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[
"Today I was told that the irrationality of square roots was once considered heretical. Is this true?"
] | [
"math"
] | [
"fyvm6"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.73
] | Where can I find more information about it? Edit: my source was from a guy pursuing a masters's degree in Mathematical Behavioral Sciences. | For a sufficiently large value of "once", yes. | http://en.wikipedia.org/wiki/Irrational_number#Ancient_Greeks (There's also a legend about Hippasus being drowned at sea to keep it secret but that's probably apocryphal) also see http://www.math.ufl.edu/~rcrew/texts/pythagoras.html | The assumption they were making seemed quite reasonable at the time: for every two lengths, there exists some small quantity that fits evenly in to both. Effectively, they were assuming that every quantity is measurable and that every length can be assigned a discrete value. That's about the extent of my knowledge on the subject. I've read a few math history books and the Pythagoreans don't seem to get much attention. | Wow, thanks for that- you caused a small explosion of connections in my head. | Who was the first? |
[
"Can someone with Math skills explain this?"
] | [
"math"
] | [
"fzcf3"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.25
] | Why is i raised to the fourth power equal to one? | -i | Radians measure how many times you can wrap the radius of a circle around the edge of the circle. One radian is the angle you get when you travel exactly one radius around the edge . And another picture . | i = ( i ) = (-1) = 1 | wow thanks! What about to i to the third...? | Ok, I got another one.... How exactly do radians work? |
[
"DAE realize how awesome Pascal's triangle is?"
] | [
"math"
] | [
"fybbp"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | Sophomore in high school so i really don't know much about the math in general, but I was toying around with Pascal's triangle and I noticed some things. Such as the sum of every set of numbers is a power of 2 (1=2 1,1=2 1,2,1=2 Or for the first several sets of numbers are powers of 11 (1=11 11=11 121=11 | There are a whole lot more patters than just that. You should look some of them up. Pascal's triangle comes up in a lot of places you might not expect as well. For example, last quarter I used the triangle to decompose [; V_1^{\otimes n} ;] using the formula [; V_k \otimes V_{\ell} = \bigoplus_{j=0}^{\min(k,\ell)} V_{k + \ell - 2j ;] where the V_i are the irreducible representations of SU(2). Sometimes the uses for the triangle aren't that obvious. | DAE think pascal's triangle is just what you get when you convolve square functions over and over again? | Color in all the even numbers one color and the odds another and you get a Sierpinski triangle. There are all sorts of neat patterns with it. | They also represent combinations. The nth row shows all the possible outcomes of nCx where x =< n. | Thanks but by god man speak english |
[
"Factorial Question"
] | [
"math"
] | [
"fy6dj"
] | [
0
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""
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true
] | [
false
] | [
0.47
] | [deleted] | Thinking in terms of the prime factorization (breaking up this big number into its prime factors), you probably want to find out how many fives and twos get racked up along the way. Since each zero at the end can be though of as multiplication by ten, you need a five and a two to make each ten. Thus, the number of zeros (or tens, in terms of factors), is limited by the number of fives, as you will likely rack up way more twos along the way than fives. So how do we get a figure on the number of fives? Well, 2011! = 2011 * 2010 * 2009.... (going on till you hit 1). You only rack up a five when you hit a multiple of five. The problem is, some numbers will give you more than one five. For example, 25 = 5*5, will give you two fives. How do you factor this into account? Well, first count how many non-zero multiples of 5 there are from 1 to 2011. The answer is 2011/5 = 402.2 ~ 402 (rounding down). The numbers who give you an extra five are non-zero multiples of 25. Of these, we get 2011/25 = 80.44 ~ 80. The numbers who give you a third five are multiples of 125. So, 2011/125 = 16.088 ~ 16. The numbers who give you a fourth five are multiples of 625. So 2011/625 = 3.2176 ~ 3. Lastly, numbers who give you a fifth five are multiples of 3125. Well, you won't find any of these before 2010, so we're done. Now add these numbers together. 402 + 80 + 16 + 3 = 501. Thus, there should be 501 zeros. I hope this solution makes sense =D. | I don't think it's possible to obfuscate the algorithm any more than that in any serious language. Bravo. | This is just an unfamiliar kind of notation - no more obfuscated than mathematical notation of aliens would be to us, or ours to them. I mean, it's not intentionally obfuscated - it has its own strict and non-contrived logic, you just don't know the notation yet. Let me explain. <. is floor @: is function composition % is division, %&5 is division by 5 is repeated function application is repeated function application until convergence So, (<. @: %&5) a: is "integer-divide by 5 until convergence", t.i. until 0. You'll get 2011, 402, 80, 16, 3, 0. }. is "drop first item". + is sum f/ is folding a list with an operation (x1 f x2 f x3 ...), so +/ is list sum. So together you've got "integer-divide by 5 repeatedly, sum all terms but the first". | In J ( http://jsoftware.com): +/ }. (<. @: %&5)^:a: 2011 501 | Try posting this in r/learnmath or r/cheatatmathhomework . |
[
"Math major at UCLA wondering what kind of volunteer opportunities are out there for the summer using my knowledge for good, rather than evil."
] | [
"math"
] | [
"fyxuj"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.62
] | Guys I know in similar situations are looking to intern at places like KPMG and Mercer, but I'd rather use what I know to help out communities and NPOs instead of these money grubbing psychos. Does anyone know what I should be looking for? Edit: Thanks so much guys I posted a similar question in the past on and all I got was "boohoo grow up hippy." You all really helped me out! | Neighborhood groups get a lot of actual work done. Tree planting and urban forestry groups make a big difference with practical steps, and often need help understanding what has been done, what should be done, what resources are needed, what permits are required, and how to examine results by estimating tree cover and age and building databases. | A couple of ideas. Hope this helps. | Maybe go to work for a community farm. If Jan wants to plant ten acres of corn and Rick wants to plant 7 acres of soybeans... | Doesn't UCLA's IPAM offer anything? Your professors should know some things you can do this summer. | Go Bruins! Good luck with your search man...I'm an engineer from UCLA and I too would rather use my powers for good than evil...I second the notion of talking to professors or people at IPAM and see if they know of any good volunteer or productive opportunities to intern or something of the sort. Sorry I'm not of much more help. |
[
"r/math, I'm learning my first language this semester (FORTRAN) and I'm loving the freedom. However, I'm crippled by the low overflow number. Suggestions?"
] | [
"math"
] | [
"fy9gq"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
0.84
] | I've having very, very much fun with my first forays into programming, and I'm accomplishing a lot. I just finished a simple recursion for the n-th fibonacci number, for binary conversion, for finding base 10 narcissistic numbers, for the Collatz conjecture algorithm. However, quite a few things I'm trying to do are just impossible with the overflow number FORTRAN has (which I calculated to be ((2 )-1)). Is there any programming language accessible to someone like me (who knows little about computer science) that allows calculation with bigger numbers? Or is that a reasonable number for any language? I thought FORTRAN was science language, but I'm confused why it can't handle as big as 3 Thank you! =] | Fortran allows variables to be declared as INTEGER(8), which gives you up to 2 -1 signed integers. Here is a reference with some examples . Python would be pretty much transparent and worry free with respect to arbitrary precision integers. However, it is an interpreted language so it might be too slow for computationally intensive tasks. There are various high-precision fortran libraries available. The ARPREC package claims that "In most cases only the type statements and (in the case of Fortran-90 programs) read/write statements need be changed." My impression is that David Bailey (one of the principals on this site) is a real computational mathematics honcho. You might be interested in his experimental mathematics site . | that is not all he said; did you not read I don't know that I've read a science paper published after 2000 (probably early) that mentioned using fortran. ? | Ah, but Dijkstra's famous article, The goto statement considered harmful is the reason for it's absence in some modern programming languages. Veteran programmers will often (but not always) bend over backwards to avoid its use even if it is available. If you are trying to maintain a list containing zillions of entries, you may be going over the amount of memory physically available on your computer. A whole gigabyte of memory would only be enough for 125 million 8-byte integers, for example. By the way, if you are happy using Python, you should definitely look into Sage , which uses Python as its scripting language. I'm not sure about this, but Sage may even be faster than Python for some kinds of calculations because it goes off into specialized compiled packages. Anyway, the section on Performance in the wikipedia site claims that performance is "competitive". There are also some links to benchmarks. For a math person like you, I think Sage would be a "kid in a candy store" kind of thing. | It's still used pretty heavily in the finite element community. In my computational science grad program, probably 60% of the research codes are written in fortran, including my group's code. However, I think we're one of the last fields where it's common. | You want to use 64-bit integers instead of 32-bit integers. FORTRAN allows that, but I don't know the details. |
[
"Help with a basic maths calculation"
] | [
"math"
] | [
"fzc93"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | I'm embarrassed to ask this because it is so simple, but I need to know how to solve for y when x is known: 1000000 * 10 = x | This is a good question for /r/learnmath. What you need to do is divide by 1000000 and the take log base 10. | log [base 10] of (x/1000000). or log (base anything) of (x/1000000) divided by log (same base) of 10 | Before I knew how to think about logs I would simply ask myself 10 to the something equals blah. It helped me limp along until I really understood what the log function does. So 10 = 1/1000000 Try a few positive and negative integers. 10 = 10 10 = 100 looks like that is going the wrong way, right? Lets go down. 10 = 1 (closer) 10 = .1 = 1/10 (closer) 10 = .01 = 1/100 (closer) Keep that pattern going until you get to: 10 = 1/1000000 edit: fixed the spacing | Sorry root45 I didn't realise there was an /r/learnmath but thankyou for answering me anyway! | Glad I could help :). |
[
"Counting sheep"
] | [
"math"
] | [
"fydst"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.55
] | Can anyone help me with me sheep counting ? | So I'm guessing that "Cat girls and Catamorphisms" a furry harem romance about category theory is right out? Edit: To reduce the amount of lame. | So I'm guessing that "Cat girls and Catamorphisms" a furry harem romance about category theory is right out? Edit: To reduce the amount of lame. | What annoyed me is not the furry part, it's that it's badly written. Hadn't I known about the problem beforehand, I wouldn't have understood a damn thing. | Yes, something really goes wrong with the grammar at Given the cute ω look on her face I decided then and there that I was going the time compressed event ω and this lamb ω + 1, the sheep after ω. | I've refreshed the page and the missing word hasn't appeared and I cannot guess where or what it is. Worse than that, lamb omega is left standing at hotel reception while a room is found for omega plus one, omega plus two, etc. It must really suck to have infinitely many guests push in ahead of you. |
[
"Reverse Polish Notation help?"
] | [
"math"
] | [
"fyho5"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | SO I need some help with RPN, I checked the wiki page but I still don't quite get it. Like I get simple multiplications, aditions etc. But how would you for example write: \int_{0}{2} \sqrt{ (\frac{dx}{dt}) + (\frac{dy}{dt}) + (\frac{dz}{dt}) } Latex pic: | Here's a version of your link that's not broken and has proper parentheses. The people in /r/learnmath might also enjoy this question. | I understand that it is the derivative, but the point is that you need to know the operator if you want to write it in RPN. In regular notation, dx/dt is ambiguous (especially in the context of an integral) because it can either be viewed as the unary operator "d/dt" applied to x, for example like negative x is "-x", or it can be viewed as a "formal" quotient of the differential dx with dt (which seems contrived, but it might depend on who you ask), in which case it needs to be treated and expressed like you would a fraction "3/5". | here, I will treat sqrt and int as unary operators, it will look like this: dx dt / 2 ^ dy dt / 2 ^ dz dt / 2 ^ + + sqrt \int_{0}^ {2} | Is dx/dt viewed as the d/dt unary operator applied to x, or as the "formal quotient" of dx with dt? | Yea I couldn't edit the link after submitting =/ I got to start using those link tags :P Also thanks for the fix and I'll throw them a link to this question. |
[
"Kuhn-Tucker conditions without Lagrange constrains"
] | [
"math"
] | [
"fyj2n"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.87
] | Hi there. I wonder if I can get a little help with this, I just don't know how to write the equation system. For example, lets say: minimize f f(x,y) = ((ax+by)-c)²+((dx+ey)-f)² with a,b,c... positive constants No Lagrange constrains And the list of Kuhn-Tucker x>=0 y>=0 So the partials would be: f(x,y) = (a²x²+b²y²+2axby)-2cax+2cby+c² + (d²x²+e²y²+2dxey)-2fdx+2fey+f² df/dx = (a²x+2aby-2ca+d²x+2dey-2fd) df/dy = (b²y+2abx-2cb+e²y+2dex-2fe) And the minimum point would be solve the equations 0 = (a²x+2aby-2ca+d²x+2dey-2fd) 0 = (b²y+2abx-2cb+e²y+2dex-2fe) But I don't know how to input the x,y>0 constrains there :-( | If you want to minimize f(x,y) with x and y non-negative, the Lagrangian is The first-order necessary conditions are In practice, it's easier to do it in cases and solve for the interior minimum if there is one, and the minima if x or y is zero. | solve the equations and throw away negative points? | Cool, thanks! | I agree with necroforest. The last system of equations is linear in x and y so it can be solved simply. Then, depending on the coefficients a,b,c,d,e,f, you can throw out the solution if it doesn't satisfy your inequalities. Perhaps the example posted by the OP wasn't complicated enough? | But for this examples a2,b1,c3,d4,e7,f2 The minimum in -2<x<2 and -2<y<2 is 0.11 Plot The minimum in 0<x and 0<y is 3.22 Plot So the thing is, a functions which look likes x²+y² has its minimum in one of the 8 region of the 3D space, so if the minimum is not in the region of x,y>0 where does the surface of f cut the x,y>0 region and in that cut where is the minimum? |
[
"5 years on and I still can't solve it..."
] | [
"math"
] | [
"fyl6l"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.65
] | I just read through the other thread on the ladder problem and it reminded me of a problem that I've been playing around with for a couple of years and haven't been able to wrap my brain around. I'm hoping for some insight on it. The problem involves taking a piece of flat stock material like a 4 ft x 8 ft piece of plywood and cutting it in several different size pieces to complete, say, a construction project. It seems like there should be a way optimize the cuts that would be made to the sheet of material to minimize waste to get the needed pieces. Anyway, the only way that I can figure out how to solve it is to write a program that would brute force through the combinations and use the metric of minimizing waste to optimize the cut locations. I haven't actually written the code so I can't speak to the details, but it doesn't seem like it would be too bad. I also think that this problem might end up in P vs. NP realm. | This sounds like the 2D bin packing problem . | It's definitely an NP-hard problem. Classic example I might add. | Just to provide some google-food/terminology: In practical scenarios, e.g. paper cutting and some automatic sawmills, a common constraint is a , meaning you only allow cuts from one edge of a piece to the other (i.e. it's impossible to make an L-shaped piece). | This phrasing is, as mentioned above, the 2d bin packing problem. Namely, constrict yourself to rectangles (which seems ok if you're building a book shelf), for your required pieces p_i. You are given sheets of wood for stock that are of a particular size W. So you are trying to figure out what is the minimum number of 'bins' W that you can fit all of your pieces p_i. The 1d case of this has a cool reduction to 3SAT if I remember correctly. | I also think that this problem might end up in P vs. NP realm. Just a quick word on this. As pointed out in the Wikipedia link, this problem is NP-hard (you can think of it as being "at least as hard as every NP problem"), and I guess certain ways of phrasing it will make it NP-complete. However, one should not lose hope simply because a problem is NP-hard, as many day-to-day puzzles are specific instances of NP-hard problems (such as sudoku, minesweeper, tetris, etc.) If the specific example is simple enough, there might be some brute force ways to get to solving a puzzle. In general, the way people tackle these is to give approximation algorithms that don't necessarily achieve the optimum configuration, but gets darned close. So in your example, writing a program that just tries a bunch of simple configurations will probably get close enough to the optimal solution that you might say this is sufficient for your purposes. Of course, if you were a large company that is constantly manufacturing these things, you probably want to spend some effort into finding the optimal solution. |
[
"/r/math, I plan on getting my PhD in Number Theory, but as a HS senior, what fields in math should I be focusing on?"
