circles.) Then you do some reasoning on the mathematical concepts, which is fine in itself. But then you map the mathematical concepts back onto the everyday concepts. . You're implicitly assuming that you're dealing with a bijection here, but you aren't necessarily. (To put it another way: In the real world, if I put a fine thread across a dartboard, p ≠ 0 that it will break on a typical throw. So your metaphor assumes a contrafactual, and points it makes are not fair to insist upon.) Neither your friend nor you is correct, because neither of you have well-defined terms. If you want to explain to your friend that a line does not have area in ℝ yet does contain points, find another way. Abusing his common sense is not rigorous and discourages him from thinking of math as connected to sanity. I don't mean to sound harsh. I'm really glad you're explaining things to your friend. But please don't use oversimplified models that may discourage people.
|
[
"Mathematicians invent a new way to pour stout"
] |
[
"math"
] |
[
"g2osf"
] |
[
157
] |
[
""
] |
[
true
] |
[
false
] |
[
0.89
] | null |
one junior lecturer and a couple students could be worth millions of dollars to beer companies used his previous knowledge from reducing air bubbles in milk products reducing waste and extending shelf life. Better?
|
In that spirit representatives of Diageo, which owns Guinness, one of the most widely sold brands of stout, approached Dr Lee in 2009. Perhaps they are funding him.
|
This article implies that all stouts are nitro stouts...
|
Actually, the fluids behind beer bubbles and how they behave (as well as the fluids done by William Lee) is extremely complicated. Also, there is no "waste of academic funding." Understanding the physics of our universe, no matter how ridiculous it might sound, is a step for humankind in the right direction. You never know what side applications or inventions could be produced from something like this. Maybe a particular process for modeling bubbles can be produced, thus reducing cavitation in other several applications where cavitation is very dangerous.
|
This is another reason why reddit is wonderful; it is unlikely I would have found this article on my own, so thanks for posting! I can't wait to share this with my stout-loving mathematician father.
|
[
"“It is possible to translate any Turing machine into a set of Wang tiles, such that the Wang tiles can tile the plane if and only if the Turing machine will never halt.”"
] |
[
"math"
] |
[
"g1r53"
] |
[
70
] |
[
""
] |
[
true
] |
[
false
] |
[
0.91
] | null |
Something tells me that Turing would have been very fond of Wang had he lived into the 1960's...
|
The halting problem is undecidable (that is, you cannot construct an algorithm to solve it for every input). Since it is equivalent as determining whether a set of Wang tiles can tile the plane, determining that is undecidable too.
|
Wikipedia's not that fantastic for learning mathematics, IMO. The articles tend to be written assuming you already fully understand most of the related articles, and they usually try to use the most succinct/elegant notation rather than the most easily understandable. To paraphrase one person's comment, (I believe it was on the discussion section of WP's article on Maxwell's Equations), "Undergrads don't come here to learn [because the material isn't presented in a highly accessible way] and grad students only come here to nitpick." Having said that, I do agree with you; it's far better than nothing. However, for mathematics, Wikipedia falls short of being the wonderful tome of knowledge and understanding that it often can be for the other sciences.
|
I wish Wikipedia existed when my brain was young and flexible. You aspiring mathematicians have it so much better than we did.
|
The quote in the title is taken out of context. It's part of a proof that Wang's algorithm (which was said could determine if a given set of tiles tile the plane) didn't work and that no such algorithm is possible. The argument sketch says something like: The Wang tiling problem is undecidable, because it could be used to solve the halting problem, and therefore no such algorithm can exist. edit: reworded for clarity
|
[
"Philosophy and mathematics share Thales, Pythagoras, Descartes, Leibniz, Newton, Pascal, Bolzano, Frege, Russell, and Gödel. But at UNLV, the sister of mathematics is under deathly threat."
] |
[
"math"
] |
[
"g1mf6"
] |
[
13
] |
[
""
] |
[
true
] |
[
false
] |
[
0.77
] |
[deleted]
|
It's sad, but inevitable in my opinion. In the U.S. I'm afraid we will see more and more of this at public universities. So many people (voters) don't really understand education - they confuse it with training - that as the state budget woes deepen, politicians will realize that this kind of cutting is acceptable to voters. It may well be that within ten years, only the most famous and prestigious of state universities (North Carolina, Virginia, Texas, Berkeley, ...) will survive as real universities.
|
The dean summons the physics department chair to his office. “You people are bankrupting us!” he fumes. “Why do you need all this expensive equipment? All the mathematicians ever ask for is pencils, paper, and erasers. And the philosophers are better still: they don’t even ask for erasers!”
|
I am majoring in math, but philosophy has always made me want to pull my hair out. I still think it is important and can only upvote this post since I don't attend that college or live anywhere close to Nevada. Hopefully things work out and they realize the importance in philosophy or at least try to combine it in someway to save money, because most schools sadly won't make cuts to popular programs.
|
Psychology is applied Biology, Biology is applied Chemistry, Chemistry is applied Physics and Physics is applied Math...and Math is applied Philosophy.
|
math/philosophy double major (listed in that order for a reason). this is a sad day. it is very strange that they refused to consider horizontal cuts in funding.
|
[
"HELP! I need help with a Calculus II problem my teacher gave us."
] |
[
"math"
] |
[
"g28hi"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.4
] | null |
http://www.reddit.com/r/cheatatmathhomework/
|
Holy fuck, you don't know how lucky you are. You're learning about using the properties of a family of polynomials to evaluate the limit of an integral. You're synthesizing two seemingly unrelated areas of mathematics to find the solution to a problem that is simple to state but, in reality, is hard to do simply. Try your best to understand how fucking awesome what you're doing is, and you may just get something out of the assignment. I wish I had these kinds of assignments when I was in Calc II. Thanks for the image, saved it in case I ever need an interesting problem to assign. Is there another page to the assignment?
|
Focus on the Bernoulli polynomials, forget the Riemann sums. Now, this shit is tedious but not that hard. The [; B_n(x) ;] are just cool polynomials, that in your context, will serve the practical purpose of calculating Riemann sums. First off, you need to find out what they look like using the recurrence relation [; B'_n(x) = B_{n-1}(x) ;] and the fact that [; \int_{0}^{1}{B_n(x)} =0;] . To do this, integrate [; B_0 ;] . This will give you [; B_1 (x) = x + a ;] . Now, we have that [; \int_{0}^{1}{B_1(x)} = 0;] and so [; a = -1/2 ;] . This way you can find [; B_2(x) ;] and so on.
|
Thanks!! Just did that!
|
As for the second part, by the fundamental theorem of calculus, we have that [; \int_{0}^{1}{ B_{n}'(x) } = B_{n+1}(1) - B_{n+1}(0) ;] and so the result follows.
|
[
"Ronald McNair, then 9, wanted to check out books on calculus, but the librarian wouldn’t release them. “We don’t circulate books to Negroes”"
] |
[
"math"
] |
[
"g1zyq"
] |
[
305
] |
[
""
] |
[
true
] |
[
false
] |
[
0.92
] | null |
Seriously a 9 year old who a racist tries to get arrested for borrowing a maths book, then he becomes and astronaut? #mynewhero
|
The usual crap about "that's just the way it was" or "those were different times".
|
This man is actually one of the main reasons I've been able to attend graduate school. There's a program that was started in his memory called the McNair Scholars program that helps disadvantaged students move toward research and into graduate school. Its sad because almost every year the program had problems getting students to apply/finish the program.
|
If the librarian would have succeeded in preventing him from getting those books, he would probably still be alive. :D
|
Based on your past comments and submitted links, this man's legacy probably does not want to be associated with you
|
[
"What's a good reference for differentiating under the integral sign, even when the integral is improper, i.e. limits +/- infinty?"
] |
[
"math"
] |
[
"g0xqq"
] |
[
13
] |
[
""
] |
[
true
] |
[
false
] |
[
0.89
] | null |
Wikipedia has a very nice, detailed article on Differentiation under the integral sign . By the way, it turns out that this was one of Richard Feynman's favorite tricks (see note at the end of the wiki article).
|
Here's a pretty comprehensive list depending to what generality/context you're looking to differentiate under the integral sign: http://planetmath.org/encyclopedia/DifferentiationUnderIntegralSign.html I think the last source cited by the article is probably in your wheelhouse
|
Folland's Real Analysis book gives necessary and sufficient conditions to be able to do it. its on page 56 and its theorem 2.27.
|
Integrals of this form are exactly the kind you can move the derivative operator inside the integral for. It's called Leibniz's rule .
|
Yes. According to the Algebraic Limit Theorem, Liebniz's rule still applies with improper integrals expressed as limits to infinity so long as the limits exist (and are finite?). You can see this by writing your integral as a limit, then looking at how it would fit in the proof of the basic form of Liebniz's rule on the wikipedia page. Just remember the constraint that f and f' need to be continuous everywhere in your case.
|
[
"\"I don't think math is a science. I think it's a religion.\""
] |
[
"math"
] |
[
"g0zrm"
] |
[
55
] |
[
""
] |
[
true
] |
[
false
] |
[
0.71
] | null |
He's right, math isn't a science. It's philosophy - applied logic.
|
It need not relate to the physical world.
|
True. But mathematics can be studied for the sake of mathematics, without any knowledge or interest in the real world.
|
The pursuit of knowledge of the world we live in.
|
- John Barrow
|
[
"Mathematica Demonstrations now run in the browser"
] |
[
"math"
] |
[
"g0gvu"
] |
[
14
] |
[
""
] |
[
true
] |
[
false
] |
[
0.8
] | null |
Oh I thought they were demonstrations... Nice anyway :)
|
Was that sarcastic or are you from 1998?
|
Well they run in some silly plugin. If you like it you should look into shockwave and vrml.
|
Ask yourself if those things were good in 1998.
|
Boring. You could do that with MapleNet and Maplets in 2002. The only thing this shows is that Wolfram is really good at Marketing.
|
[
"I need a closed form for this, anybody?"
] |
[
"math"
] |
[
"g04yo"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.4
] | null |
There isn't a closed form.
|
Well, yes, that too. But unless OP is willing to expand the "standard" set of functions allowable in a "closed form", there isn't a closed form.
|
Expanding to include a list of analytic functions that Mathematica happens to support won't help; none of the functions have the requisite periodic behavior. (If you allow number-theoretic functions, I retract my statement; there may well be some contrivance there. But this gets at the quintessential problem of defining a "closed" form and provides no performance boost.) The reason I am so quick to dismiss this is because the sequence exhibits a high degree of quasi-periodicity - in fact, the Fourier transform for this sequence is fascinating. (Try writing it out sometime. It's not too hard.) You aren't going to shove gammas and Bessels and Meijers into a box and spit out something with that sort of behavior. If you could elaborate more on why you need this, maybe I could be of more help. It looks like from another post that you're interested in something like this (from the OEIS page): G.f.: Product_{k >= 0} (1 + y*x^(2^k)) = Sum_{n >= 0} y^a(n)*x^n. - N. J. A. Sloane, Jun 04 2009 Like I said, there's enough periodicity that working with the sequence is not so hard. There's not a good closed form, though. And if you need fast machine calculations just take sign(AND(1,x)) + sign(AND(2,x)) + sign(AND(4,x)) + ...
|
Oh, one more thing that I looked into because I was bored. If you're working in Mathematica, write then your function is given by Sum[SquareWave[{1,0},x/2 ],{n,1,:infty:}]. However, this will of course fail to evaluate. But it is relatively easy to Fourier-transform this now.
|
Or have any ideas about finding such a form?
|
[
"Tan() demystified [GIF]."
] |
[
"math"
] |
[
"g15ei"
] |
[
1198
] |
[
""
] |
[
true
] |
[
false
] |
[
0.94
] | null |
I made this animation to illustrate what tan() does in Processing. If anyone is interested, I can post the code as well.
|
Maybe your head isn't oriented correctly. Stop being so self centered.
|
Well, what I posted indeed wasn't a graph at all, but rather a visual explanation of how the values for tan() are defined. Understanding how it relates to graphs of functions such as tan(x), arctan(x), tan(kx+t), arctan(kx)+t leads to understanding, zen and peace on earth (or, at least, somewhere in that direction).
|
You should label your axes. It looks like arctan(), using the conventional arrangement.
|
Here is the thing running in browser. Hover mouse over left edge to see the code. It's nothing insightful, just something to get the job done without much thinking. EDIT: here's how to modify it for sin(x) . EDIT2: fixed accidentally replacing the original code :)
|
[
"Found this while grading some algebra homework."
] |
[
"math"
] |
[
"g0exy"
] |
[
175
] |
[
""
] |
[
true
] |
[
false
] |
[
0.74
] | null |
I see you're deriving around town with the group I love.
|
And I'm like, ∀ u.
|
math joke
|
I guess LaGrange in my pocket wasn't enough...
|
So I'm like, function of two
|
[
"Statements of propositional calculus that assert their own unLaTeXifiability, Advances in Notation, to appear."
] |
[
"math"
] |
[
"g0qul"
] |
[
47
] |
[
""
] |
[
true
] |
[
false
] |
[
0.89
] | null |
Cocomputing cocohomological coobstructions to cocombing the cohairs on a cococonut using coCoCoA This is fantastic.
|
Upvote for Jeremy Martin. I have had the pleasure of learning mathematics from him at the University of Kansas.
|
Every once in while you'll hear someone ask about the implications of Gödel's Incompleteness. I wish these were real publications.
|
This is comedy gold, good sir.
|
"Sesquinonequihypermultidesingularizationalisticity" - I think I found my new topic of research.
|
[
"Neat fractal I made, related geometry / number theory questions inside"
] |
[
"math"
] |
[
"fzdub"
] |
[
5
] |
[
""
] |
[
true
] |
[
false
] |
[
0.69
] | null |
This is called Apollonian circle packing (see http://en.wikipedia.org/wiki/Apollonian_gasket ). The 3-dimensional version is called Apollonian sphere packing (see http://en.wikipedia.org/wiki/Apollonian_sphere_packing and http://graphics.ethz.ch/~peikert/papers/apollonian.pdf for nice pictures) and works in exactly the same way. If your 3 starting circles have radii of the form 1/n for some natural number n then all circles have radii of the form 1/n also (for some other natural number n). Although I don't know about them having rational centers, I doubt that this would be the case in general. You can do this perfectly well in spherical and hyperbolic geometry, for the latter see "Indra's Pearls: The Vision of Felix Klein" by David Mumford, Caroline Series and David Wright ( http://en.wikipedia.org/wiki/Indra's_Pearls_(book) ).
|
What are these points you offer good for?
|
Karma. For every 100 points you earn, I will upvote one of your submissions.
|
Could you publish your Mathematica source?
|
This is a problem I have had for a while. It's based on just random doodles in notebooks and the like, and I recently solved it - at least the main part of it (part 2), but I'm curious if anyone has more insight. I'm giving each part a weight based on how interesting I think it is. Given any triangle on a Euclidean plane, construct three circles centered on the vertices that are tangent to one another using a compass and straight edge. I have an answer to 1 and 2, but I haven't attempted any part of 3 or 4. My answer to 2 is rather unintuitive. Perhaps someone can find something a bit nicer. I have this programmed in Mathematica, but I'm not very good with the language, so it's pretty clunky. Or maybe that's just Mathematica in general. Edit: I also submitted this to /r/CasualMath - discussion is here . Thanks for any thoughts you might have!
|
[
"r/Math... Please help with this math problem? There is a lot of money on the line."