] | [
"math"
] | [
"fxmhl"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.45
] | I am thinking of majoring in math so I can get a PhD in Number Theory afterwards, what should I be focusing on now because I'm going to self teach more high level math since I can just test out of it once the time comes. And maybe to clarify, what fields in math I should learn is kinda all I'm asking? Currently in AP Calc and tested into Analytical Geometry and Calc I at Kent State. | take the right courses and not math courses that will do me no good in grad school. Honestly, ALL math courses you take will help you in grad school. You'd be amazed how often ideas from seemingly unrelated fields can be synthesized to solve a problem. Planning a path now rather than just taking what interests you at the time (when you can actually make semi-informed decisions) won't help you at all. Right now, you literally can't know what you will find interesting. | Not to sound patronizing, but if you're in high school you likely (though not necessarily) don't know what "real" math is. Wait until you study groups, topology, maybe even analysis (ugh... but whatever floats your boat), differential geometry, etc. to figure out what you like. As for high school: pretty much everything you learn in high school 'math' is just mechanical stuff, so I don't imagine you'll take much away from there. I'd recommend finding a good undergraduate book and teaching yourself math; not only will you learn stuff relevant to your degree, it's a great experience if you've never done it before. Among other things, it forces you to learn . A bit of advice on learning math in general: | OP, you to read this. I hate to sound patronizing, but you currently know nothing. Hell, I don't know anything either, but I probably have a better idea of how little I know. If I can expound on this fantastic exposition... If you plan on doing graduate-level mathematics, your university experience should be very challenging. While there are people who go to university already knowing what they want to do, I recommend you expand your horizons before you arrive at such a singular conclusion. When you actually start learning mathematics at the university level (mostly upper-division), you'll start to realize what branches of math you enjoy more and what branches you enjoy less. As I'm told, your interests and focus will continue to develop and change well into grad school. Saying that you want to get a Ph.D. in number theory is like a kid saying he wants to be an astronaut on an expedition to Callisto, one of the moons of Jupiter. | OP, you to read this. I hate to sound patronizing, but you currently know nothing. Hell, I don't know anything either, but I probably have a better idea of how little I know. If I can expound on this fantastic exposition... If you plan on doing graduate-level mathematics, your university experience should be very challenging. While there are people who go to university already knowing what they want to do, I recommend you expand your horizons before you arrive at such a singular conclusion. When you actually start learning mathematics at the university level (mostly upper-division), you'll start to realize what branches of math you enjoy more and what branches you enjoy less. As I'm told, your interests and focus will continue to develop and change well into grad school. Saying that you want to get a Ph.D. in number theory is like a kid saying he wants to be an astronaut on an expedition to Callisto, one of the moons of Jupiter. | You'd be amazed how often ideas from seemingly unrelated fields can be synthesized to solve a problem. To me, this is the main point of a PhD. If you have a PhD, the thing you have demonstrated is the ability to take ideas from one field and apply them to another field. I had a professor say that a person with a PhD ought to be able to hear a full explanation of a problem in any field, with all the relevant information, and then go walk around the building for a few hours and come back with an idea about the problem. Maybe not a revolutionary or original one, or even a feasible one, but some idea about the problem. A PhD program is to teach you to think. It is not, for the most part, to teach you the deep secrets of your field that are withheld from undergrads. |
[
"Tomorrow, I'm entering a 14 hour math competition. Bring it."
] | [
"math"
] | [
"fxoap"
] | [
71
] | [
""
] | [
true
] | [
false
] | [
0.82
] | It's the . Anyone done this before? It basically involves a team of four or five high school students working on a real-world applied math problem. All day. Challenge accepted. Thirteen hours down. One to go. Shit has officially hit the fan. this year's prompt if anyone's interested. That was seriously an insane way to spend 14 hours. It was a blast though, if anybody's thinking about doing it. | I hope they have an overly enthusiastic Mexican soccer style announcer calling the competition. "He squares the right then he squares the left, he multiplies to get rid of the fractions, now the numbers are WHOLE! WHOLE! WHOLE!". | Last years http://m3challenge.siam.org/about/archives/2010/problem10.php Seems open to too much subjectivity. | I've heard good things about M3 - I have a friend who competed last year. Best of luck! C: | What I'd like to see is a Social-Network inspired math competition, where you take a shot every time you use an epsilon or quote a theorem. | What am I to bring...? |
[
"If numbers are infinite, does that mean eventually a number will break a law?"
] | [
"math"
] | [
"fxoyx"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | I'm curious but uneducated in maths, so I am here to learn. I am sure you have heard the conjecture that due to the infinite nature of irrational numbers, unlikely patterns exist. Through an infinite set of numbers could a particular number ever break a theorem or mathematical law? | If there isn't a proof, it is not a theorem, by definition. | All theorems are backed up by proofs; that is, a logical argument which shows that no counterexample could exist despite there being an infinite number of possibilities. | If you are interested, there are a couple of simple and elegant proofs of there being no rational number (despite infinitely many of them), which when squared gives 2, here . | Excellent! Thanks! After reading a recent askscience thread about believing in currently unprovable things I started to mull over many questions. It's quite amazing that despite infinite quantity, laws are still followed. | Whoops. You're right. I had a faulty definition in mind. |
[
"thoughts on pi..."
] | [
"math"
] | [
"fynhd"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | So, by definition, pi is the ratio between the circumference of a circle and the diameter.... But also, I've seen the proof that pi is irrational (see wikipedia) Since the circumference can be anything (take a string, stretch it into a circle) does this imply that if you construct a circle by stretching out a string into the shape of a circle that you can never precisely cut a string that will measure exactly its diameter (the existence of a physical length seems to me to suggest it must be rational (am I right in assuming this?)-- but then pi, the ratio of 2 rational numbers would be rational...) or maybe a perfect circle doesn't actually exist for any fixed circumference?!?! Likewise, if you construct a circle by say, spinning a stick, you could never actually cut a string that would measure out the exact circumference? (since then the diameter is a fixed length, ie twice the stick?) obviously, this makes little sense in real life, since you could get so close to exact that the error would be possibly unmeasurable, or at least very close.. but still... technically...? anyway, maybe I'm the only weird one who thinks this is interesting (although I doubt it in this subreddit) just saying...crazy shit... Edit: or actually, I guess this just means a perfect circle can't even exist at all? since if it existed its diameter and circumference would be actual lengths? | Why do you think you can cut a string of rational length, but not irrational length? | Indeed. How would you even test whether a measured length is rational or irrational? | I mean, with respect to some unit, the circumference or the diameter has to be irrational. Thus, if you set the diameter as your unit, there cannot be a rational relationship between the two... I guess it boils down to whether or not length is actually quantized in the real world (i.e. you could break both circumference and diameter up into small enough pieces that each had an exact number of equal-sized pieces) Anyway, I probably just don't know enough physics (sorry, hardly know any), but isn't matter quantized? ie any physical length is quantized? (...or is it that since the space in between the particles/sub-particles/whatever doesn't have any constraints length doesn't have to be quantized?) anyway, this may be a completely incorrect assumption, but I've always thought physical lengths were quantized? or do we know either way? | A rational length simply means you cannot express the length by a proportion of two integer lengths. The length of a string can be any positive real number, including irrationals. | ok, but (sorry if I mess this up, I don't really know physics, just did a quick google search) if you set your base unit of length to be Planck length (or a multiple of Planck length) isn't every actually existing length then rational? or actually, since everything is a multiple of Planck length anyway, doesn't that imply no matter what you set your base length to, every length is rational (with respect to your base)? |
[
"Measure theory/topology question I came up with."
] | [
"math"
] | [
"fy41u"
] | [
28
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""
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true
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false
] | [
0.93
] | [deleted] | It's impossible. Suppose {C_a} were such a collection (where a is indexed by some uncountable set). Then for some interval [n,n+1], there must be uncountably many C_a such that C_a ∩ [n,n+1] has positive measure (left as an exercise - straightforward measure theory). Without loss, we can assume it's [0,1]. A similar argument shows that for some positive whole number K there must be uncountably many C {a_j} with this property, countable additivity of the measure implies [0,1] has a subset with infinite measure, a contradiction. Edit: Assuming the axiom of choice and that the space has no infinite atoms , then having an uncountable collection of disjoint subsets of positive measure is the same thing as not being σ-finite . The proof that it's impossible for σ-finite spaces is exactly the same as the one I gave above for R. To show it's always possible in non σ-finite spaces, use Zorn's lemma to take a maximal collection of disjoint subsets with positive, finite measure. | I'm not sure what you're getting at, but you seem to be suggesting the line you quoted is false. Here's a proof. I know that I have uncountably many C_a such that m(C_a ∩ [0,1]) > 0. Let V_K = {a : m(C_a ∩ [0,1]) > 1/K}. By assumption, ∪ V_k is uncountable. Thus if every V_k is countable, we would have a contradiction. So I can conclude that some V_K is uncountable. | The sum of an uncountable collection of nonnegative numbers is the supremum of the sums of the finite subsets. It is easy to show (as kfgauss indicated) that if you have uncountably many nonzero numbers, then infinitely many (uncountably many, but why be greedy?) are bigger than ${1\over k}$ for some $k$, and so the sum must be infinite. Now to your question if you have an collection of disjoint subsets, the measure of the union is equal to the sum of the measures (or certainly bounded below by the sum of the measures), and so there you go. | Doesn't work. The complement of all of the rational points in R is measurable and has positive measure. | The way I read (1) and (2) is that you are constructing an uncountable collection of disjoint open subsets of R . This is clearly impossible, since every open subset of R has a non-trivial intersection with Q , which is countable. Edit: I'd imagine this is why caks thought about doing it with fat cantor sets (which was my first instinct too). |
[
"How to create a function that measure the difficulty of a set of questions?"
] | [
"math"
] | [
"fwzjk"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | [deleted] | What's "Generate"? | What is "Generate"? You could try difficulty = 100*incorrect/(correct+incorrect). That's the percent incorrect and higher percent incorrect probably means more difficult. | Why not just count the absence of an answer as an incorrect answer? | The number you gave difficulty = (correct - incorrect)/generate is the percentage right minus the percentage wrong. So if this number is 1, everyone got the question right. If it's -1, everyone got it wrong. If it's 0, the same number of people got the question right as got it wrong. This seems like a pretty good rudimentary measure to me. You could aim for your questions to be around a certain number, say .5, so that about 75% of people get them right. On the other hand, this formula loses data as well. It doesn't really take into account the people that don't answer a question. If a question is hard and no one answers it, you'll get a difficulty of 0. But this is the same as if half people answered it right. So in this sense, it's a little misleading. | Any function is going to lose some data, so we need to make a design decision: which dimensions do we not care about? I think it would be helpful for you to describe what your goal is. What are you going to do with this data? Are you revising a test for a future class? Deciding which areas need the most attention for the current class? Devising a weighting system to calculate the students' scores? You say you want to know which questions are harder, and which are easier. But this has many possible dimensions: What is it that really matters? |
[
"Dear r/math:"
] | [
"math"
] | [
"fxss0"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.53
] | [deleted] | There is some hyperbole that others have criticized. Underneath it though is a valid point. For most mathematicians, math will not yield the instinctual feeling of success that other occupations may enjoy. For most, it's an art of scratching, clawing, being wrong, being right, being unsure. However, every once in a while, you will read something amazing, you will think something amazing, and you may very well prove something amazing. You may be able to look back, , to a concept that came from you -- yet paradoxically has always been true from the dawn of time. It's not a train that you never catch, since you catch bit -- just slowly. I'd prefer the analogy of digging in a darkened cavern, uncovering bits of a remarkable precious stone -- each pebble with a unique, perplexingly elegant radiance. | You're basically whining about not being omniscient. Wtf. Yeah, I am bummed that I am not God, at most I can have some theorems named after me, i'd better just give up on life. Chill dude. | Twelve years of public education and I'm not even knee deep in the massive ocean of human knowledge. Then you're better off than most 17/18-year-olds; you that you don't know anything. If your goal is really "to get your name on a few theorems", then you probably should do something other than math. While a career in math will indeed get your name in a textbook or two, it will hardly make you famous (i.e., don't expect your name to become a household one like Pythagoras). If, however, you truly enjoy/are fascinated by math then please don't be daunted by how little you know now. It's par for the course. And in fact the more you are able to recognize what you know, the better off you'll be. | Isn't it better to know something than to know nothing at all? | I'm not hearing that you like math. I'm hearing that you want to be an expert, that the path ahead of you looks pretty hard, and that there's no big glorious payout at the end. Being young, you're low on confidence and find this discouraging. If it helps, I think this is pretty natural, especially in American society (and possibly others as well, but this is the one I know) where so much emphasis is placed on status. Early adulthood is a fairly unhappy time filled with trying to find your place in society, and society not caring because you haven't yet earned your position. It's just a hard time to feel fulfilled, you're starting to come face to face with your preconceived notions about life and finding out how different things actually are, and it's disorienting. The best advice I can give is to focus on doing something you enjoy and not "who you will be" by doing that thing. At this stage you may not know what you enjoy doing. Use this time to explore and understand that. Goals are important, and you should have them, but a life built around doing something you love is much more rewarding than a life spent chasing goals while hating the journey. p.s. Hedonism and academia aren't mutually exclusive. And the path to a tenure track position at a major research university is fiercely competitive and is in many ways similar to the kind of rat race found in industry, while paying far far less. Don't focus on the position. Focus on doing what you love and wherever you end up will be just fine. tl;dr This is normal. Focus on doing something you enjoy and not "who you will be" by doing that thing. The rest will work itself out. edit: minor grammar/punctuation changes. |
[
"Solving for \"n\" in compounded interest."
] | [
"math"
] | [
"fx0sc"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | Given the formula for compounded interest, which is A=P(1+r/n) . How would you solve for n? | You might get a better response at /r/cheatatmathhomework or /r/learnmath. | Okay, A) I never said this was homework and I never said you shouldn't have posted it here. ALL I said was that you might get a better response at those two subs. Which is totally true. The people there are much more likely to help you than your average /r/math reader simply because they are there to help people. That's what they do. Case in point, I frequently read both those subs and help when I can. I'm much more likely to help someone there than here. There's obviously no rule that whatever you post has to be homework. It's an excellent place to ask questions about math. B) I'm sorry you're "annoyed" about my suggestion, but consider this. Of the most recent 100 submissions to /r/math , at least 25 of them were people asking questions about math, a lot of them very basic, some of them not. There are another 20 or so submissions that are just jokes or ridiculous things like this. This is nearly 50% of submissions which are not really math and would probably get a better response elsewhere. I'm not even counting posts like this one , which is just a little silly (and incorrect), but isn't a question or a joke of some sort. In short, the reason why it might seem like me and "a large portion of this community" assume the worst is that it can get tiring after a while. I honestly don't really care where you post. But my suggestion may get you an answer you might not get here. It also lets others know about those subs who might not already know. I really don't see anything wrong with my intentions, and I feel it's you who is assuming the worst in me. | This has nothing to do with homework It's only the name of the subreddit. It's tongue-in-cheek. Anyway, check out wolframalpha . Expressions in this form don't have solutions in elementary functions; you need the Lambert W-function . As for your question below about the derivative, see wolframalpha again . | Bizzare question, to me. Given an annualized rate, term, and future value, solve for the frequency of compounding? Odds are you are going to have to use something like newton's method | Newton's Approximation Method? What would the derivative of P(1+r/n) be? |
[
"What do you think about online math courses ?"
] | [
"math"
] | [
"fx0up"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.66
] | I will be teaching an online math course in the Fall and would love to hear of anyone's experience with online math classes, either as a student or an instructor. Personally, I see online math courses as little more than independent study reading courses designed to save money for the administration. But I am hoping for the best..... | As a senior in HS I took multi-v calculus online from Stanford, and was taught by a pre-made animation with recordings. I failed horribly and learned nothing. | I took an online math course in probability/statistics (high school, nothing too in depth) earlier in the year, and I'd be happy to share my experience. You're right about it being not much more than an independent study course, but there's one thing you could do as an instructor that would make the process a lot smoother. If all your course materials/lessons have been prepared by somebody who's not you, I'd suggest looking over the answer keys to practice questions. Now, I was in the first or second class to ever take the class I did online, so your situation may be different, but I found that a lot of the answers we were given were incorrect or weren't in line with the material we'd been provided, and that made studying for the exam a real bitch. Also, providing the class with more practice questions never hurts. Apart from that, I can't think of anything that was majorly objectionable. I actually really enjoyed being able to take things at my own pace/not have to worry about having homework done for the next day and such. Good luck! | If you have a degree in math, don't bother studying for the CSET. It's a waste of time, since you'll pass it with near-perfect marks the first time you take it. You can even take all 3 (Alg, Geo, Calc) in one sitting, although that might be more of a challenge. But it's worth trying just to feel like a math badass. :) | I'm doing an online refresher (aka material I have already covered) in maths for the CSET. My degree is in applied math so I'd like to think I have a strong background in math. I'm finding this difficult. Granted, I don't have a teacher in my refresher, but I still think this will be a pretty hard way for students to learn. | I have taken several online classes in completion of an MS in Technology Management. This format frustrated both the instructors (who often enjoyed presenting in front of real people) an the students, who felt cheated of a real education. I think your observations of the motivations of the administration are correct. |
[
"Terry Tao and I"
] | [
"math"
] | [
"fx53m"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.6
] | [deleted] | Did you smell his hair? jk, I'm sure the talk was awesome. There wouldn't happen to be a video, would there? | It took all of my self-restraint not to ask him out on a date Sorry, no video :( | Why Tao? Heck, ask my dad, or Barack Obama, or Keanu Reeves. The secret is just eating less and healthier, and a bit of exercise. The rest is just details. | Why Tao? Heck, ask my dad, or Barack Obama, or Keanu Reeves. The secret is just eating less and healthier, and a bit of exercise. The rest is just details. | Erdős also did amphetamines. |
[
"Why was ε afraid of ζ?"
] | [
"math"
] | [
"fxepc"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | [deleted] | It's the same as this version. | Why was epsilon afraid of zeta? Because zeta eta theta. | This is the version I heard. | I read eta as nu, my bad :> | no worries, me too... |
[
"How do I calculate the number of different lock screens on an android phone?"
] | [
"math"
] | [
"fxgyt"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
0.85
] | How do I calculate the number of paths that can be chosen in a 3x3 grid, with diagonals, but limited to three steps? (Like the Android lock screen) If it requires a counting algorithm, I can do it myself, but if there is some nifty purely mathematical solution, it would be cool. Edit: The path must be continuous over the cells. [(0,0), (1,1), (1,2)] works, but not [(0,0), (0,2), (0,1)]. Edit2: Knight moves (as in chess) and step counts above three is valid too. Also, no cells can be used twice. I'm sorry, I'm so sorry. | a b c d e f g h i length three paths starting at a = length two paths starting from b + length two paths starting from d + length two paths starting from e length two paths starting at b = length one paths starting at a + length one paths starting at c + length one paths starting at d + length one paths starting at e + length one paths starting at f length one paths starting at x = 1 length one paths: 1 1 1 1 1 1 1 1 1 length two paths: 3 5 3 5 8 5 3 5 3 length three paths: 18 24 18 24 32 24 18 24 18 Total length three paths = 72 + 96 + 32 = 200 (This can also be expressed as convolution with the kernel 1 1 1; 1 0 1; 1 1 1, but dealing with the boundaries makes it just as hard as just doing it out by hand like this.) | You can construct a graph with the 9 points in the grid as the nodes and add vertices between those that can be connected in a lock pattern (those that are unit distance away from each other, including diagonal moves). You can then compute the adjacency matrix of the graph, and raise it to the power k to find the number of walks of length k between all the nodes. You would have to exclude the walks from nodes to themselves (on the diagonal of the adjacency matrix), as those are not valid lock patterns. On second thought, this won't work because it will count walks that traverse the same edge more than once. Hmm, I'll have to think about this. Also: on my Android phone the minimum walk length is 3 as you say, but it can be up to 8. Edit: the distance being unitary is also not a constraint on my phone, e.g the move from (0,0) to (1,2) is valid. So in the graph, those nodes would also have to be connected. I don't know how to count it yet, but with this information I can tell you the number is going to be large. Here are some links to analyses, and a paper: http://beust.com/weblog2/archives/000497.html http://www.quora.com/How-many-combinations-does-Android-9-point-unlock-have http://www.usenix.org/event/woot10/tech/full_papers/Aviv.pdf | This is very interesting! About the lock screen; I don't own an Android myself, and the friend who approached me with this problem has been a little vague about how it works. As you say, it seems like knight moves and step counts above three are valid too. | You can also move across any cell without it counting as a step if you've already used it, so [(0,0)(1,1)(2,2)(1,2)(1,0)] is valid even though it crosses (2,2) again on it's way to the last place. This can be done with any cell except the ones in the corners (it's impossible to cross those twice.) | He was asking for pure mathematics, and specifically said he could do an algorithm himself. |
[
"Sampling proportionally to values when you only have their logarithm."
] | [
"math"
] | [
"fxljm"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.72
] | Figured the math subreddit might be able to help me out on this one. I'm trying to sample proportionally to some values which happen to be either extremely large or extremely small (such that dealing with them outside of their logarithmic form causes overflow/underflow errors). I'm wondering how I can sample according to them when I can't just convert them back to their actual values. For a more concrete example, say I know: p[0] = 1000000 p[1] = 100000 p[2] = 10000000 p[3] = 1000 p[4] = 10 What I can work with is: log_p[0] = 6 log_p[1] = 5 log_p[2] = 7 log_p[3] = 3 log_p[4] = 1 What I want to do is sample according to p, using log_p without having to convert log_p back to p. By sample I mean I would choose p[0] if rand() < p[0] /(p[0] + p[1] + p[2] + p[3] + p[4]) and so on. Any suggestions? | If there's a huge gulf between the probabilities of the events you want to generate, I'd be worried that you'll have a hard time overcoming sampling noise. Maybe if you describe the problem you're trying to solve, someone here could comment on the strategy? | Would this do what you need? Sort the log-p values from largest to smallest and keep an vector of the corresponding x-values Divide through by the largest p (i.e. subtract the largest log_p from every element). These rescaled log_p's have at least one 0 and then are monotonic decreasing Exponentiate and sample. The values that are too small and underflow would be extraordinarily unlikely to appear in your sample unless your sample was phenomenally large anyway. If there are a great many values that would underflow, then another possibility would be to collect together all of them into a single category that appears in the list of large probabilities, and if the combined small-number group is selected, a second round of generation (following the same scheme as just outlined) is then carried out. (But for this to be of any use there'd need to be squidzillions of underflowing values.) | I think they're all going to be all extremely large or extremely small. Basically what I'm trying to do is calculate the probability of shifting a model model within DNA sequences. Basically the motif model is a set of probabilities for each position of the model being A, C, G, T. The probability of the model being at a position in a sequence of DNA is the product of those probabilities divided by the background probability of the letter in the sequence. The problem is that when you calculate the probability of a motif model being at a set of positions across a large number of sequences, the number is either extremely large (all the positions are pretty good matches) or extremely small (all the positions are bad matches). The learning method we use converges to partial model matches pretty swiftly and can't break out of that local optima; even though shifting the model positions across all the samples 1 or 2 to the left or right would be a much better fit with higher probability. So basically calculating the models probability where it is, shifting all those positions to the left or right 1 or 2 spaces results in 3-5 numbers that are all either really large or really small, and I want to chose one proportional to those probabilities. | Interesting. Yeah, I know jack about optimization. Good luck! :) | Interesting question...if you're looking for a practical answer, the easiest way to deal with these numbers is a bignum library. But I'll think about it and edit if I come up with anything. |
[
"Math Mistake about Infinity?"
] | [
"math"
] | [
"fw7gd"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | So I was posting in another and jokingly corrected someone's math. This caused a minor flamewar. Given that infinity is one of my favorite topics in mathematics, I don't think I am mistaken. If I am, though, I'd appreciate an explanation. Again, sorry if this is poor reddiquette. I am new and curious. | An infinitesimal e is a number so small that, for any integer N, N * e < 1. For example, 1000e < 1. A finite number divided by an infinitesimal number is greater than any integer, hence an infinite number. For example, 1/e is infinite, and indeed 1/1000e is infinite. javafreakin's statement may reasonably be interpreted as implying that the accomplishment of a hand clasped in prayer is infinitesimal. If we accept the premise, then the logic checks out, and your "correction" is misguided. Even if we interpret javafreakin as implying that the accomplishment of a hand clasped in prayer is 0, then the logic is still consistent. You're assuming that you can cancel fractions when infinity is involved, which is wrong. Some things to consider: Levi-Civita field Extended real number line#Arithmetic operations Edit: fixed an expression | Writing 0 infinity=0 only makes sense in the context of limit operations. In most any discussion, these "equations" are meaningless and invite endless, pointless flames. | The issue is in what you mean by zero. Qxzkjp was referring to a sequence whose limit is zero. You meant plain zero. In the case of a real number, any number multiplied by zero gives zero. However, in a limiting process, 0 * infinity could give anything. Take for example x * 1/x as x->0. As x->0, x goes to zero and 1/x goes to infinity but we know that x/x = 1. So in this case the limit can be seen to be 1 (I'm not being rigorous about this at all). Or take 2x * 1/x. As x->0, 2x goes to zero and 1/x goes to infinity, but we know that 2x/x = 2. In this case the limit can be seen to be 2. tl;dr: Don't mix math with religious politics. You're quibbling over something stupid. | Ah, I had an incorrect assumption on how zero works over the extended reals. Thanks. | The usual multiplication is an operation that takes two real numbers, and gives one real number. "Infinity" is not a number, so you can't multiply it. By the way, 1/0 isn't defined, either. You can say that 1/x tends to infinity when x tends to 0 (with x>0 ). That means that for any N>0 (as big as you want), you can find x>0 for which 1/x>N . That does not mean anything about 1/0 . TL;DR: Qxzkjp is right. |
[
"Why do we use a + bi as the most common notation for complex numbers?"
] | [
"math"
] | [
"fxlis"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.64
] | It feels weird, really. Why do we use the symbol for addition when we are actually representing a pair of elements? Why not (a,b) instead? a + bi is just confusing. | It's really very natural because a + bi actually is the sum of a and b*i. And you can add and multiply complex numbers using the usual commutative and distributive laws and then reduce using i = -1. So, (a+bi)(c+di)=ac + bdi + bci + adi = ac - bd + (ad+bc)i. | It's a bit like asking why we write p+q+r+s instead of +(p,+(q,+(r,s))). Let x,y in R and i in C, then x + iy is the sum of x lifted into C with i times y lifted into C. There are other ways to define complex numbers than a quotient of pairs and this notation is nice because it doesn't demand a specific implementation of C. | We're representing a pair of elements! We're representing a single element of . The distinction may seem arbitrary but it is important. We often write it in terms of (as a+bi) because we develop the intuition for by looking at , and the subfield of is important, but there's nothing 'pairish' about the complex numbers considered in themselves. | Because (a,b) could mean an element of R instead of an element of C. Are they the same thing? Sort of. C tends to come with more algebraic structure attached than R does. | Right, I think he realizes this, but his point is that it's extremely convenient (at times) to forget about the "ordered pair" aspect and treat them as single elements. Differentiation and analyticity, for example, are two aspects where you often want to treat complex numbers as numbers and not as ordered pairs. There are obviously other times when the ordered pair notation is useful, but I think the point of saying "complex numbers considered in themselves" was to emphasize that they have properties as a field without considering them as a plane. |
[
"Grad School Question"
] | [
"math"
] | [
"fwbht"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.8
] | Hello All, It's coming down to decision time for students like myself who have been accepted to grad school. I have a tough decision to make, and I have a question. How much does the ranking matter? For instance, if I go to school B that's ranked, say, 25th instead of school A that's ranked like 15th, will it really matter in the end? Will potential employers six years from now consider a degree from school A as being better than a degree from school B? To put things in context, I know I would be happy at both schools. I'm not going to blindly go to a better ranked school simply because it's ranked higher. I'm just curious as to how much it really matters. Thanks in advance for your opinions/experiences! Sincerely, The Balrog Edit: For reference, I'm going by the US News 2011 rankings. Edit 2: Thank you everyone for the insight. It appears that small differences in rankings don't matter too much, except in extreme circumstances. It is more important to find a good faculty doing research you are interested in. Your input helped quite a bit! Thanks again. | It can matter but not as much as it might think. Here are my thoughts. (1) Keep in mind the rankings may not reflect what you really want to do. If you want to do commutative algebra for example, well there are many great schools in addition to the usual ones. If you have a specialization in mind, please post it and I'm sure the community can make good recommendations. (2) Usually, the larger and higher ranked (AMS Group rankings, not the US News ones) are better options. This is because, (a) you will likely not be settled on an area and having a large dept. leaves you options and (b) typically there are better people at the top AMS grouped schools. That being said, bring me to the next point. (3) The name of the school is no where as influential on your job as (a) who is writing your recommendations and (b) how influential your work is during graduate school. Even at a small or not great in the rankings type school, if you do seminal work then it will get attention. On the other hand, most of us struggle to get a few papers out or just finish a thesis at all in grad school and that's . That being said, if you are at say U Mich or Harvard or MIT and you have names like Mel Hochster or Noam Elkies writing letters for you, that will go much farther than being at a small school. Unless you go to lots of conferences. On the other hand, I think the absolutely most important thing about finding an advisor is finding someone you work well with. That will be a much more rewarding experience. This is a stressful process (grad. school), and anything you can do to make it less stressful the better. Finally, I used to be told when I was choosing that larger schools are more competitive and thereby less friendly environments. Thus far, every large dept. I've seen has been perfectly friendly and I think there are competitive people everywhere, but doing things like preliminary or qualifying exams have a way of getting the graduate students to bond. At the end of the day, only you can say what choice is right. However, remember the 'name' the 'ranking' of the school usually comes from the faculty. That should be the deciding factor. | In my experience, where you went to school is less important than who your advisor is. School A may have lots of prominent mathematicians, but if you're not interested in working with any of them, it might not be so important. On the other hand, if School B has just one highly renowned person, but (s)he's the one you plan to work with, that might have more weight. | You're going to be there for quite a few years. Go with the place and people you're more comfortable with. If the rankings are relatively close, then it probably won't matter as much as who you work with and in what area. I turned down a $30k/yr x 4 yr fellowship to one university, because I decided I didn't want to live in that city. I don't regret that. | http://www.ams.org/profession/data/annual-survey/group_i http://www.ams.org/profession/data/annual-survey/group_ii http://www.ams.org/profession/data/annual-survey/group_iii | Small "distances" in rankings (I'd consider the difference between 10th and 25th to be small) are really only likely to be a big deal at the very very top end (i.e. choosing between MIT/Stanford/Harvard and anything else), and it is much better to choose based on (a) how good they are at your particular field of interest (and/or the people that are there) and (b) other stuff like how much funding you can get. |
[
"Question on radar graph area's."
] | [
"math"
] | [
"fwcgo"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.75
] | [deleted] | I think he wants to know if permuting the axes will change the area. In which case I think the answer is yes it can change if there are more than 3 axes. For instance, consider a 4d chart with 2 short values and 2 long values. If the long values are opposite each other, then the are is very small, while if the long values are adjacent, then the area is at least as big as the triangle they make. | I can't decipher your question. Could you rephrase it? | Oh, yeah that makes sense. I was kind of guessing at what he meant. | It can change. Imagine if you had three spokes and three points with equal values. The area they form is an equilateral triangle. Now imagine fixing one spoke and bringing the other two towards it. The triangle's area will decrease until you are only left with a line. | This is why you should use segments of Archimedean spirals instead of line segments to connect points on a radar chart. ;-) |
[
"Complex Analysis vs. Analysis on R^2 ?"
] | [
"math"
] | [
"fwadb"
] | [
21
] | [
""
] | [
true
] | [
false
] | [
0.87
] | [deleted] | 1) The Cauchy-Riemann equations are very strong restrictions on the real and imaginary parts u and v of a holomorphic function f(z). In particular, suppose f is holomorphic on some connected region D. By Green's theorem from multivariable calculus, the integral of f(z) around ∂D can be computed as some double integral over D involving the partial derivatives of u and v. The key point is that the C-R equations make this integrand equal zero, so that ∫_∂D f = 0, but for a generic function on R this would certainly not be the case. The Cauchy integral formula follows from this and a single model computation, and much of classical complex analysis then comes soon after. 2) I think you have the causation backwards. The fundamental theorem of algebra is a consequence of analysis, and many proofs by complex analysis are implicitly using the fact that complex polynomials satisfy the Cauchy-Riemann equations. This is not necessary to prove the theorem -- some proofs use only the intermediate value theorem, to show that real polynomials of odd degree have a root -- but I find the proofs by complex analysis to be the best motivated ones. | There isn't anything magical about C vs R , as in you could easily define a condition on a function R -> R which gives you all the beautiful properties we know from complex analysis In general, the derivative of a function R -> R is a 2x2 matrix, one for each pair of variable and component. When we translate from a pair of points in R to something we consider as one number in C, it is logical to then think of our functions as a function of one variable instead of two, and the next logical step is that their are functions of one variable instead of a matrix. Imposing the condition that we can treat the derivative of a complex function as a complex function itself is where the nice theorems from complex analysis come from. The condition turns out to be what we know as the Cauchy-Riemann equations, the definition of analyticity. But the complex numbers do a bit more than give you that definition, it turns out that polynomials and power series over C, which use complex multiplication, become basically exactly the objects which give you these nice functions. | These proofs all use some results from analysis (not necessarily complex analysis) in an essential way, though. The winding number and homology arguments don't work if you can't show that winding number is well-defined and locally constant, for example; and the Galois theory proof requires the fact that polynomials of odd degree have roots (again, by the intermediate value theorem), so that if F is an algebraic extension of R then the fixed field of a Sylow 2-subgroup of Gal(F/R) has odd degree, hence is equal to R. As for specifically analysis, I admitted that it isn't necessary in these proofs. I just find it far more persuasive to say that complex analysis gives you FTA than it is to say that FTA causes any particular phenomena in complex analysis. | The other posters are correct. Assuming the Cauchy-Riemann equations hold, the analysis is identical. However, this seriously restricts the functions we get to play with. You can think of complex analysis as a very special case of analysis on R . | To be fair, C is also a real vector space... |
[
"DAE feel rage when you are required to use a WYSIWYG editor?"
] | [
"math"
] | [
"fwn7w"
] | [
0
] | [
""
] | [
true
] | [
true
] | [
0.5
] | [deleted] | I'm not sure what a WYSIWYG editor is, but I do agree that all mathematics should be typed up in LaTeX. | Yes, definitely. Not just because it sucks, but because I feel like I'm not in control. | What You See Is What You Get. WYSIWYG. | ...did you make this post just to pull of that joke? | ...did you make this post just to pull of that joke? |
[
"Where are the online math degrees?"