] |
[
"math"
] |
[
"g0set"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.09
] |
[deleted]
|
More still. What's the angle it's sitting at?
|
A perfect sphere would roll off the plank, leaving you a 4'x4' plank sitting at an angle on the scale weighing it in at 260lbs.
|
There are other variables needed.
|
it is sitting on a standard pallet - 4'X4' if that helps
|
These are multiple problems. How do you have some details but not others?
|
[
"FINALLY after 4 hours of working on this blasted thing! (xpost from self)"
] |
[
"math"
] |
[
"fzlxe"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.47
] | null |
Crosspost from /r/self Basically, had to prove the transversal through the harmonic pencil lines would create points that were also harmonic conjugates. Took me 4 hours finding 8 collinear ratios that canceled correctly to leave me with this darn thing.. the ratios on the right are the collinear ratios. For those who DO understand geometry and are interested, the things that are hard to read are: P is the pencil point to line ACBD Q is where A'C'B'D' intersects ACBD tl;dr I kick this geometry problems ass.
|
There's a reason this is /r/math ... grammar nazi.
|
Projective geometry?
|
Yes. This is part of my take home test.. its hell.
|
Yeah, I had a similar question on a midterm last year. It was a poorly chosen question, since no one had time to solve it. Just writing down the solution would have taken a decent chunk of the time. I hope your test goes well.
|
[
"Banach-Tarski yogurt (x-post from r/pics)"
] |
[
"math"
] |
[
"fzutn"
] |
[
200
] |
[
""
] |
[
true
] |
[
false
] |
[
0.83
] | null |
Serving Size: 1 container Servings per container: 2
|
Sure! My favorite anagram of "Banach-Tarski" is "Banach-Tarski Banach-Tarski".
|
math joke
|
No. You could get any arbitrarily large finite number of identical spheres :)
|
I'll be the unofficial math counterpart of joke_explainer. So the banach-tarski paradox, in a nutshell, states that "standard" mathematics technically allows you to finitely decompose a sphere and then reassemble the pieces into two spheres identical to the first. And the container of yogurt says there are 2 servings in the container, but each serving is one container....get it?
|
[
"Calculating pi by dropping a needle on a table"
] |
[
"math"
] |
[
"fzf14"
] |
[
302
] |
[
""
] |
[
true
] |
[
false
] |
[
0.95
] | null |
It is not hard to show, with a little bit of calculus, that the probability on any given drop of the needle that it should cross a line is given by 2/pi. But why is this? That's what I would like to know. This sort of reminds me of when textbooks say, "This proof is left as an exercise to the reader."
|
No one said it would converge fast.
|
Good point, I'll contact the Texas Science Fair Board and ask for his score to be retroactively reduced. I'm sure he and his wife will be very disappointed, but it's the right thing to do.
|
With 22/7 you're dividing 7 into 22. Here we have a table and are dropping needles on it.
|
Easy argument. Fix the x-axis perpendicular to the lines. Suppose that the needle falls at an angle y measured from the x-axis; then it has length |cos y| in the x-direction. This is exactly the probability that it will intersect a line if you drop it randomly. Integrate |cos y| from 0 to 2pi and divide by 2pi to normalize. You will find the answer readily.
|
[
"What is the radius of the circle?"
] |
[
"math"
] |
[
"g009f"
] |
[
5
] |
[
""
] |
[
true
] |
[
false
] |
[
0.69
] | null |
Label the points A, B, C, D in clockwise order such that AB = 1, BC = 2, CD = 3. For convenience, let d = |AD|, e = |AC|, f = |BD|. By Ptolemy's theorem, we know that 3 + 2d = ef. As AD is a diameter, we know that AB and BD are perpendicular, as are AC and CD. Thus the Pythagorean theorem gives 1 + f = d and 9 + e = d We may combine all of these equations as follows: (3+2d) = e f = (d -1)(d -9). So we have 9 + 6d + 4d = 9 - 10d + d which becomes d -14d -12d = 0. The only positive root of this equation is , which gives a radius of
|
Agreed. I used Law of cosines. Draw line from center of circle to each vertex of the quadrilateral. You get a system of equations: 1 = 2r - 2r cos(a) 2 = 2r - 2r cos(b) 3 = 2r - 2r cos(c) a+b+c=pi Then r=2.05655... with angles near the center of the circle being about a=0.491, b=1.02 and c=1.63 radians. You can get rid of a variable to make a system of 3 nonlinear equations. (edit: added details of method and formatting)
|
Considered it, but still preferred since it required no extra effort to get r in the equation (which was the goal) and would have at most 1 trig function in any equation. Used MATLAB for numeric solution.
|
The proportions of the of the angles match the lengths - not the angles themselves.
|
Oh, hey, yeah, you're right.
|
[
"How do I calculate the square footage of a rolled up sheet? (PS - it's bubble wrap!)"
] |
[
"math"
] |
[
"inf93"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.44
] |
I won't go into just how I came to acquire it, but as of this past weekend I have in my possession a giant roll of large-cell bubble wrap. Sadly, I might be trying to sell it off to handle some unexpected bills, but I need to know how much I really have first. My original theory was that I could take an average radius and multiply by the rings, but was told that I need calculus... shit. So if anyone can help me, I'd be extremely appreciative. The diameter of the roll is 26.5 inches and there is a 3.0 inch hollow tube in the middle. The width of the roll is 48.0 inches, and the thickness of the sheet seems to be 0.5 inch. I have seen other places list the same stuff as 3/8 or 5/8 inch, but whatever. A gross estimate would be sufficient at this point. Challenge accepted? (Or anyone interested in buying?)
|
Calculus will only give you a rough answer because bubble wrap is compressible. Clearly if the roll were rolled more tightly or more loosely, you would have the same dimensions but differing amounts of bubble wrap. Here's the easy way to get the correct answer: Unroll it and measure it. Obviously, that is impractical, so let's use some maths. What we are going to do is (theoretically) cut the bubble wrap into narrow strips and add up the areas of the strips. To get an accurate answer, we'll make the strips very narrow - so narrow that they are effectively zero inches wide. That's where the calculus comes in. The area of the bubble wrap is its volume over its thickness, which is [integral from D = a to D = b of (pi h D t) dD] / t = (skipping several steps) 0.5 pi h (b - a ) where: t = thickness of the bubble wrap a = diameter of the outside of the tube b = diameter of the whole roll h = height of the cylinder (what you have called width) Based on your figures, that gives an area of 55270 square inches. That sounds a bit large to me, so I might have messed up somewhere along the line and no doubt others can point out any errors I might have made. Note that this assumes that the thickness is uniform throughout the roll. In practice, it won't be because it will be compressed in the interior. It also assumes that the bubbles in each layer lie on top of the bubbles in the next layer, which is also untrue as they will tend to fit into the gaps in the next layer. Both of these considerations will mean my answer is too small. Of course bubble wrap manufacturers don't do it this way - they know how much they have wound onto the roll. Contacting the manufacturer is the only sure way of getting an accurate answer. tl;dr: You can't do this accurately without a lot more information and more complicated mathematics, but you can get a rough idea. EDIT: I've just realised that this is the same answer as you'd get from using simple geometry (the equation for the volume of a cylinder). I'm a little concerned that the thickness of the bubble wrap doesn't feature in the solution. Could someone please check my calculations?
|
You don't need calculus, just geometry. Find the volume of bubble wrap you have based on the cylinder of the bubble wrap minus the volume of the hollow tube. Using this result divide by the width and the thickness of the wrap and you will get length.
|
Wow - you put it perfectly. Yeah, I realized that this kind of material is gonna make things tricky if I want to be exact, but this helped a lot. Btw, I converted your answer (104540 sq. in.) and got 725.972... sq. ft. And with the width being a known 4.0 ft., that means the estimated length is 189.49 ft. Considering how huge this roll is, I think that's entirely plausible. I will post a picture later, which is more just amusing to even SEE. Thank you for your input! You and your maths came to the rescue!
|
You're welcome :) Please note that I've since edited my comment - I forgot the 0.5, so the length will actually be around 90 ft. Given that this is an underestimate, maybe it's a round 100 feet!
|
Try this: to measure the length without unrolling it, get a string and lay it along the edge of the bubble wrap (the spiral). You can mark where the spiral begins and ends on the string and then measure that segment of the string to find the unrolled length of the bubble wrap. Let's call that length you measured "L". If you measured in inches, divide your measurement by 12 (to get feet) then multiply it by 4 feet (4 feet = 48 inches which was the width of your roll). You now have your square footage!
|
[
"Take the harmonic series, remove any term with a \"9\" in it. The resulting series will be convergent. This also works with any other digit or any string of digits such as \"0\", \"1\", or \"8675309\"."
] |
[
"math"
] |
[
"if4kd"
] |
[
197
] |
[
""
] |
[
true
] |
[
false
] |
[
0.94
] | null |
Neat result, but wouldn't it be more surprising if the resulting series convergent? I mean, you're removing almost all terms from the sum (more specifically: you're removing a set with natural density 1). Contrast this with the first example he provided (removing every second term), where you only remove a set with natural density 1/2, which of course doesn't make it convergent. For example, if you remove all the nonprime numbers from the series (the nonprimes have natural density 1), then the series is still divergent , which is much more surprising in my opinion. What other sets with natural density 1 can you remove that leave the series divergent?
|
If you couple this fact, with the fact that the prime harmonic (i.e. sums of reciprocals of primes) diverges, then you can show that given any finite string of numbers, i.e. 24485983 that there exist infinitely many primes whose base 10 representation contain that string.
|
The sum of the reciprocals of the primes diverges. Hence, any procedure that turns the harmonic series into a convergent series by striking out terms must strike out an infinite number of prime terms. If it only struck out a finite number of terms, the remaining series would contain all the prime terms past some point, and would still diverge. According to the original article, striking out the terms that contain 24485983 turns the harmonic series into a convergent series, and so there must be an infinite number of primes that contain 24485983.
|
Note there is nothing particularly special about primes here. If {A_n} is an increasing sequence of positive integers such that sum(1/A_n) diverges, then for any arbitrary positive integer S an infinite number of {A_n} contain S in their decimal expansion.
|
A funny remark in a string theory lecture I was at: We can write 1+1+1+1...=-1/2, we can write 1+2+3+4+...=-1/12, but the Harmonic series? That's the one true divergent series.
|
[
"What do people mean when they say \"5 times less than\"?"
] |
[
"math"
] |
[
"zjzmwc"
] |
[
0
] |
[
"Removed - ask in Quick Questions thread"
] |
[
true
] |
[
false
] |
[
0.5
] | null |
They mean they don't understand numbers. Listen to them.
|
I think they mean, if last year inflation was 3%, that it’s only 1% this year. And when they say N times less/more, they think of the ratio between the two values, if previous was 100 and current is 20, then it’s 5 times less
|
Would guess so, too. I mean, 5 times more means clearly multiply by 5, 5 times less should then be the inverse so multipy by 1/5. But I'm not really sure.
|
I would think that 5 times more would mean to multiply by 6. Multiplying by 5 would be 5 times as much, not 5 times more.
|
Why do you write N?
|
[
"As an attendee, how do you approach a math conference? What events do you most enjoy or benefit from? Any tips for a first-timer?"
] |
[
"math"
] |
[
"ke44n2"
] |
[
26
] |
[
""
] |
[
true
] |
[
false
] |
[
0.94
] |
Hello, I‘m attending the JMM this year for the first time! I’m really excited, but as an undergrad, I haven’t been to many conferences before and don’t know very much at all. From the etiquette, to how to maximize the experience, to the mysterious art of “networking”, it’s all just... a lot. If you attend math conferences, how do you find yourself approaching the whole ordeal? What are your goals? What experiences/events at the conference do you find most helpful, fun, or fulfilling to you? Specifically for those still working on their degrees, what parts of a professional conference do you find relevant? Is this the place to approach new people (researchers you admire, potential doctoral advisors, etc.)? Or does it come off as stalker-ish to admit to having read a stranger’s CV, research, or personal website, etc.? Any and all wisdom is appreciated! Especially JMM-specific wisdom! I know the circumstances of this particular year and the resultant virtual format of most (if not all) conferences complicates things, but I’m still curious. Thanks!
|
JMM is definitely a typical math conference, so I wouldn't go with the same attitude as I would a subject-specific conference. Also, my thoughts are only for normal non-virtual gatherings: The big things to do at JMM are attend the distinguished lecture/colloquia/keynote talks (they are usually really good and more accessible), attend any special sessions you're presenting at, and attend at least one fun activity (like knitting hyperbolic surfaces or something). Otherwise the rest is just wandering around, browsing, and checking out various talks, books at the bookstore, activities, etc. Don't plan a tight schedule (these conference centers are big and travel time is long), don't stress about making every talk that sounds interesting, and I would highly recommend prioritizing talks that are 30+ minutes long (short math talks are generally not very accessible to non-experts). I'd also check out some of the undergraduate presentations - they are typically more accessible and it's good to support your cohorts (plus, it's less pressure to ask questions/chat outside after the talk and make new friends/lunch buddies/future collaborators). Networking at JMM is tough because of the sheer number of people and things happening - don't have any expectations of being particularly memorable. That being said, don't be afraid to approach people to introduce yourself and converse. Mathematicians are just normal people (mostly) and a simple "Hi, I'm dwarfplanette, I'm currently in the Milky Way Galaxy, and I'm interested in the program at Pluto University, potentially orbiting other celestial bodies with you." If you've read their CV and/or are familiar with their work, you might even ask them "Your work on the asteroid belt seems interesting, do you have any recommendations on where I might start trying to learn more about that?"
|
What experiences/events at the conference do you find most helpful, fun, or fulfilling to you? the hike
|
"I'm in interested in... potentially orbiting other celestial bodies with you." u/FunkMetalBass speaking the language of the gods.
|
That would work as a chat up line on me.
|
It's going to be very weird to see how the whole virtual thing works out this year. I've been doing a few online conferences and it's very mixed. Some have really push socializing, and some people peace out as soon as the talks end. JMM in particular is really more about wandering the halls and finding people--I especially like it for catching up with people I wouldn't normally get to see at area specific conferences, but also collaborators. I think the last two I went to, I managed to got to maybe 5 talks each, including my own? This year ¯\\\_(ツ)_/¯. I also expect attendance to be wayyyy down with ``travel" budgets gone. As an undergrad, you should definitely check out the grad school fair. If there are some attempts at social spaces, definitely do that. Ask people what their research is. I'm less on the CV stalk side, but ymmv. If you are interested in applying to do a PhD with someone, then go for it, otherwise, maybe not.
|
[
"The combinatorics of stacking LEGO bricks"
] |
[
"math"
] |
[
"m0akid"
] |
[
11
] |
[
""
] |
[
true
] |
[
false
] |
[
1
] | null |
Counting LEGO configurations is a problem dating back to at least 1974, when Jørgen Kirk Kristiansen counted that there are 102,981,500 ways to stack six 2×4 LEGOs of the same color into a tower of height six. According to Søren Eilers, Jørgen undercounted by 4! I expected this to be a factor of 4!, and thought that there might be an interesting reason. But it turns out that the ! is just an exclamation mark, not a factorial, and the number was wrong by an additive error of 4 due to round-off error.
|
Nope—but the end of the article talks about some of the difficulties of accounting for stability!
|
Do you account for structural stability? :-)
|
I took a stab at computing the number of symmetric towers with n bricks (A320314), and I'm able to extend the list of terms up to ~60. Would this be helpful? What's the best way to share it with you?