] | [
"math"
] | [
"fvkr4"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.67
] | I'm 8 months pregnant and pretty good with numbers. I've gone as far as Calculus III. I just wish there was a Mathematics BS or Physics BS degree where I can study and do homework at home and at the same time get an opportunity to raise my child (especially during the first 6 months of breastfeeding). As far as tests go, having a proctored test on campus 3 to 4 times a semester would make our understanding of the material legit. Any thoughts, ideas, or links? EDIT: I'll look into the University of Illinois Springfield. I think I'll end up just finishing my upper level classes the "normal" way. Thanks for the suggestions guys. | I know nothing about online degrees, but I admire your yearning for mathematical knowledge at this stage of life (: | I have a friend who was took calc II online from the local community college, but I'm not sure about upper level classes. I don't know anything about this really but you could research what your comm. college offers online and work from there. | I'm not sure about math degrees at a purely online college, like phoenix, but if I were you I would look at taking online courses from a nearby university for your early 2000 level math courses. Then when you have time begin taking your 3-4000 major courses in a class setting, as the math can get pretty hairy and might be very difficult to pick up on your own. | University of Illinois Springfield http://www.uis.edu/math/curriculum/online/index.html | That's good to look at to start. Out of state tuition starts at over $500 per credit hour. I hope more universities offer this soon! |
[
"How hard did you think Multi variable Calculus was?"
] | [
"math"
] | [
"fvjkp"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.62
] | I am taking it in summer school and I was wondering just how many hours per week outside of class would i need to stay afloat and even do well in the course | No, its really not. Things like stokes and the divergence theeorem are not simple generalizations of stuff in one dimension (although the FTC is a nice analogous result, it doesn't simply "generalize" to stokes without considerable work). | I don't think anyone can really answer that as it depends entirely on the professor. The ideas are not very complicated, but one can come up with some fairly difficult problems. | Just add dimensions, meh. You can just answer all the questions for the first variable, then write 'the generalization to multiple variables is trivial'. This is what they do in textbooks anyways :P. | I thought calc2 was harder :-( | At my school, it's split up into 2 quarters. I found the first quarter to be almost a joke, but the second quarter was significantly harder. Most importantly, you MUST dedicate time between lectures to stay on top of all the concepts presented, because it builds, and problems can test multiple concepts (like everyone else is saying, the problems can be REALLY tough potentially, even if the concepts are simple). If you don't like your professor's presentation of the material (in that he/she is hard to understand), read the book. Heck, even if you do follow, try to read the book. If neither are helpful, search for an online resource to clarify; MIT OCW is typically excellent. If you want to get a head start, that's a pretty decent place to start, too, actually. Getting a head start by watching all the lectures and attempting some problems, even if it's just the easier ones, would probably be an excellent idea, since summer terms tend to go by VERY quickly. |
[
"I have to write a essay on ANYTHING that involves math, extra credit for a comical approach. Here are some of my ideas."
] | [
"math"
] | [
"fvjba"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.63
] | [deleted] | I would do it on optimum urinal positioning to effectively reduce awkwardness. xkcd.com did a blog post on the subject IIRC. | If you do that, take a look at some game theory. The Myerson text would be the best place to look imo. | If you do that, take a look at some game theory. The Myerson text would be the best place to look imo. | I had an idea for the probability of you fucking a chick, and her telling other chicks that you were good in bed, and then the probability of fucking a chick distance D on the social graph from the original chick. I was thinking of it as a graph where you consider the probability of fucking Q after fucking P, which is a function of the set of paths between P and Q. You have a positive chance with every chick if and only if the graph is connected. Message me if you would like to discuss this further; the math isn't hard but the results are worth noting. | Statistical analysis of errors in typing made while using Android phones. Probability of an error causing great embarrassment. How unlikely is it that such an error would lead to a series of misunderstandings and communications that would read like a plot from a 1950's sitcom or a poorly written romantic comedy that has the two protagonists glaring at each other on the movie poster. By the way, how many selves do you have? |
[
"I was playing pool last night, and I thought of an interesting problem."
] | [
"math"
] | [
"fvst9"
] | [
8
] | [
""
] | [
true
] | [
false
] | [
0.73
] | Given a frictionless universe (i.e. a ball, once struck, will continue to move around forever) can we prove that no matter what angle we hit the ball at any wall, it will always eventually go into a pocket? The trivial case (hitting a ball at the wall at exactly 90 degrees, so it oscillates between the wall and its opposite forever) is not considered. Anyone have any ideas? I was thinking of somehow using combinatorics to somehow count the possible paths the ball can take, but I haven't tried to formalize it. | Assuming you have an idealized situation with a "ball" that is a single point, the answer is no. Assume for the sake of simplicity that the table is rectangular, has integral length and width, and the pockets are the corners. Then any angle with irrational slope (which is almost all of them) will produce an infinite path never touching a corner. | You only need a counter-example to prove your conjecture wrong. First of all Billiard tables are 2:1 in dimensions, with the pockets being 1.6 times the ball size, which is ~5cm. Let's assume our table is rectangular 200cm height, 100cm width and define a cartesian coordinate system with Origin in the middle of the rectangle. By placing a ball at exactly the middle and hitting it at a 45 degree angle we will get the following repeating pattern: (0,0)->(-50,50)->(0,100)->(50,50)->(0,0)->(-50,-50)->(0,-100)->(-50,50)->(0,0)->(-50,50)->... etc The pockets have all been avoided ([-100 +100],[-100 0 100]) and the ball will always follow the same motion. I am pretty sure that for the majority of the other angles the ball will infact pocket but I do not feel like deriving the analytical solution right now. | I thought it did. The OP originally hypothesized no friction, which is already an ideal world. The OP did not define what other aspects were to be considered "real." If everything else is to considered "real" one will have to specify the shape of the holes and the rubber deflectors around them. | I thought it did. The OP originally hypothesized no friction, which is already an ideal world. The OP did not define what other aspects were to be considered "real." If everything else is to considered "real" one will have to specify the shape of the holes and the rubber deflectors around them. | But by the exact same logic the answer is also "yes", because any irrational sloped-shot will get the ball arbitrarily close to a pocket, which will cause it to go in because in the real world neither the ball nor the pockets are single points. |
[
"What's the coolest thing you've seen on/about Wolfram Alpha?"
] | [
"math"
] | [
"fvuul"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.6
] | It's an incredible resource and it's been great help to me on so many projects, but I feel like I'm only barely scratching the surface of what it can do. What have you seen that wowed you? | makes me happy. | Just to see the look on people faces, I talk out an integration question into my phone and let Wolfram solve it. Most people aren't familiar with either of these two pieces of technology so putting them together gives a good jaw-drop effect. | I like the nutrition labels . | I just applied to the Beta test (although I doubt that I'll get it). That Index is amazing! The DNA stuff is incredible. The fractal generators are also really cool. Great find! | I just applied to the Beta test (although I doubt that I'll get it). That Index is amazing! The DNA stuff is incredible. The fractal generators are also really cool. Great find! |
[
"Probability notes...."
] | [
"math"
] | [
"fw4nj"
] | [
8
] | [
""
] | [
true
] | [
false
] | [
0.9
] | [deleted] | Jaynes wrote the first few chapters to be accessible to all and sundry. There's a minimum of math and the emphasis is on the concepts. It isn't any more specialized than, say, popular books about astronomy. I grant you that it is difficult reading for those who are brainwashed by the frequentist party line; they will find that everything they know is wrong. | Look for "Probability Theory: The Logic of Science" by E.T. Jaynes. It used to be available on the interwebs as a preprint, maybe it still is. | Jaynes is hardly a "set of notes on the basic fundamentals of probability". While his book spend 70+ pages very thoroughly and carefully justifying the foundations of Bayesian probability theory, that material is hardly introductory in the entry-level sense. | This is pretty good for undergrad level: http://www.dartmouth.edu/~chance/ | If you are a computer science undergrad, I recommend this: http://www.cs.cmu.edu/~odonnell/papers/probability-and-computing-lecture-notes.pdf |
[
"Binary joke"
] | [
"math"
] | [
"fvsy0"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.55
] | Didn’t get much help from , but I’ll try again. I read this joke in the morning and can’t stop giggling. However, I think it can be phrased better. The old joke: There are 10 kinds of people in the world: those who understand binary and those who don’t. New and improved: There are 10 types of people in the world: Those who understand binary, those who don't, and those who didn't see a ternary joke coming. Source: However, I think it can be phrased better since the last 2 groups are not mutually exclusive. Rephrase 1: There are 10 types of people in the world: Those who don’t know binary, those who think they’ve heard this joke before, and those who didn't see a ternary joke coming. Rephrase 2: There are 10 kinds of people in the world those who won’t get this those who think they’ve heard this joke before and those who saw a ternary joke coming How would you phrase it? | This is my favorite version of the 'base' joke. | I like the remake: There are 10 types of people in the world, those who understand this joke, and those that have casual sex. | when I heard it in 7th grade You mean 10th grade. | math joke | That sounds like my response to a friend telling the ternary joke: "There are 10 types of people in the world: those who understand binary, those who don't, those who get ternary, and those who know an arbitrary radix when they see it." |
[
"Is a minor in mathematics worth anything or useful at all? Will it help with job placement?"
] | [
"math"
] | [
"fw1e9"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.6
] | I'm majoring in Physics. I'm interested in mathematics quite a bit and I'm deciding whether I should minor in it, or go for a double major with Physics. I'm worried that if I minor in it, it won't help me get a job in anyway. I'm worried that if I double major in it, I'll be overloaded with work and my GPA will plummet. Any insight? | Ah. Okay. I would love to find somebody who truly thinks the way you "did" though. I mean, when it concerns math degrees, there are very polar opinions out there. Some people believe that math = no income, but some take math just because they think it can get them anywhere. As you may notice, I'm on the "math = options" side. I would be glad to hear opinions (and argue them) from the opposite side of the argument. | Ah. Okay. I would love to find somebody who truly thinks the way you "did" though. I mean, when it concerns math degrees, there are very polar opinions out there. Some people believe that math = no income, but some take math just because they think it can get them anywhere. As you may notice, I'm on the "math = options" side. I would be glad to hear opinions (and argue them) from the opposite side of the argument. | It all depends on the type of employment you'll be seeking. In some areas a math minor might speak to employers, and in others not so much. I can't really think what else to tell you than that. How I would see it, as a software guy currently in planetary science, I would always view math as a plus. Yes, even as a minor with physics as a major. | Unless you want to get a job as a physicist, then I would imagine a minor in math would make you appear more well-rounded than a double major in physics. Actually, even if you do want to pursue physics as a career, there are several mathematical fields which are extremely useful for physics. But of course asking in /r/math you're certainly going to get biased answers. ;-) | I can't tell if you're being sarcastic or not... |
[
"Ask Math: Math Analogies"
] | [
"math"
] | [
"fuw64"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.67
] | I had a hard time with math in middle and high school. For whatever reason, math didn't click with me--I struggled getting the concepts by hearing things explained in pure math terms. One day, a teacher put forth this analogy: If the line of a graph is made of glass, and you shatter it, the glass will fall to the bottom of the graph. Where the glass falls, that's the domain. It was a simple explanation, but it really helped me to get the concept without dealing with math anxiety. To have a lot of these ideas for understanding math in one place would be a huge resource to all the other confused minds. | That notion of domain, while visually intuitive, is conceptually misleading. If one advances in math, such a perspective may be harmful. A better analogy would be the following. Think of your function as a recipe. It tells you to how to combine and use the things in your pantry to make a particular dish. Everything in your pantry -- that's the domain. The menu of dishes you can make -- that's the range. | This is good. As soon as you get to multivariable functions the glass analogy doesn't work (unless you have some pieces of glass falling in all, and only, the axis directions). But the recipe does. The domain is the pantry, the function is the recipe, and the range is the set of tasty, tasty food you can make. EDIT: And the codomain is the set of tasty, tasty food that the world's best chef could make with your pantry. | Harmful? I can't imagine how. That's how you learn things: You start with some intuitive picture, and then you formalize it. The reverse might be possible much later on your education, but we're talking about , for heaven's sake! | I couldn't resist adding Wilf's quote: "A generating function is a clothesline on which we hang up a sequence of numbers for display." I've always found combinatorial word problems rather enlightening, such as the hat-check problem [ If you haven't seen this problem before, don't ruin it for yourself. Spend some time on it.] or one of the many prisoners dilemmas. The proof of Turán's theorem is also pretty fun. | This kind of breaks down when you consider you can make different dishes with the same ingredients: a multi-valued function, I suppose. A function is more like Amazon. Associated with every product, you have a price. In this analogy, the inventory (the set of all products) is the domain and the range is the set of the prices of all the products. |
[
"I've reached a wonderful place in my education."
] | [
"math"
] | [
"fuwkv"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.65
] | I just wanted to share my feelings about math. Entered college as a chem major and then bounced around through all sorts of academic fields. Took a fairly strong difficult math curriculum but I really kicked it up this year. I am currently taking both Honors Analysis and Topology as an undergraduate at a top research university. I have also learned about Group Theory/Rings/Modules earlier this year. I am finally seeing the big picture and all the connections. The thing that pushed me over the edge is the homotopy and the fundamental group. Every since I've learned the beginnings of it earlier this term I have been drawn toward it. I want to know more. I have found a new motivation. I love math. I could spend forever learning this stuff. I just wanted to share that. Have any of you had this kind of realization? | YES but I'm still on my final year of high school so I can't really say that my "realization" is as deep as yours. The connections between seemingly completely isolated areas of math just gets me so excited. I'm planning to major in math and, well, hopefully will experience the bigger revelation similar to yours. It's interesting how many of these "science to math" I hear when asking people about their college experiences - a math teacher at my school was a physics major at college, but he started finding out all this crazy stuff about maths and ended up teaching it. | I do, unfortunately my current study doesn't give me more math classes, and I don't want to switch studies. I'm considering doing something more math-ish when i'm finished. | I've just (kind of) finished my share of General Studies at my college. This term I'm taking Analysis I, Probability and Statistics I, Linear Algebra, Applied Differential Equations, Game Theory and Calc 4. So, if ever, I'm reaching enlightenment this term. | For me it was a combination of Convex and Projective Geometry. It was one of the hardest semesters I've had, but every day was a new revelation. Sometimes a week long quest to solve a problem. At the end of that week I'd read over my proofs and marvel at the way the symbols seem to invoke all the right images. | Yes. When I really focus on some mathematical endeavor, it is as if everything else in the universe melts away. Tonight, for example, I 'lost' a few hours where I cannot recall the passage of time. I've only just begun my college's first course in Abstract Algebra, so I'm still missing some of the picture, but it's already beginning to fit together so nicely. I'm glad there are others that see the beauty of this wonderful subject :) |
[
"I've tried every possible way to solve this problem..."
] | [
"math"
] | [
"fuq7w"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.44
] | Prove that there is an integral point (as in x and y are both integers) within .001 distance of the line y = 3 * x. I've tried constructing a probability distribution model of the values, analyzing the sequence of digits of root 3, and constructing equations with the distance formula. If anyone can provide some more insight to this problem that'd be awesome. | Just because y/x is very close to sqrt(3) doesn't imply that y is very close to x sqrt(3), so I think your logic is incomplete. | Check out continued fractions to get good approximations by rationals. y = 97, x = 56 is pretty close but, not good enough. The problem is that the better the approximation, the larger the denominator. I'll play with a bit to see if I can find a solution. Edit: The fact that this must be true is because the square root of 3 is irrational and thus incommensurate with any rational number. | Presumably the point [0,0] doesn't count, otherwise that is a proof by construction. But otherwise, if y = sqrt(3)x then y/x = sqrt(3). If there were no integers y/x very close to sqrt(3), then that would mean sqrt(3) would not be the limit of a sequence of rational numbers, but every real number is, by definition, the limit of a sequence of rational numbers. | How would you go about finding rational approximations of the square root of 3? if you had a rational approximation of the form a/b, then your x would be b and your y would be a. | Because it's not a convergance issue. That is, making x a larger and larger integer doesn't cause y to approach an integer. That said, if you could find a specific (x,y) pair that did satisfy the distance, then that would certainly be a valid proof. But just upping the value of x won't do it |
[
"anyone else getting rejections one after another?"
] | [
"math"
] | [
"fuyi3"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.73
] | [deleted] | Or for paper submissions? | Is this for graduate school? Or for jobs? | grad school :( it's that time of year. | MTFBWY May the force be with you? | G'lucks for the rest, mate! Hang in there. MTFBWY I'm going through a similar situation now except with undergrads and decisions come out soon. Fingers crossed for both of us. |
[
"Yet another way of solving the Monty Hall problem..."
] | [
"math"
] | [
"fv9j9"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.41
] | Read this in a probability textbook. Doubtless, dear readers, you are familiar with the MHP. If not, here is a link: I think this explanation is clearest. Let S be the event that a switch results in success. Let F be the event that the first choice is correct. We know that P{F} is 1/3, as there are three doors. P{S|F}=0 because you're switching away from the prize. P{S|not(F)}=1 because you're switching towards the prize. P{S} = P{S&F or S¬(F)} = P{S&F}+P{S¬(F)} = P{F}×P{S|F}+P{not(F)}×P{S|not(F)} = P{F}×P{S|F}+[1-P{F}]×P{S|not(F)} = (1/3)×(0) + (2/3)×(1) = 2/3 More accessible explananation: An unsuccessful switch occurs if and only if the first choice is correct. (Think: a correct first choice always leads to an empty switch, while an incorrect one always leads to a happy switch.) Therefore, P{not(S)}=P{F}=1/3 so P{S}=[1-P{not(S)}]=2/3 Therefore, you should switch, ya dummy. | I think this explanation is clearest. Yeah if you're a computer or you use conditional probability formulas every day. Part of the reason this problem is popular is because it was published in an advice column in a major publication, and millions of people wrote in because they didn't believe it. This explanation would be "clear" to very few of them. The usual explanation is not difficult to grasp, and while this exemplifies probability formulas, it's almost certainly more complicated. | You get an upvote from me, albeit 2 weeks late. I was just about to ask /r/math how to prove the Monty Hall problem using Bayes's Theorem. Every single other publication I've seen tries to describe the problem using words rather than notation. Personally, I think this is extra clear, and I'm really glad you did it. For those who said it was a mess, I suppose they would rather it was written "The sum of two and two is four," than to express it as "2 + 2 = 4." I congratulate you, sir. | Upvoted, I'll try to put the explanation in more accessible terms. | I'm a math graduate student and understand the Monty Hall Problem just fine, but this just looks like an overcomplicated mess to me. It's very far from the "clearest" explanation I've seen. | This has been done to death a million times and isn't really complicated. The "surprise" usually comes from the fact that the problem is not clearly defined. |
[
"Are there any fields of math apart from Calculus, Linear Algebra and Statistics that could hypothetically be \"simplified\" and taught to the masses?"
] | [
"math"
] | [
"fvab5"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.69
] | The three topics in math mentioned in the topic are commonly taught to everyone and their dog who studies anything related to science or engineering, usually in a rather non-rigorous form. Are there any other topics in math that could hypothetically be simplified (or "dumbed down" if you wish) and made less rigorous in a similar way to allow it to be taught to a very wide audience? | There's already a major for this called Political Science. EDIT: It's a joke. I know what you're talking about. | Obviously, geometry. Graph theory and set theory tend self-contained. | most combinatorics | Group theory is taught to us lowly chemists in a kind of dumbed-down, bastardized way. | Elementary Number Theory. Some of this could be taught from 1st grade and on. |
[
"What is a \"Free Vector Space\""
] | [
"math"
] | [
"fveig"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.7
] | I came across this in a book for the chapter on tensors, I have never seen it before. Wikipedia isn't helping me. Can someone give me a cold hard definition? And in addition, how is the free vector space of V and W different from the product space of V and W? (assuming I'm making any sense...) | In a lot of contexts free just means "has a basis", where basis means what it does in linear algebra. That is, a module is free if it has a generating set that is also linearly dependent. So every vector space is free. When someone says "take the free vector space on a set" they mean take the set as the basis and make a vector space out of that. Then the free vector space over a vector space V has V itself as a basis. You can see that this is a perfectly good vector space. Addition of two elements is done by adding two basis elements, v and w add to the basis element v + w. Scalar multiplication is similar. The free vector space on VxW is then the vector space with VxW as a basis. Which is obviously a whole lot bigger than just the product VxW. Edit: I've misspoke. The vector space clearly has no relations among the basis elements, hence the point of being "free". | Every vector space is a free vector space, so when someone says 'free vector space' they usually mean 'the vector space generated by the set X'. This is just the vector space that has X as the basis. That is, the vectors are the formal linear combinations of (finitely many) elements of X. For more details see planetmath | In the context of what you are doing, you can just consider the free vector space on a set X to be the vector space of maps X -> F (where F is your underlying field... real numbers?), with pointwise addition and scalar multiplication. So R is isomorphic to the free vector space on {1,2,...,n}, by e.g. the isomorphism that takes f : {1,...,n} -> R to the vector Tf = (f(1),...,f(n)) The name "free" has the connotation that there are no unnecessary restrictions between the elements of the generating set... this is correct. The way to make sense of this is to consider that for a set X you not only have the free vector space on X (which I will denote by F(X) from now on), you also have an injection i: X -> F(X), which is the map taking an element x of X to the function (i.e. element of F(X)) that is 1 on x and 0 on all the other elements of X. This is how we identify X with a basis of F(X). The more general notion of free construction is best understood from a categorical point of view. Excuse me while I throw out some jargon: consider a category V (in our specific case, this was the category of vector spaces). We have the "free" functor F: Sets -> V that associates to every set X the object F(X) in V, and to every map f: X -> Y the induced map F(f): F(X) -> F(Y) (in our vector space case, this is the map taking the basis X of F(X) to the basis Y of F(Y) according to f). The free objects satisfy a certain universal property: let X be a set and let S be a vector space, then any map f: X -> S lifts to a unique map f F(X) -> S such that we have f = f i This just captures the idea that a map between vector spaces is defined uniquely by its restriction to a basis. | You're correct, I misspoke and jumped the gun. There are no relations between the basis elements. The space is determined by it's basis, so it's just the vector space with that basis. You add two elements by writing them as a linear combination of basis elements and then add the coefficients to get a new linear combination. You multiply by scalars by scaling all the coefficients in a linear combination. The reason I said that above was that I was getting ahead of myself. The way you then develop the tensor product is to identify those basis elements. Namely (v1 + v2, w) ~ (v1, w) + (v2, w), (v, w1 + w2) ~ (v, w1) + (v, w2) and a(v, w) ~ (av, w) ~ (v, aw). | Very interesting, the category theory. I'm just starting to learn out of a book written by Herrlich and Strecker. Since you seem to know what's up, what is the meaning of "universal". I'm seeing that thrown around a lot. |
[
"What does r/math think about tau versus pi?"
] | [
"math"
] | [
"g3x5y"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | [deleted] | I think math is where you can define anything you want. You don't need any authority figure to issue out definitions that you are then allowed to play with. Nor do you need propaganda telling you how to do things. So the whole thing turns my stomach. It's really annoying the way it's become a kind of grass-roots movement, trying to radically change our whole view about .. I don't know, fucking lame forced meme. Just want to stop hearing about it.. | The Tau Manifesto is pretty well-written and tau indeed is likely "better", for what it's worth. The problem is it's not worth much -- despite the claims of the author and many of tau's supporters, students won't magically just "get" trigonometry and various other concepts just because a factor of 2 has been shifted around. Switching pi to tau would be a monumental worldwide task with absolutely negligible benefit. How about we convince the entire world to use a more sensible base than base 10 while we're at it? | ators. | ators. | Ah, come on, most of mathematics consists of looking at familiar things in a new light! How can you resent people getting excited about that? Tell you what though, I'll make you a deal. If the rest of Reddit stops fellating pi every chance it gets, I'll stop upvoting the tau submissions. :) |
[
"Need help with a math problem for my sister. I used to know how to do this but that time is long past."
] | [
"math"
] | [
"g3a6a"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.25
] | [deleted] | Not enough information. How much does each cup hold? | I am assuming 8 ounces. Thats what it says in the book. There is no other information. | OK. If that is truly the case, I would preface my answer with a caveat along the lines of: Cannot be solved without being given the cup capacities. That being said, maybe they do intend you to use 8oz cups. In that case, the question is simply asking how much of the normal distribution falls above one standard deviation. You can look that up for yourselves. I will tell you, it is very easy to find the percentages for each standard deviation using google. Half of all the scores (50%) will fall below the mean. Now all you have to do is add the percentage of scores that should be from the mean up to +1 standard deviation. This will give you the percentage of cups that don't overflow. Subtract that from 100% and you have the percentage of cups expected to overflow. Multiply that percentage times the total number of cups in the machine to get the number that are expected to overflow. | BTW, there isn't a good formula to use, because you cannot do the integration analytically (not that you actually have to do any integration for this problem). | Work out the probability that a cup will overflow - which is the proportion that will overflow. From that work out the expected number that will overflow. The probability that a cup will overflow depends on how much a cup will hold, which is unstated. If it was 8 ounces, you work out the probability than a random variable with a N(7.6, (0.4) ) distribution exceeds 8.0. This is the same as the probability that a N(0, 1) exceeds (8.0 - 7.6)/0.4 = 1. |
[
"Anyone know of a good article related to math that would be appropriate for average high school students?"
] | [
"math"
] | [
"g34zx"
] | [
10
] | [
""
] | [
true
] | [
false
] | [
0.78
] | [deleted] | http://www.maa.org/devlin/LockhartsLament.pdf This is a pretty heady article and maybe aimed more towards teachers than students, but it might be able to open up a dialog about math education overall and what your students like/dislike about how they've been taught math, and might actually point you in a direction that will allow you to better teach your students. | I'm not sure about an article , but maybe some excerpts from Flatland (or the whole thing, since it's less than 100 pages) might fit the bill. It's a pity they don't know any calculus; my old professor Carolyn Gordon's article "You Can't Hear the Shape of a Drum" is a fantastic read, and a wonderfully intuitive introduction to the ideas of spectral geometry. My suggestion, if you need a true article, is to paw around online for a while for something on basic graph theory. Little tidbits like the Seven Bridges of Konigsberg are fun; or maybe an article about the four-color theorem. Graph theory is great for people with no formal math training, since it's easily visualized. | How Real People Think in Strategic Games A pretty accessible and fairly interesting study on Game Theory applied to real life situations. Or there's always Cantor's Diagonal Argument. Proving that the Real numbers are uncountable, compared to the integers. The proof takes a bit of mind bending to understand though. | Check out Steve Strogatz' series for the NYTimes. http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html | Not exactly geometry related, but this might not be above their levels: Third Base . It's an article explaining what ternary is and how it's optimal for some tasks. You might have to look around a bit to find a good one, but the feature columns from the AMS are all interesting and some of them are low enough level. |
[
"r/math, help me think of a poem to describe the Quadratic Formula.."
] | [
"math"
] | [
"g3bv3"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | [deleted] | "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value." ...it was probably catchier in Devanagari. | Not sure if this counts but it was posted a few days ago: There was a negative Boy, who was confused about whether or not he should go to a radical party. The Boy was square, so he missed out on 4 Awesome Chicks and he cried until the party was over at 2Am. | Not sure if this counts either, but there is a little jingle to help with remembering it. | I want to use that so badly, but my teacher already used that in class.. | you got this negative b who doesn't know whether to plus or minus this square group of b squared while 4 a and c were leaving. downstairs 2 a's were being loud. The b decides to do both. |
[
"expected determinant of a random NXN matrix in (0,1)"
] | [
"math"
] | [
"g2lvd"
] | [
18
] | [
""
] | [
true
] | [
false
] | [
0.82
] | What is the expected value of the determinant of a random matrix whose values are real numbers from an uniform distribution in the interval (0,1)? and in the interval (-1,1)? And if the values are only the integers {0,1}? And if the values are only the integers {0,1,2,3,4,5,6,7,8,9}? | You can use linearity of expectation and the definition of determinant to get: [; E[det(M)] = \sum {i,\sigma_i} ] ;] The term [; E[ \prod \cdots ] ;] is the expected product of N uniform numbers from [0,1]. Whatever that is, it is the same for every term of that form. But half of the terms of the summation are positive and half are negative, so the expected value is 0. The same logic works no matter what the distribution of entries is, as long as each entry has the same distribution. Of course, when the entries come from a continuous distribution, the of det(M)=0 is zero. But you will get equal positive & negative determinants, averaging out to zero for the expectation. | Believe it or not, some people use math for real, and sometimes, they come up with questions. Just because you ask a question on reddit doesn't mean you're a cheating student. I'm not saying pedrito77 is not a cheater, but I'm one of these persons using math everyday (for image processing research), and being called a cheater every single time I ask a question quickly gets old. | A more direct way of seeing this: as long as the distribution is invariant under interchange of rows or columns, symmetry demands that the expected value be zero (if it exists). | Yes, in the case of N=1, there are no negative-sign permutations in the summation so the argument breaks down there. For all other values of N, however, there are half positive- and half negative-sign permutations in S_N. | This means the determinant is either +/-1 or 0. This won't always happen. For example, the matrix 1 0 1 1 1 0 0 1 1 has determinant 2. |
[
"Looking for an explanation for part of a proof (vector math)"
] | [
"math"
] | [
"g2pih"
] | [
10
] | [
""
] | [
true
] | [
false
] | [
0.92
] | null | Didn't you miss a minus sign at equals (C●D) - (A●D) + (D●D)t = 0, The plus should be a minus, no? | Wow, silly me. That would flip the sign of the denominator in the final equation and give the correct result. Thanks a lot. So glad I spent the time typing all that out :P | I believe it’s not working because your statement for the magnitude of the vector projection is wrong. | No, that wasn't the issue. t = (V ● D) / (D ● D) t = (Cosϴ * |V| * |D|) / (Cosϴ * |D| * |D|) t = (Cosϴ * |V| * |D|) / (|D| * |D|) t = Cosϴ * |V| / |D| | Your transformation is right, but I'm saying that your assumption is incorrect. t ≠ (V ● D) / (D ● D) ∴ t ≠ Cosϴ * |V| / |D| Neither version gives you the magnitude of V projected onto D, which is given by: t = |V| * Cosϴ or, if you multiply by |D|/|D|: t = (V ● D) / |D| |
[
"Three linear equations with a common variable"
] | [
"math"
] | [
"g1lkz"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.63
] | Dear Reddit, I am conducting some analysis for a personal interest project, but have run into a problem. I have a system of linear equations, each with two variables (one common, one independent). I can't remember how to solve them. The information I have is listed below: 1.29 = a + 10w 1.52 = a + 10x 1.76 = a + 10y 1.19 = a + 10z 1.53 = b + 14w 1.81 = b + 14x 2.05 = b + 14y 1.43 = b + 14z 1.68 = c + 20w 2.25 = c + 20x 2.49 = c + 20y 1.57 = c + 20z Where a < b < c I can't recall how to solve for any of the variables (if it is even possible with this information). I apologize for my mathematical ignorance, but any help you could offer would be greatly appreciated. Thanks reddit. Edit: formatting | Normally you'd solve a system like this by Gaussian elimination. But since you have 12 linearly independent equations (not counting a<b<c) and only 7 variables, there may not be a solution. In fact, this is the case: 1.52 = a + 10x - 1.29 = a + 10w ================= 0.23 = 10(x-w) x-w = 0.023 But: 1.81 = b + 14x - 1.53 = b + 14w ================= 0.28 = 14(x-w) x-w = 0.02 Which is a contradiction. Since you can't satisfy all these equations, the next best thing is to get an approximate solution using linear least squares to minimize the error. Out of curiosity, would you mind sharing what kind of project this is for? There may be a different way to think about whatever you're trying to accomplish. | Consider /r/learnmath . That said, you have (counts twice) 12 equations in (counts) 7 variables. So you're either over- or properly determined. In particular, to solve, you can eliminate, say w, by replacing all values of "w" with, say, "(1.68 - c)/20." Now you have 11 equations in 6 variables. Rinse and repeat, and you'll either end up with a handful of consistent equations for just one of your variables, or else a handful of inconsistent equations. | As teraflop mentioned, those equations aren't independent of each other so they actually have no solution and you have to turn to methods like least squares to get approximate solutions. For what it's worth, this is a least squares solution, which in some sense about as close to a solution as you can get. a = 1.225919540229885 b = 1.405287356321839 c= 1.569339080459769 w = 0.006609195402299 x = 0.031925287356322 y = 0.047097701149425 z = 0 It should be noted that because the matrix for the given system of equations has rank 6 (not 7, as might be naively expected), this least squares solution is not unique. Using the above values of a,b,c,w,x,y,z in the 12 equations you provided gives the following left-hand sides (the number in the brackets in the number you the left-hand side to equal): 1.292011494252873 (1.29) 1.545172413793103 (1.52) 1.696896551724138 (1.76) 1.225919540229885 (1.19) 1.497816091954023 (1.53) 1.852241379310345 (1.81) 2.064655172413793 (2.05) 1.405287356321839 (1.43) 1.701522988505746 (1.68) 2.207844827586206 (2.25) 2.511293103448275 (2.49) 1.569339080459769 (1.57) | Thank you. I was afraid that this was the case (no single set of concrete answers that satisfies all the equations). I do appreciate the assistance though. As for the purpose of the project, I am trying to determine which option provides the greatest value. 1.29, 1.52, etc. represent the price of a product (which I have simplified into being made of two components). a-c represent the fixed costs of the product, while w-z represent the variable costs (I have used 4 variables to denote the 4 different products). The 10/14/20 represent the quantity of the variable component. I'll likely end up using the least squares approach, which should provide accurate enough results for my purposes, but I can't help but wonder if the problem is in my approach (assuming a linear relationship when the actual relationship is much more complicated), or if there is simply no internally consistent pricing scheme. | If you're only using two decimal places, these will give you less error than rounding NathanielJohns' answers: a = 1.21 b = 1.39 c = 1.55 w = 0.01 x = 0.03 y = 0.05 z = 0 I'm running a script overnight that will check for the best values out to two decimal places with the restriction that all variables are less than 2. I'll report back in the morning if it finishes... |
[
"What books and textbooks would you recommend for calculus?"