|
That's terrific! Thanks for doing that, and thanks for letting me know. Here are a few options for how you can get those values into the Encylopedia: register for an OEIS account
|
[
"Grokking Grothendieck"
] |
[
"math"
] |
[
"uzm0in"
] |
[
234
] |
[
""
] |
[
true
] |
[
false
] |
[
0.97
] |
I recently read the . I've read several pieces like this one over the years. Invariably, I learn from such pieces that Grothendieck, basically, revolutionized mathematics. (Formulations vary: "revolutionized the way mathematics is done", "revolutionized the way mathematicians think about mathematics", etc. What is pretty much constant among them is the inclusion of some variant of the word "revolution.") Unfortunately, none of the articles I have read have dared to "worry [the reader's] pretty little head" by delving into Grothendieck's actual mathematics , and therefore, the most they can offer to convey how revolutionary Grothendieck's work is are annoyingly feeble analogies. ("Imagine if math could be translated into poetry, and somehow it made sense to take the square root of a stanza.") Also unfortunate, for me, is that I just don't know enough mathematics to appreciate what Grothendieck's revolution is all about , i.e. by just studying the man's works. (And even if I had the prerequisite math knowledge to directly study Grothendieck's works, I don't think I have enough spare time in my life to carry out such a project.) Is there something (book, article, website, etc.) that would give me at least a real taste of exactly how Grothendieck revolutionized mathematics? I'm thinking of a presentation of Grothendieck's legendary revolution that goes deeper into than does the piece cited above, while still being accessible to someone without a doctorate in mathematics. (Come to think of it, probably something aimed at math undergraduates would hit the spot.) --- What is my math level? I'm a self-taught amateur, and not a specially talented one at that. I am currently working through Kenneth Kunen's . It is just at my level, or maybe a notch above: I'm making steady progress with it, but I'm not exactly breezing through.
|
Here is an obituary written by Mumford and Tate on Grothendieck that was rejected by the editors of Nature as too technical: https://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html
|
While things like Category Theory existed before Grothendieck, he really showed us how to stop caring about entities and to love structure. That is, contrary to turn of the century mathematics which concerned itself with fundamentals, building blocks, sets, and logic Grothendieck made progress by caring about relationships. As an example, topology is typically initially about stretchy geometric shapes and the formality looks at elements and special subsets to make intuition about this rigorous. But Grothendieck needed to do fluid topology with rigid and non-geometric objects in order to solve problems (the Weil Conjectures ). He re-imagined topology as being about specific kinds of functions/arrows between different objects. Open sets weren't subsets of a topological space, but injections from one space to another that satisfied certain relationships. These arrows between objects with these special relations were really all that was needed for a bulk of topology and so you could do topology things on decidedly non-geometric objects. This, eventually, lead to the proofs of the Weil Conjectures. Reading his stuff first hand is probably not the best way to experience it. It's extremely technical and in French (though, translations are in progress) and there are much better expositors that can talk about these things who use can use hindsight to recognize the important shifts.
|
In this passage it has nothing to do with math at all, it's used in the colloquial sense. Disdain for formality here just means not liking dress codes, using first names with each other, not deferring too much to authority, that sort of thing.
|
(Not OP here) I never knew this piece existed, thanks for sharing!! :D
|
I did my undergrad in math and I'm finishing my masters in math, soon to start a Phd in math. Much like you I have also heard that Alexander Grothendieck revolutionized math. I have taken some courses in commutative algebra but I never managed to learn anything, all of my exercises where completely hackable through noob methods so that's what I did. The only thing I have been able to do similar to Grothendieck have been a couple of times I fasted with chamomille tea.
|
[
"New formula/modification for standard deviation/variance?"
] |
[
"math"
] |
[
"uzvsbb"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.5
] |
Hi all, I’m a high-school student who’s new to statistics. I was trying to compare the average variation in data points for two sets of data and made this formula which is quite similar to the formulae used for variance (used absolute value instead of squaring). Formula: Any help would be much appreciated! Thank you!
|
See this previous thread for more details. I'll reproduce the first half of my answer from that thread here. On the (quotient, L ) space of random variables, standard deviation is the "typical" distance metric, with covariance the "typical" inner product (i.e. dot product). You get a hint of this from what is sometimes referred to as the "Pythagorean law" for standard deviation: If X and Y are uncorrelated, then SD(X+Y) = SD(X) + SD(Y) since uncorrelated <-> "dot product" zero and so are at a right angle to each other. Now this is great geometrically, but you still raise the point of why we don't just take the average from the mean. This is also something that's often done! Well, almost. Typically if you're working with absolute deviations, you instead take the average absolute deviation from the . This is because the mean and median do different things: The mean minimizes the sum of (and so standard deviation is the natural corresponding measure of spread) whereas the median minimizes the sum of (and so the average absolute deviation from the median, aka MAD, is the natural corresponding measure of spread). So now the question is: Should we use the mean + SD for our statistics, or median + MAD? In application, recently machine learning (ML) people have started favoring the latter two for their statistics. You've probably heard these reasons before: The median is more robust to outliers, MAD is simpler to calculate/interpret, etc. There are also some other more technical reasons to sometimes prefer one set of statistics over another: For example, squaring is differentiable whereas the absolute value isn't, thus favoring SD; many ML theorems require the Lipschitz property , which is a property of the absolute value but not of squaring, thus favoring MAD. To be more technical for a moment, the choice between the two is ultimately a choice in geometry: Instead of working in L space, you're working in L space; you should choose whichever geometry is more convenient to work in. So then why does it seem that mean + SD "won" over median + MAD (at least in schools)? There are essentially three reasons: The strong law of large numbers . This applies to the mean, but not the median The central limit theorem . Both means and medians have a version of the central limit theorem. However, CLT for means literally only requires finite variance, whereas CLT for medians is much more restrictive, limiting inference. Mathematical elegance. The mean of X is simply E[X] = ∫ X dP. The median, on the other hand, has no "elegant" definition and often isn't even a unique value. The existence of the covariance as an inner product. L space has an inner product given by the covariance of random variables; L space is not induced by an inner product, and hence has no analogue of the covariance. We often need to be able to talk about how two random variables vary together, so this lends itself to L space.
|
This is a good explanation, but the person asking is a high school student (so it needs to be less technical) For example, ∫ X dP doesn't have any meaning to a high school student since they are unlikely to understand Lebesgue integration.
|
https://en.wikipedia.org/wiki/Mean_absolute_error
|
I agree that this a bit over the level of a high school student. That's partly the reason I linked to the old thread, which contained several more accessible answers as well. Ultimately, this comment was just a low-effort copy+paste of a low-effort copy+paste of a response from a quick questions thread--I certainly would have tailored it to the appropriate level if I had the time to do so when originally posting.
|
Thank you!
|
[
"What is your favorite math story?"
] |
[
"math"
] |
[
"ke3w8i"
] |
[
60
] |
[
""
] |
[
true
] |
[
false
] |
[
0.95
] |
Most of us have heard the stories about Gauss coming up with a method of summing 1 to 100 as a child, or Ramanujan's conversation with Hardy about the number 1729. What are some other amusing or interesting stories about your favorite mathematicians?
|
Stefan Banach being tricked into getting his PhD. Banach apparently didn’t really have the ambition to write down or publish his new results let alone write a thesis. Fellow professors, who wanted him to do his PhD, hired an assistant who would meet with Banach and take notes of their discussions. Banach essentially only proof-read his thesis after the assistant already wrote everything down. Since also an oral exam was required, the professors asked Banach to meet them to discuss a problem they were stuck on (of course this was only a trick to get him to take the oral exam). Source: Dirk Werner, Funktionalanalysis (in German), p. 45.
|
I had a professor who seemed to take pride that a Stanford grad student who murdered his academic advisor with a hammer was taking one of his courses at the time.
|
I love the story of Marjorie Rice . Long story short, she was a housewife without a college education who managed to discover several new convex pentagonal tilings.
|
The famous topologist Hurewicz died falling from a pyramid, thus becoming the first topologist killed by a simplicial complex.
|
The story about George Dantzig arriving late to a statistics class and writing down the problem on the board thinking it was homework. Then solving the problems and returning them to the professor to discover the problems were actually unproven theorems. The professor went on to work with Dantzig to clean up the work and publish a paper. Wikipedia Article Snopes Story
|
[
"Alternative arctan function for vectors."
] |
[
"math"
] |
[
"dnr9y2"
] |
[
10
] |
[
"Removed - post in the Simple Questions thread"
] |
[
true
] |
[
false
] |
[
0.78
] | null |
Usually called atan2 ( https://en.wikipedia.org/wiki/Atan2 ) or arg(z) ( https://en.wikipedia.org/wiki/Argument_(complex_analysis) )) in complex analysis.
|
This is unnecessarily mean. While I’m not sure this question really belongs at /r/math , there’s nothing wrong with asking questions. It’s not a priori obvious what the search keywords should be to figure out the right function to use. If I do a web search for e.g. “angle of a vector”, I get a whole bunch of walkthroughs aimed at helping high school students with pen-and-paper homework problems. Most people (even e.g. many computer game programmers) do not know that the atan2 function exists in many/most programming environments. (I have seen weak and unnecessary re-implementations of its function.) I did the same thing myself when first learning to write computer programs in 2001 in 10th grade. The documentation people are familiar with is their trigonometry textbook; not many bother to read in detail through the documentation for the whole standard library / math library of their preferred programming language or environment, and it’s not necessarily the best use of time for a novice compared to just diving in building stuff using current knowledge. What would help would be for introductory math textbooks to include a 2-argument arctangent idea, instead of just writing arctan( / ) all over the place without mentioning that it is technically incorrect as stated.
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Thank you very much! This is exactly what I was looking for.
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I completely disagree. This is an excellent lesson in self discovery. Now OP really understands what is going on with arctan. Plus, it isn't that complicated of an exercise, and it probably isn't clear that atan2 exists and is readily available unless you already know about it.
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If you don’t have an atan2 function, also note that: atan2(b, a) = 2 * arctan(b / (a + sqrt(a*a + b*b)))
|
[
"Is there any differences between math at Ivy League/MIT and other top tier universities?"
] |
[
"math"
] |
[
"tno3sb"
] |
[
0
] |
[
""
] |
[
true
] |
[
false
] |
[
0.5
] | null |
burn these posts with fire
|
my university has a tendency to poach mathematicians from either Ivy League schools (especially Princeton and Yale) or from MIT It is not clear if you using "poach" in the right way. You refer later to most of your profs going to top 10 schools for their PhD. Hiring someone as faculty who was in at Princeton is not poaching Princeton. To speak of poaching a mathematician from Princeton suggests the person was on the faculty at Princeton and then moved to your school.
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Pre-selection. These already prestigious universities can afford to pick out the best people amongst thousands of already decent applicants. Thus, unsurprisingly, once you look at the graduates they'll be on average better than the graduates at another, smaller university. The universities don't have to do anything special during the student's 3 or 4 year degree, since the students they accepted were already good.
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I go to a non-Ivy/ MIT in the top 10 of US universities and will be studying at a top 5 school in the world for study abroad. I have friends studying math at Ivys and MIT. There is practically no difference. My math professors got their PhDs at Ivys, Stanford, MIT, My school, and other top universities and we use textbooks that are the exact same ones used elsewhere. We do have slightly fewer maths students then some of the Ivys so size of department might be a small difference but they are essentially the same! Edit: this is very similar to what you said is your experience, I completely agree. There is no difference
|
In rankings we are 89 and MIT 1, but I can tell you that I sometimes review the exams at MIT and find myself once and once again wondering how they can be so overrated. Maybe your confusion stems from the false belief that university rankings are based on the perceived difficulties of exams. This is not so. Does this clarify something for you?
|
[
"Is there a situation where the probability of an event equals zero but the event could still happen?"
] |
[
"math"
] |
[
"ytw42r"
] |
[
3
] |
[
"Removed - ask in Quick Questions thread"
] |
[
true
] |
[
false
] |
[
0.67
] | null |
This can happen every time you have a continuous probability distribution.
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The probability of randomly picking a real number and having it be rational is zero
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there is no uniform distribution on a countable set, or any countable distribution where a probability of 0 can still happen.
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As long as all real numbers are equally likely to be picked
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Yes. Imagine a dartboard. You throw randomly. The probability of hitting a field (say tripple 20), is its area divided by the whole board's area. While you can hit any point on the board with a random throw, individual points have area 0 and thus your probability for hitting any one point is 0.
|
[
"Does learning problem solving enhance understanding of abstract mathematics?"
] |
[
"math"
] |
[
"mmlc3d"
] |
[
0
] |
[
""
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I have read interviews of quite a few mathematicians who advise that one should learning problem solving to become better at understanding math. Now, problem-solving comes generally in the form of competitions like the IMO, Putnam, etc. In these competitions combinatorics play a major role. A person who knows combinatorics well can become a better problem solver. So, is it advisable that we learn discrete math (combi) first and wet our feet in rigorous problem solving before diving into abstract mathematics? Does it make our understanding better? We all know starting out with abstract math can be a bit dry and daunting while problem solving is fun. But does it really influence the learning that is what I am asking. Does combinatorial thinking ability make us better at understanding math in general?
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We all know starting out with abstract math can be a bit dry and daunting while problem solving is fun. Are the two different? Mutually exclusive? 👀
|
We all know starting out with abstract math can be a bit dry and daunting while problem solving is fun. This is news to me.
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Now, problem-solving comes generally in the form of competitions like the IMO, Putnam, etc. This is not true. Every theorem, proof, definition, concept in math has been developed in order to help solve some problem. Math concepts aren't just born from someone thinking "You know what, I think a 'function' would be a cool thing to define", instead it came from having to solve problems and this idea crystalized as an important tool in the problem solving process. For example, a lot of complex analysis was done in order to solve problems about geometry, analytic functions, and even number theory. The reason complex analysis looks like it does today is because of the problems mathematicians were interested in 150 years ago. One thing that is unfortunate is that this is often how math is presented in the undergrad classroom. Group theory came from Liouville trying to decipher Galois's work for the Abel-Ruffini Theorem, and I don't even know who the first person to write down an axiomatic description of a group was, but you're not going to be introduced to groups as a tool to prove the Abel-Ruffini Theorem and so it will seem like something someone just thought of out of thin air. Number Theory is better at this, since you can basically just say "This number theory concept was introduced to solve the Prime Number Theorem/Fermat's Last Theorem/Twin Prime Conjecture/Riemann Hypothesis/BSD Conjecture/Langlands Program" and fit it into a nice problem solving narrative. See or Washington's for books written on some of these premises.
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A person who knows combinatorics well can become a better problem solver. I find this statement strange. Are you defining as doing well in competitions that involve combinatorics? If so, wouldn't the statement be more precisely expressed as 'A person who knows combinatorics well can become a better problem solver in combinatorics problems'? Or are you claiming that studying one branch of Math, i.e. combinatorics well somehow implies that one will be able to understand a very different strand of math better? If so, I'd like to know why you think so. Personally I have interpreted someone saying that one should learn as a more general statement of one should learn how to make educated guesses, confirm or deny the hypotheses that arise, learn how to prove results (stronger or weaker) etc. The path to that might involve combinatorics, or other branches of math. My understanding is that there is a big deal of emphasis on combinatorics in competitions because the amount of mathematical material needed to solve those corresponds to what people are taught pre-high school.
|
Like isn't proving theorems (of any level of abstraction) a form of problem solving? Isn't coming up with good definitions and axioms for structures you encounter frequently across various problems problem solving? Yeah, I would think so. Problem solving seems like a word invented by marketers While, IDK if I agree that marketers have invented the notion of problem solving, Polya for e.g. seems to have a great deal (atleast 3 books worth) to say about the subject, some of which is quite interesting. However, I do agree that marketers have definitely exploited that term to sell other lesser books under that umbrella.
|
[
"Do you agree that mathematical theories, posing as algorithms/software, can be patented?"
] |
[
"math"
] |
[
"mmisuu"
] |
[
5
] |
[
""
] |
[
true
] |
[
false
] |
[
0.65
] |
[deleted]
|
I tend to think that IP laws should be weakened, but if we're going to have patents, then implementations of mathematics needs to be patentible. That seems to be what Trueskill is -- I didn't look at the details but it seems like the thing Microsoft is billing as novel about Trueskill in the description of the patent is the way that they achieved the desired computation time, which is implementation, not mathematics. I agree that if Microsoft somehow managed to patent the idea of a standard normal distribution or something we'd have a serious problem, but that doesn't seem to be the case.
|
So, would you need to pay money to develop or study the theory? What would the effects be? There's people who think software shouldn't be copyrighted.
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but if we're going to have patents, then implementations of mathematics needs to be patentible. Yeah, a few years ago, I heard that Vapnik (a famous Statistician/Machine Learning Scientist) patented a variant of an algorithm that he invented. It seemed strange to me and bizarre that someone would patent that, however, I am not quite sure I can justify why that shouldn't be patented when we have a system that allows us to patent things. My understanding is that the claimed benefit of the patent system is that it gives people some time to recover the cost of their investment by having what they come up with be exclusive. However, in practice, I don't see how it is effective at all. People move jobs, ideas mutate. There are other countries with weaker regulatory practices where you could copy something word for word and get away with it.
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I'm anti-patent except for in a few limited areas. The Trueskill and most math and software patents are jokes.
|
I am not an intellectual property lawyer, but this patent was awarded pre- (and, in fact, pre- ), so it's not entirely clear that it would hold up if challenged today.
|
[
"Decimals to Radicals?"
] |
[
"math"
] |
[
"tld076"
] |
[
0
] |
[
"Removed - ask in Quick Questions thread"
] |
[
true
] |
[
false
] |
[
0.5
] | null |
If the exact answer to the original problem is sqrt(3)/2, then the answer you gave is actually approximately correct. So, if I had to guess, you couldn't figure out how to obtain the exact answer, and probably used a computer to obtain the numerically approximate one. Is my guess right?
|
it sounds like you're relying too much on a calculator and not understanding what the difference between "exact" and "approximate" is, but i'm going to seriously answer your question anyway. if you want to write that number using a square root, take your number, square it, notice that it's close to 0.75, which is 3/4, which means your original number is also close to sqrt(3/4), which simplifies to sqrt(3)/2 but for real, put the calculator down.
|
I know a little bit of Galois theory and would like to know how it can help here.
|
How is an algorithm supposed to decide that, given the input 0.8660254038, the approximately equal number sqrt(3)/2 is a better answer than the exactly equal number 8660254038/10000000000?
|
I have no clue. The decimal number is the answer to the problem but the teacher wants it in radical form.
|
[
"I'm looking for a certain function"
] |
[
"math"
] |
[
"mmnx8y"
] |
[
174
] |
[
""
] |
[
true
] |
[
false
] |
[
0.94
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So I'm looking for a function which puts a number on how "regular"(I used "periodic" at first but realized that was terrible wording) a set of random placed points along an axis is which does basicly this: If something is perfectly "regular"(periodic) it should return a 1. The more the values vary from perfectly periodic the closer the returned number should be to 0 An example: Let's say I measure 12 times in a span of a year. If those 12 points of measurement are equally distributed over the 12 months in a year the function should result in a high number close to 1. If all 12 points were measured in one month of the year the function should return a very low number close to 0. If I have 3 points of measurements every 3rd month that is still very periodic and should also return a number close to 1. Is there such a function ? -______________________________________- I'm not even sure if that what I want is describable by an actual function or if I should rather ask for an algorithm. I'm asking this question out of a programmers stand point. My goal is to write a program which evaluates how often you visited a certain place and how consistent you visited that certain area to evaluate how likely it is you will visit that place again. A better example for my problem is this: Let's say you were on holidays for 2 weeks on some far away island. You been there for 14 days so you have 14 GPS points saved for that area (1 for each day) . This means over the year you generated 14 Data Points for that Area. Then let's say you visit your grandma every second month for a day. that means in 12 months you only gather 6 data points. Over the year you generated only 6 Data Points for that Area. That means you have way less data points for your grandmas visit then for your 14 days holiday visit but it is much more likely you will go to your grandma again than to that island. I thought there has to be a function that evaluates just that. -_________________________________________- another Example: Everytime you go to your favorite cafe, let's name it Starbucks, I will register that you been to that specific Starbucks. Now those points can be completly random along the time axis. What I want to analyze is how regular you go there. Let's take a time span of 3 months for example. If you visit Starbucks every 3rd day then you are there quite regularly. If you only went there for 4 weeks every day but didnt visit that Starbucks for 2 month straight afterwards you are quite irregular there. Now if you only go to Starbucks when you feel like it like Day 2,7,8,9,23,31,32,34,50,60,65... those points are very random in time yet they are qiute regular.
|
A fourier transform converts a function from a time domain to a frequency domain. Namely if a function has roughly a period of n, then the fourier transform of that function will have a high value on the frequency 1/n. The fast fourier transform is an efficient algorithm to calculate this on a discrete number of data. This could be what you are looking for. https://en.m.wikipedia.org/wiki/Fast_Fourier_transform
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I would maybe ditch periodicity and just look at it as a statistics and probability problem: determine the average and standard deviation for the frequency of visits, then use that to determine the probability of a visit on any given day.
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If you are looking to determine how periodic the data is "at all," I guess you would have to take some norm of the FFT. Something like L1 norm if you're interested in summing over the periodicities in each frequency, L-infinity if you're interested in how periodic it is in the "best fit" frequency.
|
Agreed. I'd model it as a Poisson distribution along the lines you've given. All that would need to assume is that the events are nonsimultaneous, independent, and occur at a consistent average rate. The OP's assumption of periodicity seems unnecessarily strong.
|
This is absolutely the way to go.
|
[
"What are the most exciting new or upcoming developments in your field?"
] |
[
"math"
] |
[
"o2p2uz"
] |
[
300
] |
[
""
] |
[
true
] |
[
false
] |
[
0.97
] |
I am a homotopy theorist, and I'm so excited for all the ways people have begun applying homotopical techniques to other areas of math -- like algebraic geometry, low-dimensional topology, and number theory. However, I am woefully unaware of what's going on in other fields. What has you the most excited for the present and future of your field?
|
I'm (shamelessly) excited for things related to my own research -- higher algebraic K-theories and categorified homological algebra. It's fun that "higher algebraic K-theory" now means something different from what it did 10 years ago -- it's an algebraic K-theory spectrum associated to certain (\infty,n)-categories. Conjecturally related to somw exciting things in number theory.
|
Oh tons! There are just so many bright people working in set theory and topology at the moment. I just finished attending the second of two big conferences in these sorts of topics and there are so many things it’s hard to choose. One absolutely incredible talk was on Countable Borel Equivalence Relations, or CBERs, and their relationship with symbolic dynamics. There was another session on Scott Domains which included way more category theory than I know how to deal with. A crazy cool talk by the somewhat famous Alan Dow on some things I’m more familiar with involving something called T-algebras and applications of PFA to topology. Another fascinating talk on covering and partitioning topological spaces with Polish spaces that surprisingly involves an application of 0†. Oh I almost forgot to mention Vera Fischer’s work on cardinal spectra and Maximal Cofinitary Groups or MCGs. She is absolutely brilliant. Michael Hrušak has done some great work on something called the Katetov order. Some work on ℵ₁-free groups and forcing descended from the work of the amazingly clever Alan Mekler. Steven Clontz is working on two-player infinite length games, as he loves to do. KP Hart did some work evolving from a question on MO about something called soft compactifications of N. Dave Milovich is doing some cool stuff with hypergraphs and infinite length games. Michel Smith did some cool work on hereditarily indecomposable continua that surprisingly he needed to consider Suslin lines for. Sorry that got long. It’s been an interesting couple weeks. Edit: Oh my god, how could I forget about Olga Kharlampovich?! She’s doing some awesome stuff with countable elementary free groups and something she calls universal Fraïssé classes.
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Not super close to my research, but the Unique Games Conjecture and the work going on around whether NP intersect Co-NP=P are pretty exciting.
|
People in geometric topology have finally gritted their teeth and done some hard work with Goodwillie calculus , and it seems we are very close to having a somewhat complete understanding of the rational homotopy type of BDiff(M) for simply connected manifolds M (of dimension >4). The techniques are very cool: the usual approach is to finagle some very important results of Goodwillie-Klein-Williams about Goodwillie calculus for manifolds into working in a more general setting by using something called the Weiss fiber sequence. Then you use combine this with results of Galatius and Randall-Williams about what happens when you connect sum with an infinite amount of copies of S^n x S^n , and then you use their homological stability results to try to go back down.
|
I've got a new species of strawberries that I never grew before, can't wait to taste them !
|
[
"Do equations that include complex/imaginary numbers have domains?"
] |
[
"math"
] |
[
"o26zq2"
] |
[
2
] |
[
"Removed - post in the Simple Questions thread"
] |
[
true
] |
[
false
] |
[
0.6
] | null |
Yes of course. If you allow f(X) to be complex than the domain for f(X)=sqrt(5X+10) is all the complex plane. (Or all the real line if you restrict X to be real) There are functions which domain is not all the complex plane, for example f(X)=1/X does not have X=0 in the domain, these are called zeros (or poles) of the function f(X).
|
Technically you've always been using the complex plane, but you've been restricted to the x-axis, where all the real numbers live
|
There is no way to (continuously) define sqrt(5x + 10) on the whole complex plane. The whole "figure out the domain from the formula" concept is questionable even in the real case but it completely collapses for complex functions.
|
Oh yeah yeah you need “a cut” (I don’t know the right word in English). 'Branch cut'.
|
Honestly, I never really thought about the possibility of the complex numbers existing on their own separate plane. That kinda makes sense.
|
[
"How is the Klein Bottle 4th Dimensional？"
] |
[
"math"
] |
[
"o27zmg"
] |
[
4
] |
[
"Removed - post in the Simple Questions thread"
] |
[
true
] |
[
false
] |
[
0.67
] | null |
A Klein bottle is neither 4D nor 3D; it's a 2D surface. Formally, it is a manifold of dimension 2. By the Whitney embedding theorem , any smooth manifold of dimension n can be embedded in R - that is, it can be represented by an actual geometric shape, without self-intersections or other weird behavior. Since the Klein bottle is a 2-manifold, this means it can be embedded in 4D space. If you consider its construction , it should seem intuitive enough that it cannot be embedded in 3D space without self-intersection. I do not know if there is an elementary proof of this fact. if so, how do they know that the equations have traversed to 4th dimensionality? You look at it and count the number of dimensions. There is not much special about having more than 3 dimensions; that just means you have more than 3 coordinates. The equation x+y=0 is an equation in two variables, and so you can interpret it as a shape (specifically, a line) in 2D space. Similarly, the equation x+y+z+w=0 is an equation in four variables, and so you can interpret it as a shape (called a hyperplane) in four dimensions.
|
Imagine a self-intersecting figure 8 in two dimensions. Add an extra dimension, and you can pick up one part of the curve which is intersecting the other part and pull it into the 3rd dimension to get a non-self-intersecting structure. You can do the same with the circle where the Klein bottle intersects itself. Add an extra dimension, then pull one of the tubes in that extra direction so that there is no longer any intersection. You could also write down formulas for what this process looks like, and then verify using algebra or calculus that it is not self-intersecting.
|
There are various elementary arguments available, see for instance https://mathoverflow.net/questions/18987/why-cant-the-klein-bottle-embed-in-mathbbr3
|
Whitney embedding theorem is great but you can also just provide a parametrization! https://en.wikipedia.org/wiki/Klein_bottle#Parametrization
|
most simple explanation I've heard here's an award
|
[
"This Week I Learned: June 18, 2021"
] |
[
"math"
] |
[
"o2sg7j"
] |
[
9
] |
[
""
] |
[
true
] |
[
false
] |
[
0.99
] |
This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!
|
This week I learned that q,t-Catalan numbers are symmetric polynomials in q and t with connections to Dyck paths and Young diagrams that are not understood completely. My plan is to work on these and hopefully write my dissertation on some open problems involving them.
|
What u/Falcelmo wrote is correct, but there's a more direct method in this case. We can just compute 0 , 1 , ..., 4 mod 5 and note that in every case the result is 0, -1 or +1. In fact, the non-zero squares mod p, where p is an odd prime, have a special name - the 'quadratic residues' of p. It turns out there are exactly (p-1)/2 of them, which can be proven with a little group theory (I can show you the proof if you're interested).
|
I learned a bit about logistic regression from Bishop's Machine Learning textbook, but I'm currently lost on his Bayesian approach and will fix by next week.
|
I didn't technically learn it this week, but there goes. A finitely generated group G has only finitely many subgroups of any given finite index n. This is because each subgroup H of index n induces a homomorphism G -> Sn given by the natural action of G on left cosets of H, and it is unique because H can be recovered as the stabilizer of 1. And since Sn is finite and G is finitely generated, there can only be finitely many such homomorphisms.
|
I had my discrete maths exam on Thursday, and it was quite nice. Some bits were tricky: one bit was genuinely hard, and one bit involved taking the determinant of a 5x5 matrix, so it wasn't difficulty. Still got it wrong though lmao. (As an aside, is it true that every square number is a multiple of five, one more than a multiple of five, or four more than a multiple of five? I said so in my exam but didn't prove it beyond employing the universal law of It Worked For All The Numbers I Checked.) Today (Friday) was the last day of term for me. My first year of uni is at an end. To be honest, it's been a bit shit. My mental health has deteriorated to depths I didn't think were possible; my sleeping and eating have been utterly atrocious; another year passed without my second puberty starting; and I spent half the year cooped up in my room with only my dad to talk to. On the other hand, it's been really good! I've made a whole bunch of friends (I have FIFTEEN people coming to my birthday party later this year!!); I've discovered that I really can pass as a cis woman; in the brief times when things have been open and people have been on campus my social life has proceeded apace; and I've even fallen in love. There's every reason to believe that (up to online learning continuing for the autumn term at least...) next year and the years afterwards will be very good indeed.
|
[
"There is a post mostly discussing US grad schools ; Europeans, how is/was your experience at your university ?"
] |
[
"math"
] |
[
"o24n9m"
] |
[
74
] |
[
""
] |
[
true
] |
[
false
] |
[
0.92
] |
(edit : by Europeans I mean students in Europe)
|
Did my bachelors, then my masters and now I‘m doing a phd all at the same university. Chill work environment and the pay is alright.
|
I just want to note that I found the difference between being a master student and a phd student to be huge, as a master student I felt the institution didnt trust me and professors just werent interested in having much interaction outside what was mandatory. this is certainly the case at many labs in france.