] | [
"math"
] | [
"g1r6c"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.57
] | So, from what I hear, it is normal in my school for students to take calculus at least 2 times. I am coming to terms with this right now, as I just realized I am going to fail. Is this a normal pass rate for calculus? . These scores are a significant improvement over last year's scores where only 46% of the students passed the course. Is there anything we can do to change this? There are no curves or extra credit. So, since I HAVE to pass this course with a C-, what books would you recommend? The one I am studying out of is , by James Stewart. It is pretty much like flipping through a book of heiroglyphics for me. I am not asking for homework advice, as I know there is a sub-reddit for that, but I am looking for some other, more user-friendly, textbook, that maybe you had some success with in your early days. I would also like to pick up a math history book on this voodoo magic as well, to help spark some interest in this subject. Any help would be awesome. Someone asked for the exam, so here it goes! Notice the exam grades linked also, as I just want to emphasize I wasn't the only one who thought this was difficult. I hope you guys can see this ok. Thanks for the words, I really appreciate it. I feel much better. After re-assessing my situation, and talking with my older Phd bro, he made me realize that even if I don't take a W, fail miserably with an F, and have to take it again, I will still have a GPA which can keep me in honors engineering. | Are you at a community college? I'd say that is about normal. I didn't take calculus twice, but it really is something most people have to try at. Especially if you didn't do super well in previous math courses. I've learned out of the book you are using. University Calculus by Thomas is another that I have learned from. It is very similar to Stewart, but it might be different enough for you. If you are planning on taking the course again, I would just drop the course, but still attend the lectures. Try to get as much as you can from the first time through. The second time through, go slowly through the material (This means more hours per week, as you can't add mores weeks to the semester, get a head start now.). Trying to read chapter 13 when you don't understand 1-12 can be really difficult in calculus as much of the material is inherently cumulative. My last suggestion is http://www.khanacademy.org which is the typical suggestion by redditors. I've liked what I have seen on it so far, but I have not used it personally except for entertainment. | I am on Khan academy for about 3 hours a night, but they are limited on their exercises when it comes to calculus. I can differentiate explicitly and implicitly pretty well. I need step by step world problem explanation or something. I am having trouble with rates of change and such. I'm at one of the best engineering schools in the country. This is the weed-out course for the engineering program. Diff EQ isn't as bad as this. I forgot to mention that they had to replace the department head last year bec of the failure rate. He was all theoretics, but all of our math is applied. I did very well on the first exam, receiving an 81%, but did um, shall we say, terrible on this last exam. I really appreciate the advice, and that is normal protocol in my school. Take a W, continue on with quizzes and exams with no pressure, retake, and repeat with calc 2. Is this really how it is? I have a 400 level engineering text which has very light calculus in it, most of which I can do already (exponential growth and decay, implicit differentiation, etc...). I do like Khan academy, and his videos are great, but his explanations can't hold a candle to the stuff I have to deal with. My quizzes have harder questions than he goes over. | Do you have a scan of your calculus test by chance? I'd like to see what is on it. I went to a community college and the pass/fail rate was similar, but it was mostly due to laziness. I'd say our tests were perhaps too easy and people still were not passing. EDIT: Also a note, if your school is very theoretical that Calculus Made Easy book might not help too much. It gives intuitive explanations when you might need more rigorous definitions. If not another approach is http://www.math.wisc.edu/~keisler/calc.html which is free online. I also found this on slashdot http://books.slashdot.org/story/04/03/04/028253/Five-Free-Calculus-Textbooks | Ok, I will scan the test, and post it, but it will take me a bit, as I will have to edit out my embarrassing answers. I think I now have a slight intuition about calculus, but anything that sheds light on the subject will help. Give a an hour, I'll scan and post. | As someone who recently went through Calculus your test does look harder than what I got, so I don't think you should be too worried about your ability. A couple of points: Khan Academy is great but his Calculus lectures are lacking. He learned Calculus before the mid 80's when there was a substantial change in how Calculus was taught, so his lectures don't correlate to what/how you're learning. You are allowed to say that reading the book is like "flipping through a book of heiroglyphics". All of those equations are 90% material that you've already covered. You just need to walk through them step-by-step (and maybe draw a picture) to figure out what they're telling you and then what you need to figure out. If you want understand the equations faster you should go find a study group and use your collective brains to figure out the problems. That was always the biggest help for me. I'm sure someone has sent out a mass email advertising a study group and if not just ask around or start your own. Edit: Also, remember to figure out where you' have the most trouble and focus specifically on that. Don't retread old material if you don't have to (minus practice tests of course). Good luck. |
[
"Which companies hire math majors?"
] | [
"math"
] | [
"g1o4t"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.71
] | So I'm trying to get a summer internship as part of my Master's program, and I've gotten a number of applications out there (roughly 50). While there are a few promising prospects, and over half have yet to officially turn me down, the fact remains I haven't gotten accepted anywhere yet, either. So, do you guys know of any other companies that may be hiring interns with a mathematics bend? I'm going for a Master's in Applied Mathematics, and I've already tried the companies listed on the AMS and ASA websites. Beyond that, I'm not sure where else I could go. | International Genetic Technologies, Inc. If only you also had a degree in Chaos Theory, otherwise you'd be a shoe-in. | can you code? wall street likes math majors who can code. hail to the quants.... | If you're in the US, you can check out government jobs. In particular, I know that the NSA and the Air Force have various internship opportunities for math majors, and other agencies probably do as well. | NSA | Nah, dinosaurs aren't really my thing. Save perhaps Yoshis. (To your credit, I did have to Google that first. Hadn't seen those movies since I was... 8? 9? Too long ago.) |
[
"Is it still necessary to teach logarithms and fractions to kids?"
] | [
"math"
] | [
"g1z0y"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.31
] | We live in a digital age--decimals and calculators. What value do fractions have in the decimal world? I haven't used a log in 30 years! Do physicists/engineers/and others use them still? | I everyone understood logs and fractions. So many things are log and exponential based. It's a very common scenario for real world data. But think about how many people actually understand logs, even on a rudimentary level. You almost never see log-based graphs in the media, even though I'm sure they'd be more appropriate. Case in point, yesterday's earthquake. I bet tons of people don't know that there's a major difference between a 7.9 and an 8.9 magnitude earthquake. Even if you told them the scale was logarithmic, lots of people wouldn't understand. Fractions are even important. You must know someone who has trouble calculating a tip, or who reads a study or listens to the news and doesn't understand the percentages being thrown around. We do indeed live in a world of calculators, but there are a lot of times when people need to do "math" and they're not using a calculator. | I use logs all the time in physics and maths and modelling. Also decimals are just an awkward subset of fractions. | Yes. Without a doubt. Just because you can do something on a calculator doesn't mean you can ignore how it works. If you do, you become a slave to memorization, pressing buttons because someone told you that's how you got the right answer, unable to think critically or understand any mistakes. | Logarithms are incredibly useful. They turn a product into a sum, when doing calculations, this can make things quite a bit easier. | Absolutely! Duh!! Mastery of fractions should be attained by fourth or fifth grade. This is fundamental to all later mathematics education. Logarithms are a topic for later in high school, but logarithmic and exponential functions are a cornerstone of virtually all mathematics and science. That means genuine UNDERSTANDING of these topics, not where the button is on a calculator. |
[
"How do you count numbers?"
] | [
"math"
] | [
"g1yw0"
] | [
17
] | [
""
] | [
true
] | [
false
] | [
0.7
] | Do you say the numbers to yourself verbally (inside your head), see a tape of numbers sliding by, or some other mental framework? In your opinion, does your framework make you successful with mathematical thought and reasoning beyond number counting? | Related : Richard Feynman talks about different ways of counting. Interesting stuff. | In my book there aren't very many numbers, you've got; zero, one, big number (n), small number (1/n), other unitary number (like -1, or i, or a basis vector). Don't know if it's made me successful though. | I say numbers in my head; I'm terrible at visualization, even though I'm a very visual person (I learn best visually). So, I'm probably at a disadvantage when it comes to doing mental arithmetic. I think the only advantage this might confer is that it may be easier for me to consider things purely mathematically, without the usual objection of intuition from experience. So, I can't really imagine these compact, curled up, dimensions in String Theory or something like a tesseract; I can distance myself from my intuition. They don't have to make sense spatially or visually to make sense mathematically. Overall, though, I think my inability to visualize is probably a disadvantage, definitely one when it comes to considering numbers. Any synaesthetes out there doing math? Daniel Tammet can see (and has painted) pi. | Damn - because of your link I watched several Feyman videos on yt and read some wiki articles. It took me about 3 hours!! Thanks (I nearly forgot to mention: Feyman's counting idea is as simple as brilliant: People use different facilities of their brain for the same task. I wonder whether a deaf person has a fundamental different way of thinking than a blind. And what happens when some regions of your brain are damaged? I've heard several times, that other, intact regions can sometimes substitute these defect regions. The human being has to learn a different way of processing information: Instead of literally telling things to himself he has, for example, to visualize them. I've heard there are people who can't differ between their senses: They are hearing colours, smelling tunes, and so on. Very interesting stuff) | I think because of the way I visualise numbers I can tell almost immediately if an integer is prime. How accurately can you do this for larger numbers? |
[
"Problems copying equations from original word document to other word document: the equations become images :(. Anyone know how to solve this?"
] | [
"math"
] | [
"g1x81"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | Hi math, to my shock and horror, I just discovered that copying and pasting the equations (exercises) for my students from one word document to another word document results in an image of the equation. You can still edit the original equation in the original document with the equation editor, but in the copied document, you just have an image which can not be edited anymore. This is not what I want: I want to be able to edit the equations later, when needed. Did anyone else encounter this problem? Better yet: anyone know how to work around this problem? I want to be able to edit the equations in the copy of the document as well! : Ok, I'll not be the asshole who says: never mind, found solution and leave it at that :). The solution was... that the original document with the equations was a 2007 word document and the document I tried to copy the equations into, was a 2003 document. Saving that document as a 2007 document solved the problem. Nothing to see here, move along people. | Googling LyX. | I bet you're the guy who draws pictures in Excel | I bet you're the guy who makes snarky comments from a basement. | Your life will almost certainly be better if you use more appropriate software, on the other hand it's dangerous outside the basement and I get all my meals brought in, so why would I leave? | What would you recommend then instead of making condescending remarks? LaTeX? |
[
"just screwing around with tex the world"
] | [
"math"
] | [
"g203f"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | [deleted] | [; \pi + x ;] [ 2 ] | [; a + b ;] | [; \pi + x ;] | [; e + 1 = 0 ;] | this is a weak ass script |
[
"Does anyone know anything about the grad program in Mathematics & Statistics at Loyola in Chicago?"
] | [
"math"
] | [
"g22eb"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.67
] | [deleted] | I go to Loyola, and I'm in the Master's program. Personally, I love the program. I can't speak to financial aid, as I am a combined undergraduate/graduate student, so technically I get a scholarship through undergrad. The program does not have any particular focus. You take nine courses that can be in any discipline of math you choose. For example, I'm computer science based, so next semester I will be taking algebraic coding theory, as well as numerical methods. Some are more business focused, so they are taking financial math this semester. We cater to whatever flavor of math you prefer, and if there is a particular topic you'd like to study, you can do an independent study relatively easily. But ask around, and you will tend to find other students in the program might also be interested. The faculty isn't very large, which I personally enjoy. Beware, most of your classes will probably be cross-listed with undergrad, for whatever it is worth. Generally the grad students have to do something more, like write a paper, and typically are assigned harder problems/more complex proofs. I'd highly suggest meeting with a professor. Email Dr. Huffman to set up a meeting. Also, PM me if you want more information, or would like a tour or something if/when you visit. | I was there for my undergraduate degree. I transferred out eventually though. I can't speak for grad school, but the undergrad courses definitely lacked rigor. I transferred to U of I. The impression that Loyola left upon me was that it was really more geared toward their nursing and pre-med students. You rarely ever meet anyone besides people who are there for those two things. But like Kgreene2343 said, he loves it. The thing about Loyola is that you either love it or you hate it. Personally, I did not enjoy my time there. High cost of living, and high private tuition. For undergrad, I definitely had scholarships, but even combined with federal loans, I paid more there than I did at a state school (UIUC), and am getting (I believe) a better education and experience. Not sure what you wanna end up doing with your PhD or Masters, but consider also the networking advantage of going to a more well known school? However, if you do end up there, Dr. Doty is great and SUPER smart. | Loyola does this thing where you can work towards getting an undergraduate degree, while at the same time progressing in your master's degree. So I am going to Loyola as an undergraduate math and computer science student, but because I have already finished the math major, I am taking graduate courses. Eventually, these courses will build up, and I will earn a master's, even though I took most of the courses at the same time as I was progressing towards an undergraduate degree. | Loyola does this thing where you can work towards getting an undergraduate degree, while at the same time progressing in your master's degree. So I am going to Loyola as an undergraduate math and computer science student, but because I have already finished the math major, I am taking graduate courses. Eventually, these courses will build up, and I will earn a master's, even though I took most of the courses at the same time as I was progressing towards an undergraduate degree. | Do you have to take any "basic" exams for the MS in Math? |
[
"Need 10 seconds of your time... Ive got (4) 2’s, (4) 4’s, (4) 6’s and (4) 8’s."
] | [
"math"
] | [
"g242p"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | Ive got (4) 2’s, (4) 4’s, (4) 6’s and (4) 8’s. Whats the maximum number of combinations if the total has to equal 40. Numbers can repeat, etc... so could be (20) 2's; or (18) 2's and (1) 4, etc... Much appreciated. Someone helped me last time with a computer programming system... It involved 'memory,' cant remember much else. THANKS! | Try r/cheatatmathhomework or r/learnmath | its not for homework actually. Im 30 years old. ha. just trying to solve some problems. made a throwaway here. Last time someone did it on some computer program and it only took a second. It would take us a day to work this equation by hand. | ghci> [ (a,b,c,d) | a <- [0..4], b <- [0..4], c <- [0..4], d <- [0..4], 2*a + 4*b + 6*c + 8*d == 40] [(0,0,4,2),(0,1,2,3),(0,2,0,4),(0,2,4,1),(0,3,2,2),(0,4,0,3),(0,4,4,0),(1,0,1,4),(1,1,3,2),(1,2,1,3),(1,3,3,1),(1,4,1,2),(2,0,2,3),(2,1,0,4),(2,1,4,1),(2,2,2,2),(2,3,0,3),(2,3,4,0),(2,4,2,1),(3,0,3,2),(3,1,1,3),(3,2,3,1),(3,3,1,2),(3,4,3,0),(4,0,0,4),(4,0,4,1),(4,1,2,2),(4,2,0,3),(4,2,4,0),(4,3,2,1),(4,4,0,2)] ghci> length it 31 | Nice solution using formal power series. Problem interpretation: Fill up a string of n symbols from an alphabet of 16 characters. Order doesn't matter. There are 4 kinds of characters, each kind containing 4 characters. The string must contain an even number of characters of the first kind, a number of characters divisible by 4 of the second kind etc. Now if you have a Num instance for lists of integers that corresponds to that of formal power serieses, then in f1 = cycle [1,0] f2 = cycle [1,0,0,0] f3 = cycle [1,0,0,0,0,0] f4 = cycle [1,0,0,0,0,0,0,0] result = (f1 f3*f4) result !! n is the solution for the desired sum n. Here are the first 21 (indexing starts at 0) entries of result : [1,0,4,0,14,0,40,0,105,0,248,0,554,0,1164,0,2344,0,4524,0,8450... ] For your problem you take the value at index 40, which is 1214398. | man that is so awesome. If we did this by hand, which is the only way our analysts know how to do it, the problem would take a day or so. I will pass this along to them, and see if they can learn from what you said. Man, I appreciate this. I know you said it only takes you a second, but it has earned me a little acclaim around the office. Much appreciated. THIS IS AWESOME. |
[
"An approximation for sine"
] | [
"math"
] | [
"g29tq"
] | [
12
] | [
""
] | [
true
] | [
false
] | [
0.83
] | I seem to have having some trouble with Tex The World and reddit, with powers messing it up, so I've typeset the question here: Anyone have any ideas? | The Weierstrass product/factorization theorem is what you are looking for. The sine and cosine functions are mentioned specifically at the end of the corresponding wikipedia article . The class of functions with prescribed zeros is determined up to multiplication by a non-zero entire function. So there is only one function equal to the infinite product over the zeros multiplied by the non-zero entire function, g(z)=1. By the way, it was Euler who originated the idea of an "infinite polynomial" in connection with his solution of the Basel problem, as redditor "271828" has noted in another reply. | Might you be thinking of Euler's answer to the Basel Problem ? | Hmm I met the idea before and I'm desperately trying to recall the details, i.e. not the answer to your question, but assuming what you did is true already. It was something whacky and totally unrigorous, and looked really cool. Also was made by someone famous like Euler or Gauss and involved pi. Anyone help? It went: -assuming that a sine function is equal to its zeroes as you wrote, with cn=1 -multiplying out and getting an expression of a coefficient, lots of fractions you were trying to sum up in an "original" problem -equating this coefficient to its value from the power series -... -cool result. | My quick thought on this: Your function has the property (in the limit) : S(x) = S(x + 2π) So it is a wave and can be expressed as a sum of sine-waves. As it happens it is a very easy sum of sine-waves. EDIT: actually there must be a bit more to it than this, because F(x) = sin^2 (x) also has zeroes at nπ (n*pi). So we need to do more to justify that it must be sin(). | Maybe take a look at the second derivative of S and try to show that S'' = -S. If so then the general form of S(x) is a cos(x) and the conditions S(0)=0 and S(pi/2)=1 would then force a=1 and b=0 so S=sin. |
[
"Self-Taught precalculus?"