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I just want to note that I found the difference between being a master student and a phd student to be huge, as a master student I felt the institution didnt trust me and professors just werent interested in having much interaction outside what was mandatory. this is certainly the case at many labs in france.
|
I'm Spanish but did my undergrad in the UK. I'm halfway through my PhD in representation theory. If you don't mind the US, grad school here is a pretty good deal. In terms of research obviously, although this is very dependent on your interests. Some big differences I find: The program is longer. It starts with a master's, though the specifics vary. You can always start talking to your supervisor in advance though. Personally I really didn't mind one extra year of preparation, where I could learn topics a bit further from my research or ones that I felt like I had skipped but were important. You usually have to teach. I personally don't mind this. I would even say this is reflected in your pay. Grad students in my uni make $35k/year +$3k the first year, and you can teach in the summer up to two times for $3k each. My friends in the UK make ~£14000 if I recall correctly, and they can also do some grading throughout the year, which is paid. Of course the cost of living here is higher: I pay $1300/month in rent. You have to pay a lot just to apply. To me, the whole process felt like a scam: I had to pay things at every step of the way. The only exception being the flights for the open house. I remember paying $300 just to have my diploma checked once I was accepted. The GRE (a prerequisite in almost all big unis) was both expensive and tedious, especially if you're finishing your degree at the same time.
|
Mfw Im neither american nor european. Yeah, Australia exists too! Rest of the world? What's that?
|
[
"Multiplying Numbers and Finding Primes using a Parabola"
] |
[
"math"
] |
[
"o2fqis"
] |
[
278
] |
[
""
] |
[
true
] |
[
false
] |
[
0.99
] | null |
I like the mathematical tidbit offered here, but looping gifs are maybe not my favorite way to read a proof....
|
Connecting two lattice points (-a,a ) and (b,b ) together with a line yields a y-intercept at (0,ab). Therefore if you connect all the lattice points (except those at x = ±1) on a parabola together, they will have intercepts passing through every composite number, but none passing through prime numbers.
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While this is cool and I appreciate the effort that was put in here, I personally think this could have been explained much more clearly than it was. There is very little actual analysis and much of the detail seems to be left to the reader to figure out by staring at the gifs. A logical step to connect any two points on the parabola… Why is that logical? And more importantly, why the hell do I want to connect two points? The thesis of the article hasn’t been stated by this point, so I have no clue what I’m trying to achieve or why this should be an interesting or natural step to take. After drawing several random lines, what might lead the reader to focus on the two lines that intersect at y=12? What if none of the random lines I drew intersected on the y-axis? How would I be drawn to this result still? They are interesting because they do not have equivalent slopes and do not have symmetry about the y-axis, yet they share a y-intercept. I assert that this is not interesting. In fact, it is so not interesting that there are infinitely many pairs of lines with non-equivalent slopes and no y-axis symmetry which all still pass through the same point on the y-axis. (Actually, I think the complement of this set of lines has Lebesgue measure zero.) You need something stronger to reasonably claim this is interesting. Like perhaps that ? That reduces the size of the set of lines with these properties . (To the set of line segments with endpoints which are factorizations of the y-intercept.) Let me just remark here that I don’t say this to be cruel or rude, but in the hopes that these valid criticisms will be taken into account in future articles. I think the gifs are helpful and I’d love to see more of that in expositions, but don’t make that the only explanation you give.
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After going back and reading my work I believe all your criticisms are well founded. My article had some gaps which I left without properly addressing. As you mentioned, I definitely should have mentioned the integer endpoints of the lines. Thank you for taking the time and leaving me with something I can reflect and improve on.
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We multiply numbers and use a parabola to find prime numbers
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[
"Interesting observations by a 3rd grader"
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Wow, pretty cool for a third grader. :) Keep him learning!
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This is awesome! Does he just have a sense for when some new algorithm should be possible or is he just constantly trying things out? Or both?
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That multiplication by 9 algorithm can actually be generalized. So if you want to know (b-1) * x, calculate b-1 + x in base b, reverse the digits. Now calculate b-1 - x and add these together. The result will always be (b-1) * x.
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Its hard to say really 😃.. I would like to say both, but he’s all over the place.. there was a time when it was all drawing 😃
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Indeed, those algorithms really are more efficient to make those multiplications more quick!
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[
"A pretty cool new distance formula for functions"
] |
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"math"
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"ntjvvm"
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1
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Your notation is non-standard but I think I can see what's going on. Let dx denote an infinitesimal increment of x. Then the length of the line piece between (x, f(x)) and (x + dx, f(x + dx)) is sqrt((dx)^2 + (f(x + dx) - f(x))^2), from Pythagoras' theorem. You're just summing this over all points x, right? If so, this ultimately reduces to a standard formula for arclength. To see why, first observe that f(x + dx) - f(x) = f'(x) dx. Therefore our term is sqrt((dx)^2 + (dx)^2 (f'(x))^2), which is equal to dx sqrt(1 + f'(x)^2). Summing this over all points x is the same thing as an integral, so your formula reduces to the integral of sqrt(1 + f'(x)^2) over the interval [x_1, x_2]. This is a fairly well-known formula, one place giving it is this Wikipedia article . Still, it's cool you're playing around and rediscovering things like this for yourself. Note for pedants: yes my derivation is not rigorous. If you're the type of person to point this out, then you should be able to take the gist of this and turn it into a rigorous argument.
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Some questions not meant to discourage but to clarify: What is the motivation for this formula? What kind of distance to you mean? Between which two points? What is the point of the 1/i² term? What does "infinitive power" mean? What is x?
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I can't answer all your questions but I believe from experimentation, the distance it gives you is the total distance traveled across the line from the point (x1,f(x1)) to (x2,f(x2)). So it is not a straight line from point to point, its the line following the f(x) function. Or at least an approximation...
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Is this the same thing as the arc length of f from x1 to x2?
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incredible - you just reinvented a simple form of numeric integration for curve length approximation
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"Function: sqrt((sin(x))^2)"
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From the sidebar: Homework problems, practice problems, and similar questions should be directed to /r/learnmath , /r/homeworkhelp or /r/cheatatmathhomework . Do not this type of question in /r/math .
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From the sidebar: Homework problems, practice problems, and similar questions should be directed to /r/learnmath , /r/homeworkhelp or /r/cheatatmathhomework . Do not this type of question in /r/math .
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From the sidebar: Homework problems, practice problems, and similar questions should be directed to /r/learnmath , /r/homeworkhelp or /r/cheatatmathhomework . Do not this type of question in /r/math .
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From the sidebar: Homework problems, practice problems, and similar questions should be directed to /r/learnmath , /r/homeworkhelp or /r/cheatatmathhomework . Do not this type of question in /r/math .
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From the sidebar: Homework problems, practice problems, and similar questions should be directed to /r/learnmath , /r/homeworkhelp or /r/cheatatmathhomework . Do not this type of question in /r/math .
|
[
"A nice problem I solved, do check it out and critique it. (idk any graph theory so I didn't directly use results from it, do tell me if there is a way to do this more simply)"
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I only skimmed it so maybe I’m missing details here, but the two main things it seems you’ve proved are the graph must be connected, and every two nodes are connected by a unique path. These are the two conditions for a spanning tree, and we can conclude immediately that we need to have n-1 edges.
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Represent a configuration as an -tuple of integers i.e. an element of the free abelian group of rank . A move in the game consists of subtracting one of the columns of the Laplacian matrix of the graph, so the equivalence classes of configurations are the quotient by the subgroup spanned by the columns. If the game is fair this quotient must be isomorphic to . It is well-known that the kernel of the Laplacian consists of those vectors that are constant on each connected component; by rank-nullity the image is a free abelian subgroup of rank - where is the number of components. We want this to be rank - 1, so the graph must be connected. It is then necessary and sufficient that the the cokernel of the Laplacian (i.e. the aforementioned quotient group) is torsion-free. The torsion subgroup of this cokernel is the sandpile group of the graph, a finite abelian group which (by a variant of the matrix-tree theorem) has order equal to the number of spanning trees of the graph. In particular it is trivial if and only if the graph is a tree. Trees have - 1 edges. Whether this counts as a simpler way to do it may depend on one's perspective...
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I see. In the second part I tried to prove that as best I could. Thank you for going over it!
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For what it's worth, I was deliberately doing a sledgehammer argument for the fun of it and because the problem statement immediately made me think of sandpiles. The first part of what I did is really the same as the first part of what you did: write the configurations as tuples of integers and make use of the commutative addition. The kernel of the Laplacian being the vectors that are constant on each connected component is really just another way of saying that the total number of money in each component doesn't change when you make a move, which is exactly what you used to argue the graph must be connected. Talking about cokernels and the sandpile group isn't really necessary, now that I think about it; getting from one configuration to any other corresponds fairly directly to inverting a (reduced) Laplacian, which is possible over the integers iff it has determinant ±1, and then the matrix-tree theorem says the determinant is the number of spanning trees, so the graph must have exactly one spanning tree i.e. be a tree. This is a more sensible way to do an algebraic proof, probably. And of course, the combinatorial arguments about unique paths and such are really just hidden inside the proof of the matrix-tree theorem. It is true that this proof shows that it's fair for all trees, and I don't immediately see a more elementary way to prove that! That said, I'm better at algebra than I am at graph theory, and it's quite possible that there is a nice way to do it.
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Here's an elementary proof that every tree is fair. It's by induction. For the base case, it's clearly true for trees of one node. For the inductive case, let's consider a tree with at least two nodes, an initial state, and a final state. A tree always has a leaf. Let x be a leaf, and let y be the node adjacent to x. Subsume node x into node y to form a tree with one less node. For the initial and final states, transfer the money from x to y. By induction, this tree is fair, so we can perform a sequence of moves that will take the (reduced) initial state to the (reduced) final state. If we perform this sequence of moves on the original tree, then the initial state becomes the final state except possibly for the values of x and y which may be incorrect. However, the sum of the values on x and y is correct, and we can attempt to fix them as follows: Since the sum of their values is correct, performing enough transfers between x and y is guaranteed to end up in the final state. Therefore, the original tree is fair. ^ The proof is complete, but we can generalize the main idea in the inductive case: it's always possible to transfer 1 across any bridge ). A bridge (on a connected graph) is defined as an edge whose removal disconnects the graph. Let (x, y) be a bridge, and let X and Y be the corresponding connected components when (x, y) is removed. Then to transfer 1 from x to y, perform a move on all nodes in X. The transfer from y to x is analogous. This idea leads to a more direct proof: Since every edge in a tree is a bridge, we can transfer 1 across any edge, so we can easily transform any configuration to any configuration (with the same sum).
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[
"Anyone have any interesting algorithms they apply to everyday life?"
] |
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"math"
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John Conway has a stair counting algorithm for example that uses mod. I'm looking for more examples of "mathemizing" the oridinary to help build more mathematical thinking into my life.
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I find myself not so much consciously applying the "best of the first ~33%" rule in optimal stopping time, but retroactively justifying my decisions to stop doing something using it. It's one of many interesting algorithms in "algorithms to live by" by Christian and Griffiths. Correction: ~37%
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I view my diet as an optimization problem. Let's say my daily total caloric expenditure is 2,500 and let's say I need at least 125 grams of protein, 100 grams of carbs, and 35 grams of fats to hit my macronutrient goals (this can easily be expended to support micronutrients too). Additionally, each gram of protein or carbohydrates are 4 calories and each gram of fats is 9 calories. This means I have 2,500 calories to spend to hit those goals. This means that I don't really need to "watch what I eat" as much as I just need to make sure that I don't let food with "empty calories" (foods that don't have many nutrients) force me to go over 2,500 daily calories in order to hit my macro goals. Many body builders and power lifters actually eat ice cream a lot. Because it is rich in protein and certain micronutrients, they can get away with eating that "junk food" because they're still able to hit all their nutrient goals without going over their calorie limit. This is actually my favorite way to connect math with fitness. I track some basic biometrics my fitness watch pulls for me, but diet optimization is just so much fun for me.
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shouldnt it be the best of the first n/e? for n=100 it approximates to 37%
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Right. Good thing I've only been using this retroactively then.
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I think the knapsack problem is a "difficult" problem that is the most likely to come up in everyday life. Some examples would include fantasy sports (especially fantasy premier league where players don't take turns drafting players), RPG's where you purchase things to maximize your character's ability, and in theory any situation where you have a budget to spend on items/tasks. I think there are also some applications in computer networks and operating systems with sending packets of data and designing schedulers, and similar problems could show up in everyday life. It also shows up in what I am convinced is the best way to structure a test. First, if there are multiple choice questions, make the student assign each answer a probability, and their points earned on that question is the probability of the correct answer multiplied by the points of the question. Then give enough questions so that the total possible points sums to more than 100, but find the subset of problems that maximizes the points earned by the student under the constraint that the total possible points of those questions is no more than 100. It's less clear that this approach is good if you have to assign arbitrary values to the items or if the items can only be given expected values, and in the latter case in domains such as poker or trading it's better to consider things like the Kelley criterion and Sharpe ratios. But the problem has nice properties and the dynamic programming algorithm solution is very elegant. Perhaps there are other ways in our everyday lives where we can improve our "budgeting" using this algorithm.
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[
"Landmark numbers"
] |
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"math"
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Landmark numbers are quick-and-easy reference numbers, used when approximating large values in daily life. Some articles and videos have already been made featuring them. A popular analogy is made with the population of the US in mind. As it's about 1/3rd of a billion, any government plan that costs N billion dollars, costs each person about 3N dollars individually. My personal favourite relates to calories; there are a bit over 7000 calories to a kg, so if you want to lose 1 kilogram of weight a week, you'd need to cut about 1000 a day. Or, you could eat an extra 1000 calorie dessert a day for a week and gain about a kg. What are your most used and favourite landmark numbers?
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A mole (or Avogadro's constant) ~6*10^23 hydrogen atoms per gram. 1 gram is roughly the mass that was converted to energy in the Hiroshima bomb. A mid-size lightning strike releases the energy of roughly 100l of gasoline. A driving car's kinetic energy is roughly equal to the calories in a pretty small chocolate bar. The moon is about a light second (technically, 1.3ish) from earth, the sun is 8 light minutes (or 150 million km) away. The universe is estimated to contain 10^80ish to 10^90ish particles. If I remember others I find useful, I'll edit.
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The kinetic energy of a moving object is (for non-relativistic scenarios) E = 1/2 m * v^2. A car weighs a ton (well, today, slightly more on average). And let's just use 20 m/s (that should be 72 km/h or roughly 45 mph, I think - again, we're just talking order of magnitude here). So we have E = 1/2 * 1000 kg * (20 m/s)^2 = 500 * 400 kg*m^2/s^2 = 200000 Joule or 200 kJ. 1 kCal (the typical calories used when talking about food) is roughly 4 kJ. A typical chocolate (100g) might have about 500 kcal (+/-100 maybe), which equals 2000 kJ. So a 10th of that - a small chocolate bar, 10g - would have 200 kJ, equal to our car's kinetic energy. Since the car's energy depends on the square of the speed, obviously there's a wide range to cover - if you drive 100 m/s (that's 360 km/h, a formula 1 car's top speed) in a 1 ton car, that's already 25 times the energy calculated above, or the calories in 250g of chocolate (which could probably then be called a large bar...)
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Number of stars in an average galaxy = number of galaxies in the visible universe = 100 billion. A rough number but it gives a sense of the scale of things.
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A driving car's kinetic energy is roughly equal to the calories in a pretty small chocolate bar. I don't understand this one
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1000.0 kg is 2202.64 lbs
|
[
"Math Books for High Schoolers"
] |
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"math"
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Hi everybody! I am currently attending college to be a high school math teacher. I’m currently putting together an Amazon list for books that I can have on a bookshelf in my future classroom, and I was wondering what books you all would recommend. I’m not looking for textbooks, but more along the lines of “Journey Through Genius” by William Dunham or “Humble Pi” by Matt Parker. I’m trying to fill up a bookshelf here, so give me all your thoughts!
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maybe the graphic novel: logicomix. i found it very engaging, and i learned some set theory and logic stuff from it. check it out!
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that can be perused: These texts (serious, but highschool accessible). still good inclusion because they have ! They’re the sort of book you can just flip through, see some neat stuff, and get a sense of what future maths can looks like (since they start at, but go beyond elementary maths) An Illustrated Theory of Numbers Visual Group Theory : Music by the Numbers: From Pythagoras to Schoenberg <— fun book on music and math; short, nicely chunked Zero: The Biography of a Dangerous Idea <— I this is the zero book I read back when I was a freshman and quite liked. Regardless, I’m confident that it’s good. :) Chaos: Making a New Science <— I haven’t read this, it’s just a very popular pop math book that a lot of people have liked so seems fitting 🤷♂️ : The Green-Eyed Dragons and Other Mathematical Monsters <— book filled with math puzzles. Again, nice because you don’t need to read the whole thing. It’s interesting even if you just read one page. Some of the puzzles are very difficult to understand (e.g. the eponymous green eyed dragons puzzle ); they’re designed to be the sort that you ponder over weeks / months. They’re meant to exhibit solutions that challenge intuition. : Oliver Byrne’s First Six Books of Euclid (one book) ^ this books is a rendition of Euclid’s Elements but with the proofs rendered almost entirely visually in a style very reminiscent of De Stijl . This may or may not tickle your fancy if you’re trying for an emphatically ‘anti-dusty’ swagger to math for your students. But it is a breathtaking bit of history rendered in a clever style. And may stoke some students imagination as a little puzzle just to decode how it’s written and then look at some of the proofs. Also an interesting talking point (re: advanced approach to proof based mathematics appearing so early and suddenly in history.)
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I strongly recommend a few puzzle books and books of “interesting stuff” like Martin Gardner’s The Colossal Book of Short Puzzles and Problems and Professor Stewart’s Cabinet of Mathematical Curiosities. I loved those in high school.
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Art if Problem Solving
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idk how accessible this is, but if someone showed me An Infinitely Large Napkin in HS I would have been elated
|
[
"Books that teach you both the how and why of a topic"
] |
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"math"
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There are mainly 3 types of books on any mathematical topic. The reason I like 3rd type the most is that they motivate the topic very nicely and then goes into rigorous analysis by proving the same topic. This is more natural for someone learning the subject for the first time. Even mathematicians who came up with the idea for the first time were probably working on it using some geometrical diagram or some small numerical example. This is an important strategy used in competition math i.e. create a miniature version of the problem assuming some numerical values and try to arrive at the solution. A book on algorithms that uses this type of teaching is by It heavily uses mathematical induction and talks about the exact design of the algorithm. Type 2 books are good for already experienced people trying to brush up a concept. The 3rd type is hugely beneficial for 1st timers. Type 1 is for people who will not dive seriously into math later and are taking the course only to satisfy some requirement. I know there may be many people who like Type 2 more than Type 3. But, to me, Type 3 is the most beneficial when I study an entire unknown topic for the first time. Can you mention some books of Type 3 on any topic of maths that you have studied and liked very much?
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Tangentially, I think you are giving type 1 books a bad wrap. I would disagree that type 1 books are purely mechanical and computational. For instance, Stewart does motivate the Riemann integral as the limit of smaller and smaller subdivisions of the area under a curve. I would say it is a fine book for developing intuition about the subject.
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Most books published under Springer's GTM would fall under Type 2(Lee's smooth manifolds,...),& in general most grad school text would also be. The only undergraduate textbook which comes to mind for Type 2 would be Spivak's Calculus on Manifolds. My favourite type 3 texts from my undergrad, probably Stein's Princeton Lectures (4 books on analysis) & Topology by Munkres
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I'd say Lee's smooth manifolds falls under 3. It has a lot of examples with explicit computations, and a lot of exercises.
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I agree. I used to think Steward is bad but when I reread it for math GRE I found it surprisingly motivating. It turned out I didn’t really try hard to read/understand it the first time and most of my impression came from the lectures and homework, not the actual content of the book.
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The only type 3 book that comes to mind for me is "Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand et al. It deals with the process on how to write proofs and was an excellent resource for myself.
|
[
"I've noticed a pattern in prime numbers and after trial and error have written in in form of a equation."
] |
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"math"
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Hello everyone, hope you all are having a great day. While find out the patterns between prime numbers, I've noticed a pattern I've managed to write in the form of an equation The equation is valid only for n > = 2 Noticing the logarithimic function used in the equations used in finding the nth term of the pi function. Tried finding a pattern using logarithms. Got the equation. I have only calculated 7 prime numbers barring 2. If was done as a mathematical curiosity. Can anyone why am I getting the prime number upto 7 prime numbers when the resultant is rounded off. I've heard at smaller values there is a relation difference of primes and logarithimic function. I'm a high school pass out yet to start my undergraduate. Please, forgive my ignorance. I in no way claim I found the formula for the nth number of prime. It is more likely a coincidence. Thank you for your help. Edit: Thank you for the award!! It really means a lot. Edit 2: Sorry, It's not pi(n), It's the nth prime number , Basically, f(n) ~ -1*| nth prime number.| Edit 3: Thanks everyone for all the support. I can't believe the support I'm getting. 😊. I've updated the equation. The new equation Approximates the nth prime number upto n = 15. I haven't tested after n>15 since my calculator gave up and used up all the free computational power at wolfram alpha :p . This is the last time I tinker around with the equation and I'll try finding our the possible explanation as to why the function behaves as such. Edit 4: The equation when simplified to the natural logs and the log of factorials simplified using sterling's approximations shows that it contains ln(n)+ln(ln(n)). As the function is found in the nth prime number inequality ln(n)+ln(ln(n))-1< P(n)/n<ln(n) + ln(ln(n)). The rest of the part of the formula most likely has no significance. Hence the equation I posted above (the latest one can be written as f(n) ~{ ln(n) +ln(ln(n)) + g(x))}/2ln(e/2) Where g(x) is the negative part of the equation. If I've made a mistake in the analysis, please inform me about the error. Thank you everyone again!! 😊
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If I had to guess, and if your equation kinda holds for large n (although I'd predict that it will diverge at some point), then you may have rediscovered the prime number theorem! :) https://en.wikipedia.org/wiki/Prime_number_theorem
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It was fun trying to figure the pattern.I was obsessed trying to figure it out the whole day. It was fun.
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All those logs definitely suggest the prime number theorem 😅😅 Awesome!
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Your left side depends on x while the right side depends on n. I assume that should be the same for both sides. log(a ) = b log(a), assuming it's meant to be parsed as in the comment by /u/Away-Reading this can be simplified to: log_2 ( 2/(n+1)! log_{n+1} n ) + 1/2 (-1) log_10 n Now log_{n+1} n =~ 1-1/n =~ 1. Then we can simplify further: -log_2 ( (n+1)! ) + 1 + 1/2 (-1) log_10 n Using the Stirling formula, ln (n+1)! =~ (n+1) ln(n+1) - n - 1. (-(n+1)ln(n+1)-n-1)/ln(2) + 1 + 1/2 (-1) ln(n)/ln(10) The leading term here is -n ln(n)/ln(2). It's negative, and it doesn't match the n/ln(n) we need. This is not a result of rounding issues. the (n+1)!/2 root of n is smaller than n, so the inner logarithm will produce a number smaller than 1, so the outer logarithm will produce a negative number.
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Changing base is something that doesn’t really help, in the sense that mathematicians don’t really consider the ‘digits’ much anyway, certainly not in a way biased to the decimal system, we have much more advanced methods that are more universal, and we have results on the ‘randomness’ of primes and even their digits that apply to base. But trying to ‘think of them in a different way’ is certainly something number theorists are constantly doing.
|
[
"The logic gate adventure"
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It all started 2 months ago when i wanted to create tic tac toe in APL. APL is very basic, and is mostly just pure math, so when i had a hard time even making an IF statement, i gave up. Now, 2 months later, i got the idea to use logic gates to not only play tic tac toe in APL, but also create a fully functional tic tac toe AI using only math. The idea was to create a formula, where when i put in the current positions in a tic tac toe board, it would output the next optimal play. I would do this by kinda simulating logic gates in math. For example, in an AND gate, if input 1 and input 2 are both on, it would output; on. Like this: AND gate = a*b if a = 1 and b = 0, a*b = 0. As you can see, a*b is only 1 if both are 1. Here are the other gates (mostly made up of NAND gates): At this point i wanted to test my sytem by making a full adder (tic tac toe took too much effort). But heres where i stumble onto a couple of limitations. First of all, if i want two outputs i have to make two formulas. Anyways, this is what i did: Another problem, wolframalpha doesnt understand this. Even if i put all variables to 0, S just wont compute, it gives me the "Wolfram|Alpha doesn't understand your query" error. But thankfully C is more compact, and it works flawlessly! Also, im in the first year of high school and i have no idea what im doing, the most experience i have is making adders in Minecraft. Trying to understand what im doing is hard, and it feels like ive gone down some wierd road of existentialism. I think im making a calculator to calculate binary math, inside an equation. An equation that solves equations, but what if i translate this to binary and solve it in the equation? Why am i doing this? What am i even doing? I tried talking to my boyfriend about this, but he lost me at logic gates. This is the point where i came up with the idea to post it to to see what you guys think. Sorry for bad spelling or for rambling by the way, english is my second language so it doesnt spellcheck. tl;dr: man goes insane while making an adder. edit1: this is already all in binary, i dont need to "translate" because all possible digits are already 1 or 0. edit2: better XOR gate found! XOR(a,b) = a+b-2ab, thanks to and And it works! We have now created a computer in wolframalpha, kinda.
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Hey if you are interested in logic gates and similar I think you might get a lot out of this course if you haven't seen it already. You can find a pdf of the book online for free. https://www.nand2tetris.org/ It builds up from the nand gate which can be created using transistors, to a tetris program
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Are we talking about the same APL? APL is a high level language. The code you write is significantly different than most languages, but there’s no need to write your own primitives, except for fun. Logical AND is built in, just write A∧B (the hard part is finding a way to type the symbols…). Chances are you don’t even need an if statement. Anyway, the folks at r/apljk can help you better probably, even if you do want to reimplement everything from logic gates for fun.
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XOR(a,b) = a + b - 2ab
|
Thanks for the advice, this is the diagram i used to create the full adder: https://en.wikipedia.org/wiki/Adder_(electronics)#/media/File:Full-adder_logic_diagram.svg #/media/File:Full-adder_logic_diagram.svg) The real complicated part is the chain of 2 XOR gates. The reason i did the logic gates the way that i did was because i wanted to use it to play tic tac toe in APL ), and i havent learnt much about matrixes. I didnt know how to make IF statements, and i dont think APL even has booleans. So i kinda wanted to create my own if statements, somehow, and thats when i rememberd that and gates are kinda like if statements.
|
Thanks for the advice, this is the diagram i used to create the full adder: https://en.wikipedia.org/wiki/Adder_(electronics)#/media/File:Full-adder_logic_diagram.svg #/media/File:Full-adder_logic_diagram.svg) The real complicated part is the chain of 2 XOR gates. The reason i did the logic gates the way that i did was because i wanted to use it to play tic tac toe in APL ), and i havent learnt much about matrixes. I didnt know how to make IF statements, and i dont think APL even has booleans. So i kinda wanted to create my own if statements, somehow, and thats when i rememberd that and gates are kinda like if statements.
|
[
"Why is the empty set a subset of every set?"
] |
[
"math"
] |
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"tl8pj3"
] |
[
4
] |
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"Removed - ask in Quick Questions thread"
] |
[
true
] |
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false
] |
[
0.83
] | null |
Let’s say the empty set a subset of some other set S. For that to be true, at least one element of the empty set would have to not be an element of S. This is of course impossible as the empty set doesn’t have any elements.
|
Why is 0 < 1? It is a similar notion. The way subsets are defined is that A is a subset of B iff each element in A is also in B. But since there is no element in the empty set, it is trivially a subset.
|
When first trying to understand a confusing mathematical idea, sometimes the best idea is to try to “break” the idea/theorem/whatever and see what happens/why it can’t break. It’s a powerful analytical tool 🙂
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Every element of the empty set is also a member of any other set. (This is vacuously true)
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Oh, I got it now. Thank you!
|
[
"How do I sparkle interest in high school math to someone who is interested in history/literature/languages?"
] |
[
"math"
] |
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"tktgue"
] |
[
6
] |
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0.88
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One thing that fascinated me was reading Donald W. Engels' book on the Logistics of Alexander the Great. The first chapter was basically a linear algebra word problem: horses eat H pounds of grain per day but can carry X pounds and drinks W gallons of water per day, a human adult eats 3 pounds of grain per day but can carry 30 pounds but drinks 1 gallon of water per day, given Alexander's army has 4500 cavalry and 45,000 people, how far can they travel before resupplying? [Note: 1 gallon of water weighs 8.34 pounds.] And a plot twist: horses can work 6 days before needing rest for an entire day. A lot of military history boils down to these considerations, because they constrain the strategies deployed. (Perhaps too niche, but I thought it fascinating as a motivation for linear algebra.)
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The greeks pioneered math and tied it heavily into philosophy and logic. Try approaching it from their angle maybe?
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There is a quote attributed to Galileo that says mathematics is the language by which God wrote the universe. So maybe present math as a language. Show the language of mathematics.
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First of all, if I were you, I wouldn't go out of my way to try to convince her that math is interesting. It's rude to tell other people what they should be interested in. If she doesn't like math, then it's a pity, but it's her legitimate choice. However, since she's interested in languages (among other things), and you're teaching her algebra, then perhaps you could try to emphasize how the rules for manipulating polynomials are almost purely syntactic, so perhaps not too unlike the rules for noun declension or verb conjugation, but with far fewer exceptions.
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I don’t think your post implied at all that you are trying to force anything on her. Of course, students have to take math in the current educational setup, so it absolutely makes sense to try and make it enjoyable. If you are there to help her, you’d be doing her a disservice by not even attempting to figure out how mathematics can be interesting or relatable to her. So yea, I think what you’re attempting to do is great.
|
[
"Looking for a professional please :)"
] |
[
"math"
] |
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"tkj7dv"
] |
[
0
] |
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"Removed - ask in Quick Questions thread"
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] |
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0.11
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I really dislike these purposefully ambiguous problems and completely agree with your assessment. Depending on your age or country of origin both 2 and 4 can be argued as valid answers.
|
I really dislike these purposefully ambiguous problems and completely agree with your assessment. Depending on your age or country of origin both 2 and 4 can be argued as valid answers.
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8/4 is 2 and so is 1 + 1. so 2(2) is going to be 4
|
Parentheses first: = 8/4*2 Operations from left to right: =2*2 = 4
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If it was written as: 8/(4(1+1)) = 1, but how you have it the answer is 4.
|
[
"How do i calculate the calories added to my meals when i add stuff like oil, veggies, and anything that would add more calories to my one cup of chicken meals ?"