] | [
"math"
] | [
"g0w45"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | So here I am, finishing my first year of college with the only math class having been taken is statistics. Long since out of practice of precalculus (which I took junior year of high school). Recently, I have decided to commit myself to my dream major of Astrophysics though. Historically, I have only been mediocre, at best, in the math field. I'm not sure if this was because I didn't think I would ever use math, or I was just a bad student in high school. Regardless, I guess what I am trying to get at is does the esteemed math community here on reddit think it is possible for somebody such as myself to teach themselves a refresher course in precalc so as to skip a college precalc class? tl;dr Can I teach myself a refresher course in precalc as substitute for college precalc? | Uh, well yes, it's possible, but it won't be easy, and you can't chicken out if it gets tough. Make sure to test yourself regularly. Standard links: http://www.khanacademy.org/ http://patrickjmt.com/ http://tutorial.math.lamar.edu/ | The reviews seem positive, so that's good. The first pages leave out the important description that the slope is how much the graph rises (y2-y1) per some length along the x-axis (x2-x1), so that the slope is rise/run. It just provides the formula. Maybe the rest of the book is better. Yes, I'd definitely suggest supplementing that with khanacademy. | It's not so much that you know how to find the slope, as it is that you understand what the slope represents. The slope describes how function is changing at that instant. The understanding of the slope as the rate of change of a function at an instantaneous point in time (the derivative) is a fundamental idea in Calculus. Basically, acetv is saying that the book seems to be giving you a tool without explaining the significance of it or laying the groundwork for that significance to become apparent. | Thank you very much. I was considering also getting this book ( http://www.amazon.com/Pre-Calculus-Demystified-Rhonda-Huettenmueller/dp/0071439277 ) to kind of guide me in studying. Now that it is presented to me, Khan Academy looks like it could be a good supplement. | Perfect. Thankfully I do know enough about math to know how to find slope. Haha |
[
"We all know that the \"optimal\" water bottle is a sphere, which minimizes surface area, but maximizes volume. What if we had the opposite goal, a \"waster bottle\" if you will?"
] | [
"math"
] | [
"g107w"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | The rules for this experiment are as follows: You should construct a water bottle in 3-space that maximizes surface area to volume ratio. It has to actually be a water bottle, that is to say no infinitely thin infinitely long sheets. Nobody is going to take that to the gym. Bonus points if it's plausible to manufacture. | use your lungs as a model. Your lungs have ~=0.006 m volume, but a surface area of ~=160 m Any space filling membrane would work as well. | I'll say a Kline bottle, just to be funny. | There is no maximization. The ratio is clearly unbounded. If you add some conditions it might be a more interesting problem. Say the contained volume has to be 1 liter and the container has to fit inside a cube (or maybe a sphere) of volume, say 2 liters. Furthermore, constrain the thickness of the container to be greater than or equal to some positive value, say 1 millimeter and maximize the surface area where a point on the surface is external only if no other point of the surface is within 0.5 mm in the direction normal to the surface at that point. Given such conditions it wouldn't be too difficult to find an upper bound for the surface area, but I don't know exactly how to construct a maximizing shape. | I think the optimal thing to do would be to take the graph of 1/x in the upper right quadrant and then rotate it about the x-axis. Then just stop at some x and put a bottom on it. If you go to infinity though it has infinite surface area, but finite volume. | This has the disadvantage of having unbounded "size". A fractal-type shape (much like the lungs) is much better in that you can have a surface contained in the unit sphere which has infinite surface area. |
[
"Group theory: Can you help me understand the statement of the theorem."
] | [
"math"
] | [
"g10fb"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.43
] | Hello, Please take a look at the theorem of equation 3.33 I don't even understand the statement. What does it mean that a function "belongs" to an representation. Also, is the statement correct, or should there be some coefficients in front of each f_i? I have uploaded this definition, which might be useful Thanks in advance, Tony Bruguier | I'm not seeing an equation 3.33 or any theorems in your first link. | Thanks for taking a look. I had swapped the two links -- it is now fixed. | Based on looking hard at that book, it seems like what is by " [; f_\kappa^{(j)};] belongs to the [;\kappa;] th row of the jth irreducible representation" is just that that function is in the span of the corresponding basis element. The representation is acting on a space of functions, so basis elements are themselves functions. The span just consists of all multiples of the basis element, which is why there are no coefficients needed. All the theorem is saying is that the irreducible representations span the whole space, ie the space is totally reducible. If I may ask, is this book for a class? Or are you reading it on your own? If that latter, it might not be the best book to use. I'm not in physics, and things might be different on that side of the fence, but the language seems a little out of date (the book was originally published in 1964) and the understanding of group theory overly concrete. Representation theory is one area where a little bit of abstraction can add a lot to your understanding. | I am reading on my own, for fun. Book suggestions are always welcome. | I understand, thank you. |
[
"Tricksy 1/7"
] | [
"math"
] | [
"g16y9"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.7
] | Long ago, I realized that , but with the first decimal place knocked off of it. This blew my mind for a while until I figured out (while taking a shower) that this is because However, I've just now picked up on another pattern, and I haven't identified why it is. 1/7 = ∑ {i=0,∞} 0.14/50 Obviously the numerator (0.14) multiplied by the denominator (50) equals 7. But how does that factor into things? | 50 - 1 = (50 - 1) * (50 + 50 + ... + 50 + 1). The first factor is 49, which is divisible by 7. | Start with the summation formula for a geometric series. That will show you right away why the sum of the infinite series is 1/7. Next, the sum up through n-1 is ( 1 - 1/50^n )/7 (work it out), or (50^n - 1)/50^n / 7 (*) But 50 - 1 is always divisible by 7 (do you see why?). So this (*) is a fraction whose denominator is a power of 50, i.e. involves only the primes 5 and 2. Hence its decimal expansion stops at a finite point. | while taking a shower Most of my math epiphanies come to me in the shower. Glad to hear I'm not the only one. | In case you didn't realize, it follows that n/7 for all n where n != 0 modulo 7 have the same six repeating digits in the same order, just starting with a different digit. 1/7 = .1428571428... 2/7 = .2857142857... = 100/7 - 14 3/7 = .4285714285... = 10/7 - 1 4/7 = .5714285714... = 10000/7 - 1428 5/7 = .7142857142... = 100000/7 - 14285 6/7 = .8571428571... = 1000/7 - 142 | You can use the fact that ∑ {i=0,∞} x = 1 / (1-x) when x is between -1 and 1. |
[
"What are some good trigonometry resources?"
] | [
"math"
] | [
"g12fe"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.71
] | My nephew is a really smart kid. He's always go straight A's with minimal effort. He's also taught himself French, multiple musical instruments, and pretty much learns anything that he wants to learn with the exception of Trigonometry. Apparently during the transition from one High School to another they essentially skipped him a math class. Like a boss, he stuck it out since he wanted at least one class that was challenging. If anyone else out there was in a similar situation at what point did you finally start "getting it" or is there a resource online designed for someone that has an otherwise strong skills on math, that can be used as a quick introduction to get him back to speed? | Standard Khan Academy response | http://oakroadsystems.com/twt/ Trigonometry Without Tears by Stan Brown. | I was in a similar situation. I didn't learn trig before starting to learn calculus in college. I just dived in. My calculus I grade suffered (got out with a C), but my calculus II grade is currently an A. The Khan Academy and Trig Without Tears links others have provided helped me out. I would say I finally "got it" late in the semester. Your nephew might get it faster. I was exposed to several topics that I was behind on, so I didn't spend adequate time on trig. Hope that helps! | This is a physical resource, but I bought the Trigonometry reference from SparkCharts for $4.95 and it has been extremely helpful. http://sparkcharts.sparknotes.com/math/trigonometry/view.php | Some free resources here: http://www.e-booksdirectory.com/listing.php?category=107 |
[
"Favourite maths 'trick'"
] | [
"math"
] | [
"g0ytl"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | I don't know why but I always get a little happy/excited whenever I see or have to use the good old fashioned 1/(1-f(x)) |f(x)|<1 hence we can expand the fraction as the sum from n=0 to infinity f(x) . Do you guys have any trivial tricks that you appreciate no matter how much you've used them? | The good old multiply by one and add by zero. | The greatest trick in mathematics is always to insert a term and its inverse. | very trivial, but SOH CAH TOA | Don't know if this one counts as a math trick, but I dig the simple arithmetic trick where if a calculation is off by a number divisible by 9, then you transposed a number somewhere. Oh well, it excites accountants anyway. | I'm a big fan of putting in an extra parameter, fiddling with partial derivatives to make it nice, then letting the parameter take on an identity value. Nice ways to integrate sin(x and other things. |
[
"Best time to take GRE?"
] | [
"math"
] | [
"g185y"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.67
] | I am in Calculus 2 and I have 2-3 more semesters of "math" before I take the GRE. (calc 3, intro to probability, and discrete math for computer scientists, in that order). I need to be at my best in terms of GRE math because the average for the program for which I am applying is 90%. Should I take it after calc 3 and see how I do or wait until after discrete math? | Are you talking about the general GRE? If you are, there is no calculus on the exam. You have all of the tools needed to answer every question. The general GRE math section is pretty easy. Take some practice tests and see how you do. | The math on the general GRE is actually easier than the math on the general SAT .... subject GRE's and SAT's are a different matter entirely. Good luck! PS: One thing to keep in mind: the GRE math section is actually so easy that even if you get 100% of the questions right, you might only end up in the 80th percentile or so. Don't get depressed if you are in a lower percentile than you expected - look at your numerical score only. | I took it in October and 100% correct was 94th percentile. | The math on General is trivial; for engineering/science students the common pitfall is running out of time due to mis-timing the early questions, which -due to the adaptive algorithm- you absolutely do not want to mess up. (When i took the exam last year I almost fucked up and had to semi-guess the last 2 questions, having only 40 seconds left for both) General Verbal was easily the hardest for me though (foreign EE student), I pretty much had to guess every 2nd question because I had no clue what any of the words meant. That said, General GRE test scores are almost meaningless if you are applying for a top university. Pretty much everyone will have 800 in math, Verbal is ignored. If you really want to impress go for 90% percentile in Subject, that one is a beast. | Yes, just the general GRE. I don't think the subject tests are required except for candidates for phD. Thanks for the comment. I'll check out some practice tests and see how I do. Now that you say there's no calculus, I'll probably just need to brush up on my geometry and precalc. |
[
"My dad just posted this to Facebook, about the quadratic formula"
] | [
"math"
] | [
"g1ds8"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.55
] | Quadratic Formula: There was a negative Boy, who was confused about whether or not he should go to a radical party. The Boy was square, so he missed out on 4 Awesome Chicks and he cried until the party was over at 2Am. | That's great. There's one in spanish for integration by parts that goes as follows: Un Dia Vi Una Vaca Rayada Vestida De Uniforme: ∫u dv = uv - ∫v du The saying translates to: One day I saw a striped cow dressed in a uniform... For some damn reason it is unforgettable! | I've used this for years and I love it. One day a friend asked me something about some integral and I answered out loud "Un dia vi una vaca vestida de uniforme" and he was all like 'lolwut?' Anyway, where's the R? I think you're picturing your cow in a striped uniform :P | The rayada comes from raya... la raya del signo menos! jejejeje!! | I wish my teacher had told us this story in high school. Would have saved me so much pain! | Some old hippy caught another hippy tripping on acid. |
[
"Set Theory as the foundation of mathematics"
] | [
"math"
] | [
"g047z"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.75
] | I recently picked up a book on set theory (Jech) so I could get a more rigorous grasp on mathematics. I loved how things like functions and integers were defined so formally and it got me thinking, are all objects in mathematics defined in concrete terms with sets? How are rational numbers, irrationals, complex numbers, aleph numbers, ordinals and even more abstracts elements of math defined? Are they, or is mathematics much less rigorous than I imagined? | You can construct the naturals, integers, rationals, reals, and the complex numbers all in terms of sets. The constructions for everything except the reals are elementary, and the reals aren't too hard, just more involved. There's a short book by Landau that does all of these, you should check it out. Cardinals are defined in terms of ordinals, which are defined in terms of order types and well ordered sets. Most things that you will deal with on a regular basis can be described in terms of sets. However, due to Russel's paradox, sometimes we want to talk about things that can't (consistently) be considered sets. These objects often show up in category theory, often as objects that are "too big" to a set (see proper class ). I'm sure someone who knows more about category theory than I do can give you lots of example of categories that aren't sets. | Let [; 0 = \emptyset ;] [; 1 = \{0\}=\{\emptyset\} ;] [; 2 = \{0,1\}=\{\emptyset,\{\emptyset\}\} ;] [; n = \{0,1,\dots,n-1\} ;] This defines the natural numbers in terms of sets. Note that the cardinality of the set n is n itself. To define something like multiplication of the natural numbers (sets) [;a,b;] , we could say it is the unique set of these which has the same cardinality of the cross product [; a \times b ;] . We can define the ordered pair [;(x,y);] of the sets [;x,y;] to be the set [;\{\{x\},\{x,y\}\};] . So to define the integers, we could use the ordered pair [; (n,s);] where n is a natural number and s is 0 or 1. So we say the number is positive if s is 1 and negative if s is 0. Now, to get the rationals, we use ordered pairs of integers (ordered pairs of ordered pairs): [;(p,q);] . We'd need to define equivalencies like [;(2,-4)=(-1,2);] (possibly by defining an equivalence relation and equivalence class), but you get the idea. I thought it was so cool at first when I learned that nearly every mathematical object can be thought of as a set (except for some very large abstract collections), but in practice it's not necessary to think of, say, natural numbers as sets. Then again, it's very useful if you want to define a function which only has two possible values, since you could define it to be a function which maps into the set 2. | PM used axioms of logic, not set theory. | Almost none of the categories you care about are small, meaning that the collection of all objects does not form a set. Examples are the category of sets, groups, rings, vector spaces, modules, topological spaces, etc. But as drvitek pointed the categories you care about are almost always locally small. Meaning the homomorphisms between any two objects form a set. All the examples above are locally small. | The typical way math is done is all in terms of set theory of some flavor. Not everything is actually a "set" as people often want to talk about things like "the collection of all sets," or "the collection of all groups/rings/modules/etc." These things are typically too large to be sets in the sense that we can't call them sets without hitting Russell's paradox, or some other logical inconsistency. These are known as proper classes (every set is also a class, but not every class is a set). Many constructions used now are proper classes, because they arise naturally for many simple categories. That's not to say that set theory isn't in play. There are many flavors of set theory that have classes at their base; e.g. von Neumann-Godel-Bernays set theory . |
[
"r/math, do you think you could help out a high school junior trying to make some decisions?"
] | [
"math"
] | [
"g08l1"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.56
] | Honestly, I don't know if this is where this type of question belongs, but this is the only place I could think of with a high concentration of mathematicians/math students, so here I am! Basically, I want to ask a few questions regarding math as a study and as a career. I know that I want to do either engineering or math, and I know tons of engineers and engineering students, but I'm pretty uninformed about mathematics. I know this is a lot to ask, but I would really appreciate it if any of you can answer any of these that you feel you can contribute to, and feel free to give any other advice/comments. Thanks guys! | One comment on Q4. Lots of students going to university get an major surprise when they realise that the maths that they're being taught is all about proof. So you might start with something like logarithms that you already know about and rip it into tiny little pieces, rigorously proving what your secondary school teacher had you take on faith. If you're mathematically inclined, it's a major thrill. If you're interested in mathematics as a toolbox that you can apply to other problems, it can be a bit of a turn-off. | 1) No. As long as you're interested in math, I think you'll do fine. 1) Engineering requires Calculus, Differential Equations, Linear Algebra, and a class in Applied Mathematics at my college. That's one class short of a math minor. The math major has a lot more math than that, though, and a lot more rigorous. 1) Engineering will be able to get you a job quicker, but math jobs usually pay much better. You can work for the NSA doing cryptography and the like, become an actuary for an insurance company, or teach. Aside from that, though, the fact that you have a math degree is a sign of great intelligence for companies. I've seen a math major with a minor in computer science get a job over someone with a comp sci degree (though I'm sure that's not the norm). Math makes you viable for all sorts of other jobs. 1) What exactly do you mean by "what stuff do you learn"? I could start to list off a slew of subjects and their applications, if that's what you're looking for. | No. a) Competition math, though much better than school "math", is very different from real math. b) People in competitive math are... scary. You don't have to be an übergenius to be good. Engineers don't take very much math compared to a math major; no abstract algebra whatsoever, no topology, not much analysis, etc. Also the math is done far less rigorously, so is generally much easier. As for grad school --- it would depend on what kind of math you wanted to go into; applied mathematics, possibly (provided you took enough math courses), pure mathematics, definitely not. Don't know. Calculus, linear algebra, group theory, ring theory, differential equations, real analysis, complex analysis, topology, set theory, differential geometry, commutative algebra, and Galois theory are typical topics to cover in an undergrad. You typically take "engineering math" in the first two years: calculus, linear algebra, and differential equations. In third and fourth year you get into abstract algebra (group theory, ring theory) and rigorous analysis (real analysis, complex analysis), as well as topology. This depends on the university; my university, for instance, introduces groups, rings, and fields in the first-year honors linear algebra course, and some universities (Chicago, MIT, Harvard IIRC) skip calculus and give you real analysis from the start. | As error792 said, math competitions differ greatly from real math. I enjoy both, but most of my math course exams are week-long take-home ordeals, aka not the type of thing to be done in a competition setting. In my mind, the main difference between a math major and an engineering major is that an engineering major focuses solely on applications, whereas a math major (if you do it the way I am) focuses on theory. I happen to also be a computer science major, but I'm concentrating in theory there too. Other posts summarize the math you would take as an engineer. Basically what everyone else is saying. Engineering = sure job, math = cooler job potential. Depends on what you take and how you do the major. At my school (a huge university), there are 4000-level math courses and 5000-level math courses. You can take either for a math major, but if you want to go to grad school for math, you take 5000-level. Any core of a math major includes calculus, linear algebra, differential equations, real analysis, and abstract algebra. Complex analysis and combinatorics are often taken as well, and there are many choices of different courses (depending on where you go to school). | Math/CS undergrad, Civil Engineering phd here. Hope this helps. |
[
"Fun graph theory paper to present for class?"