] |
[
"math"
] |
[
"tkkp0v"
] |
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0
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0.27
] | null |
There exists a solution to your dilemma.
|
Unfortunately, your submission has been removed for the following reason(s): /r/math If you have any questions, please feel free to message the mods . Thank you!
|
Have you tried looking in a nutrition sub? This isnt really the place for that kind of question.
|
Addition.
|
Yes.
|
[
"Ukrainian mathematician Konstantin Olmezov committed suicide in Moscow"
] |
[
"math"
] |
[
"tkpyem"
] |
[
1217
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What's struck me watching the conflict in Ukraine are the uncounted casualties of war. Sick and elderly who die due to lack of proper care. Lifelong trauma, especially in the minds of children. A professor committing suicide because he is trapped in a hostile country. Please just let this end.
|
Deep tragedy. Some context and his massage: https://www.reddit.com/r/peacehacks/comments/tj2o2s/ukrainian\_mathematician\_konstantin\_olmezov\_has
|
If you or anyone you know are struggling, please, PLEASE reach out for help. You are worthy, you are loved and you will always be able to find assistance. Argentina: +5402234930430 Australia: 131114 Austria: 017133374 Belgium: 106 Bosnia & Herzegovina: 080 05 03 05 Botswana: 3911270 Brazil: 212339191 Bulgaria: 0035 9249 17 223 Canada: 5147234000 (Montreal); 18662773553 (outside Montreal) Croatia: 014833888 Denmark: +4570201201 Egypt: 7621602 Finland: 010 195 202 France: 0145394000 Germany: 08001810771 Holland: 09000767 Hong Kong: +852 2382 0000 Hungary: 116123 Iceland: 1717 India: 8888817666 Ireland: +4408457909090 Italy: 800860022 Japan: +810352869090 Mexico: 5255102550 New Zealand: 045861048 Netherlands: 09000113 Norway: +4781533300 Philippines: 028969191 Poland: 5270000 Russia: 0078202577577 Spain: 914590050 South Africa: 0514445691 Sweden: 46317112400 Switzerland: 143 United Kingdom: Various recources USA: 18002738255 You are not alone. Please reach out.
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Jesus Christ, it's heart breaking. One can tell just from reading his message on telegram that he was tortured with the decision. And I can tell personally that we would have been kindred spirits. I hope that he found the peace that he was searching for and that his death was not for naught.
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That was very painful to read. I don't think anyone can understand what he felt in that moment, but from his writing one can tell there was so much pain, misery and he had completely and fully given up on this earth. It's truly heartbreaking. Rip Konstantin..
|
[
"Pure to Applied Math Graduate Program"
] |
[
"math"
] |
[
"tlwbz9"
] |
[
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] |
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""
] |
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Hello everyone, I hope you are all doing well. I just had a question that I was hoping to get some different peoples insight on. I’m a pure mathematician by training. It’s what I did my masters in, it is what I published a joint paper in, did my thesis in, etc. I’ve taken a few years break after my masters to kind of reset and try some different things. I find my mind always coming back to wanting to try for a doctorate degree though. A sticking point though is in me thinking if I should maybe do applied mathematics instead of the more pure route. Now I love pure mathematics and the beauty of it. What appeals to me about applied math though is the idea of helping others. I like the idea that you could work on research that can better help us understand climate change, how to treat others in the medical field, etc. There is a very tangible product at the end that has a very real use. I’ve always been one to be interested in a lot of different topics too and I had a mathematical mentor who was an applied mathematician who said that he liked the field because it allowed him to walk down the hall and talk to a number of people who were all working in different fields but he could lend his expertise to. Also it is nice to know one might be employable in many different sectors. So here come my main questions Is it a terrible idea to try and switch up my area of focus at the doctorate level? Will I be too behind the curve in terms of background knowledge? How much programming is usually required? I’m not the best programmer though I am interested in learning more and becoming more proficient. I’ll never be able to go toe to toe with a pure computer science major though. I guess my question is, what type of programming background should I have to not be completely overwhelmed by the programming requirements? Does anyone have any recommendations on maybe a first year graduate text in applied math? It could be anything that you might see that first year. I just want to maybe take a look at a text to see if it speaks to me. Again thank you for anyone who has read this and is willing to provide some feedback. I’m just looking for any thoughts and opinions. Thank you for your time and if you would like any clarification on anything let me know! Also if this isn’t the correct place for this sorry! I can move it if there is a better forum for this post!
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It is quite typical for students to study pure mathematics or some related quantitative field (CS, physics, etc) and then switch areas for their PhD, especially if it's to an applied field. You definitely will not be behind, except possibly in the realm of programming skills. If your prior area of research was at all related to analysis, that would make the transition even smoother, but still I don't think it'll be an issue. You'll probably be thrown into programming with little direction or training, and you'll just be forced to pick it up, and it likely won't be a problem at all. This is quite typical for a student. Numerical linear algebra (easy introduction: Trefethen) underpins a very large amount of computational applied math, but without knowing what you want to do, I think this is too broad a question. It would be no different than asking what a good first year text in pure math is. Perhaps if you follow up here with some more precise questions then I can address them. I had fairly intensive pure mathematical training (did not write a single line of 'real' code in undergrad) but I did an applied math PhD.
|
Personally, I got my PhD in Pure Mathematics and then did a postdoc in a more applied direction, where I was a postdoc in a control theory laboratory. Just talk to a professor whose work interests you, and get started from there.
|
The questions are far too general to have a good answer. It will depend on many, many factors down to the specific supervisor and project you would have. But anecdotally: I did an applied mathematics master's degree with a heavy slant towards pure math and do my PhD in biostatistics now. I never learned statistics before this and have to code in R which is also new to me, aswell as me not really enjoying coding before and therefore putting little effort into it. It's still fine so far, both the statistics and coding come pretty easy to me. Something I would attribute largely to my mathematical training.
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This paper illustrates how sometimes applied math can be a bit more picky and difficult in certain situations. Writing down an exponential of a matrix using some linear algebra reasoning (or more beefy reasoning such as Functional Calculus from Functional Analysis) is straightforward. But actually implementing it for a computation is much more difficult. This paper discusses some pitfalls and challenges in actual implementation. It's easy to pontificate about what the answer should be, but when you put your nose to the grindstone and actually try to do it, it's not so easy. "Nineteen Dubious Ways To Compute The Exponential Of A Matrix" https://www.math.purdue.edu/~yipn/543/matrixExp19-I.pdf
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There's applied areas that make use of some really 'pure' mathematics as well just fyi. Cryptography comes to mind, where number theory and algebra run rampant in certain subdomains. You can definitely do a PhD in this without needing any of the more applied branches of math such as statistics and differential equations. Programming is helpful for proof-of-concepts at the very least, but you're not going to end up needing to be a full-stack developer at all. Just browse through this paper to see an example of how 'pure' things can still be: https://eprint.iacr.org/2020/1240 Edit: given you asked for intro texts, this one is open source and quite good to have a feel for the field of cryptography: https://www.math.auckland.ac.nz/\~sgal018/crypto-book/crypto-book.html
|
[
"My first (shared) paper was finally published"
] |
[
"math"
] |
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"tl5sr8"
] |
[
1776
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Hello! What a coincidence! I am one of the authors of the 2018 paper you build upon, and I am the one who came up with our first upper bound for the complementation construction. I was so surprised when I recognized the title of your paper here! I have read an earlier version of your paper about half a year ago. I was very impressed by how you managed to simplify the construction, and by the connections to graph theory that you found. I really like your new results! And I had no idea this was your first paper too. Very well done! I am still interested in the UFA complementation question, even though my current work is on something else. I think that the graph theory approach has a potential to go somewhere. Have you done anything else with it since the paper? If you have any new ideas that you would like to share, I would very much like to hear about them. You can DM me for my e-mail. Again, grats for getting published!
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Funny coincidence. PMed you.
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Wow you study at Oxford University! I’m super jealous now :D Also congrats for your paper!
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Studied, I graduated last year. And thanks!
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Link accessible to everyone: https://authors.elsevier.com/c/1enuA4ZKAiV2M
|
[
"Curvature visually and mathematically explained. (Video)"
] |
[
"math"
] |
[
"tl3vfd"
] |
[
15
] |
[
""
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[
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0.94
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Here's an interesting and in depth video on Curvature, what it actually means, and how it relates to our warped Spacetime. I made this because curvature is a central concept in General Relativity, yet it requires clear visual animations to really understand. Also, the interpretation of the Riemann Tensor is something I could not find a good explanation for on the internet, especially not the visual interpretation and its connection to parallel transport. Feedback is always welcome!
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The Riemann curvature tensor describes how an infinitesimal “geodesic volume element” expands or shrinks as it moves along a geodesic. This geometric interpretation is very important!
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Aha yes, that's also an important interpretation. How would this link to the parallel transport interpretation in the video?
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Parallel transport is actually a more general idea. But first some motivation. On R^n , we have an idea of what it means to “move a tangent vector at a point p to a point q ”. That is, we have a canonical identification between the tangent spaces of R^n at any two points p and q . On an arbitrary smooth manifold M , this is no longer the case. The tangent spaces at any two points of M are still isomorphic, but no longer so. Why is this a problem? In many situations, you need to do calculations that, geometrically, depend on a notion of “transporting vectors from one tangent space to another”. For example, to differentiate a vector field, you need to subtract the values of the vector field at two “nearby” points. However, subtraction doesn't make sense unless you have two elements of the vector space, which the tangent spaces at “nearby” points are not! Okay, now the hard part. To solve the aforementioned problem, we use the notion of . An affine connection allows us to “differentiate” a vector field v along a vector field w in a way that satisfies two desirable algebraic properties: It is tensorial with respect to w , i.e., for any scalar field f , the “derivative” along fw is equal to f times the “derivative” along w . It is R -linear and satisfies the Leibniz rule with respect to v . It follows from the tensoriality with respect to w that an affine connection allows us to “differentiate” v along in such a way that, if we reparametrize the curve, then the value of the “derivative” rescales proportionally to the speed with which we traverse the curve. This “derivative” is called the . A vector field v along a curve c is said to be if its covariant derivative is zero. From the preceding paragraph, we deduce that the notion of “parallel along c ” doesn't depend on how we parametrize c . If the covariant derivative w.r.t. one parametrization is zero, then the covariant derivative w.r.t. another parametrization will be a rescaling of zero, i.e., zero. The amazing thing is that, if v0 is a tangent vector at a single point p0 , and c is a curve starting at p0 and ending at another point p1 , then there is a unique way to extend v0 to a parallel vector field along c . This is the . Finally, every Riemannian manifold has a canonical affine connection called the . The parallel transport mentioned in the video is the parallel transport obtained from the Levi-Civita connection, but other affine connections induce their own parallel transports.
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I like the intuitive aspect of saying that if there is at least one coordinate-independent representation then the space is not curved, but then you just pull the Levi-Civita symbols and the Riemann tensor out of nowhere. How about intuitively reasoning that things are coordinate independent when their derivative is zero, so perhaps we can construct something from the derivatives of the metric that is zero iff space is flat. It’s no proof, and only delays pulling the Riemann tensor out of nowhere, but I think it gives some insight to the form of the tensor. You could throw in some index symmetry stuff, too. Nice job on the video. I tried to watch pretending I know nothing about the subject. Many of your demonstrations work well. The parallel transport on the cylinder, however, didn’t really demonstrate well. It seemed like a bit of trickery.
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Thanks for the specific feedback, I like it a lot. I agree with you that the transition to the Levi-Civita symbols and Riemann tensor is somewhat ad hoc, I perhaps could have made it more smooth. I also recognise the concern about the parallel transport on a cylinder part, I've had the same thoughts when I made it, but did not know how to make it more precise without adding too much time to the video, since it's already 30 minutes long :) Thanks again :)
|
[
"When do textbooks get written, versus survey papers?"
] |
[
"math"
] |
[
"tl56wq"
] |
[
38
] |
[
""
] |
[
true
] |
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Like, at what stage does a field of research reach the point in its evolution that someone is asked to write a textbook? Of course there’s no one-size-fits all rule, but it’s a question of interest to me regardless :)
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When someone thinks it's worth the time and effort to write a textbook. Most of the textbooks I know the creation process of, were written because one or two professors wanted something a bit more structured and worked out than a handout for their students. Some of those were fields that have been around for a long time with multiple textbooks available (but none quite fitting), but there were also some which were basically just fresh research just done a few years earlier, with no textbook available, not even a survey paper.
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I don't think many mathematicians set out to write a textbook and then write one completely from scratch. It's more common that they've been teaching the same course for so long that they've accumulated a bunch of material over the years. As this material grows and its internal organization is refined, eventually they have a “proto-textbook”, and then the logical thing to do is to clean it up into an actual textbook. Also, textbooks are written with the expectation that they will be , especially by students, so every textbook author should have a clear idea of how his textbook is supposed to be better than the competition.
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The tone here seems needlessly unkind to masters students, community colleges, and middle-aged people
|
This project began as the twin sibling of a computer program... [description of computer program]... Quickly we discovered that the literature contained many different conventions concerning coordinates on complex hyperbolic space... Computers, like humans, are not fond of inconsistent mathematical formulas. Therefore we must establish all of the formulas correctly once and for all. With an internally consistent exposition, we rest assured that the bugs in our programs are caused by our own stupidity and not by inconsistent formulas from the literature. - The preface to Goldman's One big motivation for writing a textbook or survey paper is simply to combine a bunch of literature into one central repository. The choice to move to a textbook would probably depend on the amount of work you're willing to do to tie the ideas together for cohesion, whether to include certain background prerequisites (which are largely not included in survey articles), whether to include full proofs, and maybe what conventions you might want to introduce for the entire field.
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The books I alluded to are 3264 and All That, A Second Course in Algebraic Geometry , by David Eisenbud and Joe Harris. This is a textbook for advanced graduate students. Intersection Theory , by William Fulton. This is a reference book, written primarily for other researchers. I can't make heads or tails of most of it.
|
[
"What is your favorite undergrad math subject?"
] |
[
"math"
] |
[
"tlppys"
] |
[
44
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[
""
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[
true
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I work in probability but I feel like undergraduate probability and analysis can be very dry. So I would argue the best undergraduate subject is complex analysis. To me that is the subject where undergrad students can see interesting and meaningful results with minimal hand waving. So I'm curious, what is your favorite undergrad math subject?
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Standard: Linear Algebra is super fun with a lot of applications. Nonstandard: Nonlinear Dynamics and Chaos Theory with Strogatz's textbook felt like learning to love math all over again.
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Measure and integration theory, no contest. I feel like I didn't really analysis before taking that course.
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Galois theory by far.
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Mine's complex analysis too. Personally, I've never seen something so intriguing, so indescribably elegant. I'm still quite mind blown by it even after learning it, it's like the fascination never died down for it.
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I am really enjoying combinatorics. I also think complex analysis is really cool !
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[
"Is there a simple way to explain the residue theorem to a fourth grader? My nephew got into one of my books and keeps asking questions on what it means."
] |
[
"math"
] |
[
"e37y7e"
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[
2
] |
[
"Removed - post in the Simple Questions thread"
] |
[
true
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[
false
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[
1
] | null |
Not directly about the residue theorem, but as someone who has had plenty of experience trying to explain math to non-math oriented people, here's my advice. Focus on explaining the concept, the math is something to be learned but people can grasp the concept with a wee bit of explanation. Once they have that, they'll have a bit more of a comprehension of what the moon runes mean (math). Been finding myself explaining things like I did the Monty Hall problem, they understand where the logic leads. Won't have full comprehension of how the math works, but math is the language for those concepts.
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I think the real bottleneck is that the theorem relies on holomorphicity, and it's hard to imagine a fourth-grader ready to understand what a holomorphic function is. On the other hand, the concept of flux in physics (e.g., https://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity#Qualitative_statement_of_the_law ) is broadly similar, in that it relates something about the interior of a shape to something about its boundary. So you could lower the bar and explain that instead ... and then just mumble something about the residue theorem being like that.
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Oh right. I guess it should have been r/askmath . Technically I'm bad for replying too, I guess, but I always forget to look what the sub is. Anyhow, I hope it goes well, & that your nephew keeps asking tough questions!
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Oh right. I guess it should have been r/askmath . Technically I'm bad for replying too, I guess, but I always forget to look what the sub is. Anyhow, I hope it goes well, & that your nephew keeps asking tough questions!
|
Unfortunately, your submission has been removed for the following reason(s): /r/learnmath books free online resources Here If you have any questions, please feel free to message the mods . Thank you!
|
[
"Looking for someone to do math with"
] |
[
"math"
] |
[
"e37uhv"
] |
[
0
] |
[
"Removed - post in the Simple Questions thread"
] |
[
true
] |
[
false
] |
[
0.5
] | null |
If you want to find a math buddy, you should probably state your level, and be more specific than "not super advanced, above average for my age". What's your age? What courses have you completed? What kind of math are you interested in looking at? As it stands your post is too vague to be actionable.
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To be more specific I am a 14 year old that has competed in a statewide math competition and I placed 2nd. I am strongest in geometry and algebra but struggle with pre Calc and Calc. Trig comes easier to me but I struggle on my own studying these things
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United States? 8th grade, 9th grade? You've taken courses in algebra and geometry, but not calculus? Have you taken a course in trigonometry?
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Oh ok sorry
|
so close, yet so far
|
[
"A question pertaining to history of application of mathematics."
] |
[
"math"
] |
[
"tkjdbd"
] |
[
0
] |
[
""
] |
[
true
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[
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I was curious about knowing which field of mathematics remained "useless" for longest period of time. My definition of useless would be no application whatsoever in any field of engineering. As an example, Boolean algebra was useless before computers and so was number theory before (modern) Cryptography. I am also willing to consider answers for useless with the "usable but not mainstream" connotation. For instance, Quaternions come to mind, they were usable but Vectors remained mainstream from 1850's to late 1900's.
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Vectors remained mainstream from 1850's to late 1900's. Vectors are still mainstream! Conic sections were studied by the ancient Greeks purely out of intellectual interest. Kepler discovered in the 1600s that ellipses could be used to describe the motion of planets around the sun. So that's 2000 years from conception to a practical use: a rather long time. If you're going to declare that to be a useless application of math because there was no engineering relevant to physics in the 1600s, then you are being unreasonable. It was essential to have much of the infrastructure of celestial mechanics already worked out the 1950s and 1960s when satellites and rockets started being launched into outer space.
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Euclid's fourth postulate remained useless for approximately 2,000 years. The open question of whether there are odd perfect numbers remains useless. Neither is really a "field" on its own.
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What do you mean by the 4th postulate being useless for 2000 years? It is part of the mathematical foundations of ordinary geometry.
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If you're going to declare that to be a useless application of math because there was no engineering relevant to physics in the 1600s, then you are being unreasonable. Haha. No quite the contrary. I am constantly fascinated as to what lead to such developments even though there was nothing practical or motivating to base them off! For an example, I don't think euler knew how important graph theory is to computer science, yet he created it just for the sake of it! And I genuinely cherish the spirit of doing maths for just the sake of it! I was also a bit apprehensive to call it useless, particularly because people might misinterpret it as me looking down on a field (which is what happened with you I guess...) but for the lack of a better word, I went with it.
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Boolean algebra is not a field
|
[
"Is this theorem already discovered?"
] |
[
"math"
] |
[
"e32ug7"
] |
[
0
] |
[
"Removed - post in the Simple Questions thread"
] |
[
true
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[
false
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[
0.14
] | null |
Yes. It is trivial. Just expand (a-1)
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This is like asking if (x-3) has been discovered. It doesn’t prove anything new or expand upon an idea, it’s an example of some basic algebra.
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been around since at least ancient greeks
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There's not going to be a person who discovered this, or a name for it, since this is a straightforward equation. Not much to discover, just a simple consequence of algebra.
|
Unfortunately, your submission has been removed for the following reason(s): /r/learnmath books free online resources Here If you have any questions, please feel free to message the mods . Thank you!
|
[
"Why is i defined the way it is?"
] |
[
"math"
] |
[
"e35doq"
] |
[
2
] |
[
"Removed - post in the Simple Questions thread"
] |
[
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[
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] |
[
0.75
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Basically, the reason why mathematicians only write square roots for positive numbers is that you can't define a square root function on the whole complex field that is continuous. Moreover you kinda want your square root function to have some nice properties like being multiplication. But if you write i = sqrt(-1), then sqrt((-1) = sqrt(1) = 1 =/= sqrt(-1) So in general you can't manipulate square roots for complex numbers the way you can with positive numbers. With the i "definition" you don't have that impression
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i is not the unique square root of minus one. -i is also the square root of minus one.
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We defined the complex numbers as a field extension R/(x2 + 1) and defined i as the solution to the polynomial in that field.
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i is the principal square root but it is not thw only square root.
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Might be a language thing, In german „Quadratwurzel“ which translates „square root“ is actually synonymous with „principal square root“. So in german there is literally only one square root, wikipedia even says so (the german wiki).
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[
"What journals, books, articles, etc. should I read if I’m in college courses?"
] |
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"math"
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"e32v3b"
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Edit: someone let me know too!
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Im in calculus 2, foundations of higher math (set theory and proofs). Next semester ill be in linear algebra, calc 3, intro to actuarial science, math seminar, and a random core class. Im a math and actuarial science double major. I just love the pure math, i think it’s mind blowing and as my professor describes it “gorgeous.”
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You're not giving us enough information to give a good answer on this. Give us a list of interests and your background and maybe we could give a some recommended readings. There's very little one could do with "I'm in college, and I like math, and I want to read books."
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Hey! I have the same question too. I'm in my 3rd year of BSc (Honours) Mathematics, and would like to know about some good books and journals. I want to pursue research, so tips for that are appreciated as well. Thanks!
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!RemindMe 1 week
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[
"Where can I check if a theorem has been discovered already?"
] |
[
"math"
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[
"e32m9g"
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0
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"Removed - incorrect information"
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true
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0.5
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First, use it to generate a sequence of numbers, if possible. Then look that sequence up at OEIS.org . Here's one of mine: The Perkel graph and the 57-cell are the same thing. I *might* have been the first one to notice this. Perhaps likely. But it doesn't matter, several people immediately verified it the day I announced it. It would have been noticed eventually. It may have been noticed earlier.
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So I basically just place it here?
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Unfortunately, your submission has been removed for the following reason(s): If you have any questions, please feel free to message the mods . Thank you!
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Yes, just post it and people here will be able to tell you if it is original.
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In general it is very hard to check, since any statement can be equivalent to plenty of other theorems, sometimes even in other areas, a bit like Axiom of Choice is equivalent to a million different things, or the Riemann Hypothesis. The simplest way is to post it here. If it involves a specific sequence in any way, you can check the sequence database.
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[
"Can you call length of a circle it's perimeter"
] |
[
"math"
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[
"e31atm"
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3
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"Removed - post in the Simple Questions thread"
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[
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[
0.71
] | null |
A circle's perimeter is called the circumference. What do you mean by length of the circle? Are you talking about its diameter or something else?
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Ah, sorry, I meant circumference. I was thinking. Perimeter is the length of the line it we combine all sides into one line. And circumference is kinda the same, if I'm being correct with terms(not English speaking)
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Generally, perimeter is the term we use when talking about polygons. For instance, the perimeter of a triangle is the sum of the lengths of the three sides. The perimeter of a square is the sum of the lengths of the 4 sides. For circles, we use the term circumference.
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Thank you!
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The perimeter of life.
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[
"Is there an equivalent of Phi in non-base-10 number systems?"
] |
[
"math"
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[
"e34kqq"
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0
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[
"Removed - post in the Simple Questions thread"
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true
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0.36
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Bases systems don't really matter nearly as much as you might think. They're just different ways of writing down the exact same concepts. Your question is basically like asking "would the golden ratio still work if we spoke French instead of English?" So yes, other bases would still have the exact same Golden ratio, it would just be written a little differently. In base 2 it would be 1.100111100011... In base 8 it would be 1.4743357156277...
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The definition of the golden ratio is independent of the choice of base. It is the positive root of the equation x - x - 1 = 0, and whether we have 10 or 8 or 20 fingers, we can rest assured that we’re still talking about the same number.
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In base 8, phi is the same number, just written in a slightly different way. The equation 1 / phi + 1 = phi has nothing at all to do with the base, so that equation holds in any base.
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Yeah, you still get phi=(1+sqrt(5))/2. It's independent of base.
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Do you happen to live in a glass house?
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[
"Quick Questions: March 23, 2022"
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[
"math"
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[
"tkxne5"
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[
10
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[
""
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[
true
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[
false
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[
0.87
] |
This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread: Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.
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Is your calculator set to degrees? If so, cos(x) is a number between -1 and 1, which in degrees is a very small angle. Feed that into sin and you'll get a really small number. Feed that into tan you get an even smaller number still, and feeding it into sin it should be so small it's basically 0. From there cos(0)=1.
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The of Lebesgue integrable is that the integral of |f| is finite. This implies the integral of f is finite, but not necessarily the other way around (for example the Dirichlet integral ). So by definition Lebesgue integrable for the counting measure is equivalent to absolutely convergent. The Lebesgue integral for the counting measure doesn't impose any requirement on what order you sum in, and this matches with the fact that an absolutely convergent series can be rearranged in any order to sum to the same value.
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A poset can be viewed as a category in which each homset has size at most 1. In such a category, products and coproducts correspond to meets and joins.
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Euler claimed, without justification, that the Eulerian integers have unique factorization: that every Eulerian integers can be uniquely factored as a product of irreducible numbers (unique up to multiplication by root of unity). Or in other word, Eulerian integers also have its own fundamental theorem of arithmetic. Eulerian integers (also known as Eisenstein integers) are complex numbers of the form a+bw where a,b are integers and w =1 is the 3rd root of unity. His claim was indeed correct, but not justified.
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There's no reason the X_i themselves should be of the form ∂/∂x_i, all this tells you is the rather trivial fact that if you pick the full tangent space and some local coordinates, then the ∂/∂x_i span it... Anyway OP, the answer is when the we have a commuting frame, i.e. [X_i, X_j] = 0. [∂/∂x_i, ∂/∂x_j] = 0 so this condition is necessary, and it also turns out to be sufficient. It's a lemma in some proofs of Frobenius' theorem, so this does tie into involutive distributions.
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[
"Let me know what I’m getting into (courses)"
] |
[
"math"
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[
"e30mgu"
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[
0
] |
[
""
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[
true
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[
false
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0.5
] | null |
Calculus 3 is often referred to as multivariate calculus, it will basically revolve around doing calculus when multiple variables are involved. In particular, you'll be covering double or triple integrals, which will then allow you to compute volumes of 3-D shapes. These methods include the disk method, washer method and some other method I'm blanking on. There will also be some brief coverage on integrating between polar coordinates and cartesian coordinates, which will then be applied to the various methods. Beyond this, some more calculus practice will be had. Linear algebra is working with matrices. Most courses differ in the depth of linear algebra they cover, largely dependent on the college. It's probably the most powerful of the mathematical fields, in terms of application, so a professor can really choose to cover some interesting topics. But an entry course may involve simple matrix operations, notations, and famous theorems. In particular, you will probably cover the invertible matrix theorem and it's (10) interconnected conditionals, if you count the left and right ones independently. Oh, and you'll probably do some linear algebra, so a lot of row reduction, and various ways to expedite that process. Both classes are crazy interesting. There are tons of opportunities to apply what they cover to the world around you, both in thought as pure mathematics, and in application as applied mathematics. I'm excited for you, have fun!
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Thank you! Will do
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what topics did you study in calculus 1 and 2? i love calculus the most too, its the kind of maths i find the most rhythm in. linear algebra is also great, its a lot of matrices and vectors and all the different things you can do with them. once you get used to them its super easy
|
Unfortunately, your submission has been removed for the following reason(s): Career and Education Questions /r/matheducation If you have any questions, please feel free to message the mods . Thank you!
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You're getting yourself into a typical undergrad load for a first/second year. I'm not sure what you want to hear? Those classes are taken together by hundreds of thousands of people every semester.
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[
"Redditors, if i^2 = -1, and (-1)^2 = i^4 = 1, why tf doesn't Sqrt(1) = Sqrt(i^4) = -1?"
] |
[
"math"
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[
"e2q936"
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0
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[
"Removed - post in the Simple Questions thread"
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[
true
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false
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0.33
] | null |
The square root function is defined, over the real numbers, to produce only non-negative reals. You can define a different square root function in various ways on certain subsets of the complex plane to get other values, but the standard definition on R gives non-negative values (by non-negative I mean if a>=0, \sqrt{a} is a non-negative number and \sqrt{-a} = i\sqrt{a}).
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For reals x, √(x )=|x|, not two values simultaneously as suggested by ±x.
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Unfortunately, your submission has been removed for the following reason(s): /r/learnmath books free online resources Here If you have any questions, please feel free to message the mods . Thank you!
|
Sqrt(i ) = sqrt((i ) ) = | i | = | -1 | = 1
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It does. Of course every positive number has two square roots--the principal square root and that number's additive inverse. The principal square root is defined to be positive for convenience. Similarly there are three 3rd roots, four 4th roots, and so on.
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[
"\"Men and women holding hands in a circle\" riddle"
] |
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"math"
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[
"e2p0it"
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3
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[
"Removed - try /r/learnmath"
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true
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false
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0.8
] | null |
Yeah, the examples I had didn't validate this either. I still can't logically explain why the formula I gave is right though (if it is).
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So I tried to solve it and I got to the same conclusion sort of. If MW represents people holding both a man and a women’s hand and WW represents holding two women’s hands, the number of women in WW is twice as the number of women in MW, 2:1 is another way to think about it. So WW = 1/2 MW.
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This isn’t right. Easy counter example: 3 consecutive women and then men around the rest of the circle. MW=4 (the two women on the outside and the men immediately next to them) and there is 1 WW person (the middle woman).
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The thing is the riddle does give us a precise number for X, Y and Z. In your examples by the way : 10 men then 10 women : WW=8, MM=8, so MW=4 and we do get WW+(MW/2)=10 Alternate regularly : WW=10, MM=10, so MW=0 and again, WW+(MW/2)=10 So my formula does seem to be right ... but why ? Isn't there some kind of ELI5 to explain this ?
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The thing is the riddle does give us a precise number for X, Y and Z. In your examples by the way : 10 men then 10 women : WW=8, MM=8, so MW=4 and we do get WW+(MW/2)=10 Alternate regularly : WW=10, MM=10, so MW=0 and again, WW+(MW/2)=10 So my formula does seem to be right ... but why ? Isn't there some kind of ELI5 to explain this ?
|
[
"An associate professor of mathematics used statistics to invent a Scrabble game to be played in Cree rather than English. The normal Scrabble board is too small for Cree — English uses five characters per word on average, Cree uses 10 — so he uses a Super Scrabble board"
] |
[
"math"
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[
"e2t6kx"
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41
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""
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true
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false
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[
0.88
] | null |
Relevant paragraphs from the article: The research paper he is working on focuses on the way he used statistics to figure out a way to make Scrabble playable in Cree. They flipped through the pages of a Swampy Cree dictionary and took a sample of about 1,000 words from it, to find a base ratio of letters to use on the tiles, a basic scoring system and to figure out how many tiles people need to start playing.
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What does this have to do with math other than the fact that he happens to be a mathematics professor?
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it is an application of statistics and the subject of his research paper
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Cree, for anyone who never heard of it before: https://en.wikipedia.org/wiki/Cree
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Professor Doolittle has worked on other adaptations of classic word puzzles that don't translate well into Cree. For example, the "one letter transformations" like: It really got me thinking about how these games would have to differ in other languages.
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