] | [
"math"
] | [
"g06eg"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.73
] | For my Advanced Topics in Graph Theory class, I'm required to present a paper of my choice in graph theory in a 10-15 minute presentation. I did find a neat paper by Erdos involving probabilistic graph theory: . However, I wondered if any of you knew of anything you thought was really cool that would be appropriate and accessible. You can assume basic graph theory knowledge but not much more unless it involves edge colorings, which we've done a lot of this semester. My research area is topology, so if you know of any cool topological graph theory results that I could do, I'd especially be interested in that. | Do the proof that every planar graph is 5-choosable. It's got topology and coloring, it's a beautiful proof illustrating the power of a perfectly chosen induction hypothesis, and it's about a page long. | You get upvoted in the math joke threads and downvoted in the math threads. Therefore, you are a math joke. Please comment your own comments as such. | You get upvoted in the math joke threads and downvoted in the math threads. Therefore, you are a math joke. Please comment your own comments as such. | Thanks for inspiring me to pull out my copy of - that's actually Chapter 30 right there. :) I may just do this. | I'm definitely not an expert in the field, so someone else can probably give a more important paper, but I do love polynomials, so you might be interested in the paper Building Graphs Whose Independence Polynomials Have Only Real Roots by Eugen Mandrescu. |
[
"Is the set of natural numbers the set of aleph numbers?"
] | [
"math"
] | [
"g1ht5"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.17
] | [deleted] | My crank alarm is blasting at 130 decibels. | I'm confused about what you're trying to say. Are you assuming things, or asking questions? Let 2 points exist, points A and B. Two points of what? A topological space? If so, which one? There are an infinite number of points directly between A and B. We will call this set of points a line segment. What do you mean by "between"? Are these points ordered somehow? Do they live on R? "Infinite number" is not precise enough here. There are an infinite number of points between any 2 points on this line segment. I take it that this is an assumption. The cardinality of any line segment is an aleph number. I don't see how you're getting this. Aleph numbers have very specific meanings. Are you defining line segments in terms of aleph numbers? If so, you should start with that. A line segment with a cardinality of aleph zero is called an infinitesimal line. A line segment with a cardinality of aleph one is called a unit line. A line segment with a cardinality of aleph infinity is called a line. More definitions, I guess. The distance between 2 points is the cardinality of a line segment between those points. What do you mean by "distance" here? It's certainly not a metric. I'm not even sure you can show it's well-defined. I'm just not sure what you're doing. Are you trying to create a metric space based on aleph numbers? What is your goal here? | No, the problem is that I know what you mean. You start with two points, A and B and assume nothing else. Okay. I can buy that since a point is hard to define. Then you say that there are infinite number of points between A and B. This obviously doesn't follow from just two points, so I guess you are assuming that there are an infinite number of points. I don't know what "between" means since you've assumed no definitions or axioms. But I'll ignore that. These points make a line segment. Okay, great. Then you say the cardinality of any line segment is an aleph number. Well, so far I have to agree with you since you've only allowed line segments to have infinite cardinality and the aleph numbers denote infinite cardinals. Okay, I've been making my best guesses up until now, but this is where it gets rather inconsistent. You say the set of all line segments is the set of all aleph numbers. First of all, the aleph number denote cardinalities, so I'm not sure how a cardinality could correspond to a set of points (your line segment). Perhaps you meant that for each aleph number there is a line segment with that cardinality? Then I don't see how you came to this conclusion. So far I know there is line segment, namely, the set of points "between" A and B. That gives me one aleph number. How could you possibly have every aleph number represented? You go on to define names for cardinalities with different aleph numbers (assuming they even exist). Okay, great. Then the "distance" between two points is the cardinality of the line segment between them. So you've defined some sort of distance between points which takes values in the set of aleph numbers. Okay, I guess that's fine. Now, my question still stands. I have no idea what you're trying to get at. Most of what you've said is fine, but you haven't made any claims, just defined things. Since you started with an "empty universe", there's nothing much to say about this. In particular, I see no connections to the natural numbers, so I'm not sure what the point is. | The cardinality of any line segment is an aleph number. This is very imprecise. The set of points on a line segment has cardinality 2 or Aleph-1 if you assume the Continuum Hypothesis. It doesn't matter how long or how short the line segment is. Pretty much everything else you said after this is incorrect. Edit: typo | rhlewis is actually spot-on, I'm afraid. There are basically two kinds of person that could ask a question like this: Cranks Very confused undergraduates/amateurs (There is overlap between the two sets.) The thing that you may not be getting is that your question contains with it some incorrect assumptions. I'm sorry to say that it is, as Wolfgang Pauli might've said, "not even wrong." (Another good one is "I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question." .) Rather than being old and crazy, I think it's more likely that you're an undergrad or high schooler who hasn't yet learned the things that would make everything fall into place here--which means you might benefit from a little advice. My advice is to read and understand the section on cardinality of a good real analysis textbook (Rudin's is a popular choice, although it's difficult reading). (Wikipedia might be good for this, too; its math articles tend to be of high quality.) Half because it might clear up your misconceptions regarding cardinality, and half because you need to get used to thinking about these things rigorously--which means precise definitions, well-formed questions, and before you start off on tangents like this. Once you have had a lot of practice doing things is the time to even start to think about saying things like The terms may be mathematically imprecise but you know what they mean. You have to walk before you can run. |
[
"Are these two set based proofs read the same way?"
] | [
"math"
] | [
"g0ns7"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | [deleted] | And, btw, these are not proofs, these are propositions. A proof is an argument that exhibits the truth of a proposition, a proposition itself is a declarative claim. | Yes. In the first case, A is determined first, and then you can choose B depending on A. In the second case, there has to be a single B which is true for all A. In particular, the first statement is true (just take B = A) while the second is false (take A = {B} , the set containing the set B and nothing else.) edit: simplified examples. | I feel that I can be of service. | The first says: For every husband there is a wife. The second says: There is a single woman who is the wife of all husbands | Sorry, there is no "universal set". See: http://en.wikipedia.org/wiki/Russell's_paradox |
[
"What should/can I do with my life?"
] | [
"math"
] | [
"g0pdo"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.36
] | Hi . I'm a senior math major at college in the United States, and although I love math, I have no clue what I can possibly do with my degree. I've talked to advisors, career services people, and everyone is giving me the same vague answers. (Analyst, Actuary, or work for the NSA, none of which appeal to me) There are a couple options that I've been looking into, which involve subjects I've very recently discovered that I'm interested in. I love learning about things like consciousness, how people think, and how the brain works. I also took a Dynamical Systems class last year, and loved that sort of math, although I wasn't particularly good at it. It'd be my dream job to be able to study something in either of these fields, but I'm realizing that it's probably going to take grad school to get me anywhere close. Is there any reasonable way to transition from math to neuroscience or related fields? And one last thing... Ever since taking the Dynamical Systems class, I've been extremely interested in learning more about fractal geometry. Does anyone know where I could find a good introduction to the math of fractals? I would be willing to start at the very basics. Thanks | It's the same here, I don't know what to do. I would like to just study, maybe collect up a bunch of people really interested in learning and give seminars on everything. Falconer is a good intro book for the theory of fractals. | I really would ultimately like to do research, I'm just not sure about the availability of opportunities in grad school for people with bachelors degrees in math to get a PhD in something else | forget about jobs. you're smart, capable, and you have interests in your field of study. figure out what it takes to follow them, and then follow them. just do it. If you're looking for math-degree job prospects: Analyst, Actuary, and working for the NSA are all pretty good. | For the fractals part, I've been planning on picking up Fractal Geometry, by Falconer . | Thanks, thats exactly what I was looking for. |
[
"Something I've heard a handful of times throughout my life; equal pizza trick. Can someone math this for me?"
] | [
"math"
] | [
"g0qqg"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | I suck at math or I'd do it myself. I'm going to set this up as a word problem, since it'll be much easier for me to lay out the principle components of the problem: Billy and Tommy are two brothers that love their mom's pizza, but they always argue over who gets the biggest pieces. Whenever their mom Sally would cut their pizza, she'd cut it into six slices, but she could never manage to get the cuts to intersect precisely in the middle, although she always managed to make all three cuts intersect at the same point. Even though Sally's cuts were imprecise leaving some pieces wider or longer than others, she told the boys that they'd get equal shares, so long as they took alternating pieces. So, is this accurate? Thanks. | You have the wrong conditions. This is known as the pizza theorem. You need the number of slices to be a multiple of four and greater than or equal to 8. Most importantly, you need the angles between the slices to be equal. You didn't require this which is why joenyc was able to produce a counterexample so quickly. I feel like I have a quick proof using polar coordinates, but I haven't quite fleshed out the details. | No. Imagine that the cuts are close to parallel and don't go anywhere near the center of the pizza, and that the intersection is very close to the edge. Essentially, one piece has more than 50% of the total area all by itself. | Thanks for providing background - I had no idea this related to a well-known theorem. | Wow, thanks for the answer. Like joenyc said, I had no idea about this theorem. Thanks for showing me this! | see the following links: http://www.neatorama.com/2009/12/11/the-mathematics-of-sharing-pizza/ www.lsus.edu/sc/math/rmabry/pizza/Pizza_Conjecture.pdf It depends on the number of slices and who gets the piece containing the middle. |
[
"Bus stop math: Help in solving a problem based on A Pattern Language"
] | [
"math"
] | [
"g0m3h"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.63
] | Hi Math Redditors, I am an architecture student with what I think is a possibly intriguing math/logic problem. I'm looking for someone to point me in the right direction in solving it. The problem comes from Christopher Alexander's book "A Pattern Language". In pattern #16 "Web of Public Transportation", he writes: Imagine the following organization: each [bus stop] is run by the community that uses it. The bus stop chief coordinates the service at his bus stop; he charters service from any number of transport companies -- the companies, themselves, are in free competition with one another to create service. In this scheme, responsibility for public transportation shifts from lines to interchanges [bus stops]. The interchanges are responsible for connecting themselves to each other, and the community which uses the interchange decides what kinds of service they want to have passing through it. I want to test and see if it is possible for a public bus agency to operate in a way similar to what he describes. Each neighborhood gets together and decides where the people in the area want to go. They then tell the bus agency and the agency draws routes that exactly match the needs of the citizens. Now, I realize there are some practical problems associated with this model. I'm still curious to find out if it could work. TL;DR: Here's the math problem. of 16 neighborhoods, each numbered. Each of the neighborhoods has demand to travel to three other neighborhoods (these were randomly generated). Is there an equation or method of solving that would always yield the lowest number of segments between a person's home and destination? Is there a method that could also result in the lowest total number of segments (so the bus agency saves on fuel, etc.)? Is there a way to do it that would yield distinguishable routes? Please let me know if I wasn't clear of if this problem is completely ridiculous and not math-related at all. I think it is a fascinating hypothetical that Alexander posed, and I want to see if it pencils out. Thanks! | Here's one way to formalize the problem. The 16 bus stops and the immediate segments between them form a graph . You want the actual bus network to form a connected , spanning subgraph of that graph, so that you don't have buses running on each and every possible segment, but you can still get from every stop to every other. You also have a collection of (origin bus stop, destination bus stop) pairs -- like (1,12), (1,16), (2,9), and so on -- between which you want to optimize transportation. Your first question corresponds to optimizing the distance between (origin, destination) pairs, while your second corresponds to minimizing the total number of segments in the bus network graph. The latter is minimized by any spanning tree of the graph of all segments, so perhaps you want to find the spanning tree that minimizes the total distance between all specified (origin, destination) pairs. That's an interesting graph theory problem, but it's not clear to me whether there's an elegant way to solve it; it might even be NP-complete . (Another caveat: most real public transportation systems are not trees .) | Feels like NP to me, so I'd say you'd just have to brute force it. Edit: Actually it might not be. Can we verify that a given set of paths is the best quickly? It seems like it would take just as long to verify as it would take to calculate. | NP problems are a class of "hard" problems. Check the wiki , I don't know much about it. Now that I think about it though, the problem might not be NP. | I'd look into the Floyd-Warshall algorithm . | No problem - it's definitely an interesting idea. In case you're unaware, these kinds of problems tend to be called "Graph Theory" or "Network Theory", and they tend to be pretty approachable. |
[
"Differential Equations Grapher?"
] | [
"math"
] | [
"fzgdu"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.73
] | I have been trying to find a way to plot some differential equations. I have Grapher (Mac OSX standard thing), but I can't figure out how to use it. If anyone else has a good alternative that I can download (hopefully for free), that'd be welcome. Or if anyone has any clue on how to use Grapher, that'd be welcome too. Thanks! | In Grapher, go to Equation -> New Equation from Template... There's a differential equation tab, so maybe that will help. | WolframAlpha? | I've done that, but unfortunately, it's still no less confusing. | Was the first thing I went to, but sadly, it didn't let me expand the graph to see much meaningful data. Is there any way to expand it? | I don't know if that's what you want, but apparently you can specify the range you want to plot using the Plot[f, {x, xmin, xmax}] function. |
[
"/r/math, could you explain what exactly my Calculus teacher won the Fields medal for?"
] | [
"math"
] | [
"fzku1"
] | [
20
] | [
""
] | [
true
] | [
false
] | [
0.85
] | I'm taking a second-semester calculus class from him, and I noticed he won the Fields Medal for stuff I can't even comprehend. Can anybody describe his work in language that a second-semester calculus student could understand? | I'll give it a long stab. Going from where you are to where his work is will take a long while, and a lot of background material. We're going to start with the concept of a , which you probably haven't heard of. A group is a mathematical structure consisting of two things - a set, and a binary operation on that set. (A binary operation is just a function that takes two inputs and returns one output - addition, multiplication, exponentiation, and so on.) You are probably already familiar with some groups. For example, the pair (Z,+) - that is, the integers and the binary operation of integer addition form a group. Similarly, the pair (R,+) - the real numbers, and the binary operation of addition of real numbers - form a group. As a final example, the integers modulo any positive integer n - written Z/nZ - and addition modulo n form a group, written (Z/nZ,+). (If you're not familiar with modular arithmetic, you can find an excellent explanation on MathWorld or Wikipedia.) Things to note: all of the +'s in the above paragraph are different operations - one is only for integers, one is for real numbers, and one is only for integers modulo n. Furthermore, the group (Z/nZ,+) is special because it is finite. There are infinitely many integers, and infinitely many real numbers, but there are only finitely many residue classes modulo n. (If you didn't take my advice and read MW/Wikipedia, you should have.) As it turns out, finite groups are rather easier to study than infinite groups. This is because there exists the concept of something called a finite group. A finite group is almost exactly analogous to a prime number - just as a prime number has no smaller number that evenly divides it, a group has no smaller group (read: subgroup) that evenly divides it (read: is a normal subgroup). This basically means that if you have a simple group G (we're skipping the pair notation now, because we don't care about the specifics of the operation any more), then there do not exist nontrivial groups H and K such that G = H x K. (Again, MathWorld and Wikipedia are your friend. If you're not following, keep in mind that this is roughly a month or so of an advanced undergraduate algebra course. Don't feel too bad.) Okay, so we know what a finite simple group is. Well, why are they special? As it turns out, they are special because of an amazing theorem called the . This is an incredible piece of mathematics - the proof runs around ten thousand pages at last count, and there's been an ongoing project for about a decade to get that down to 2000 pages or so. It's a massively complex proof, but the theorem itself is very simple. Here it is: Any finite simple group G is a member of one of four infinite families of finite simple groups, or is one of 26 other finite simple groups. While this doesn't sound impressive, the power lies in the descriptions - either you know a lot more about G because it is one of the families, or you only have 26 possibilities for G. The 26 possibilities for G are called the , and they are very weird beasts. For one, they're big - the smallest one has around 8000 elements. The largest one is called the , and it truly is a monster - it has something like 10 elements. Quick heads up: the work that Borcherds did is intimately related to the monster group. But we have to continue on to more interesting plains. Okay, so the monster group is kind of cool - it's the largest "weird" group - but why is it so special? There was a conjecture, called because it was so unbelievable, that related the monster group's structure (as measured by tools from a field of math called representation theory) to a function called the -function. The -function is a type of mathematical object called a . Modular functions have been a central element of study across a whole bunch of fields for over a century - they pop up in algebraic number theory, Riemannian geometry, and much else. And the -function was a pretty special one. But nobody really knew why there was this crazy connection between this enormous algebraic object and this important modular function. Around 1980, two mathematicians (Conway and somebody, I think Norton) formulated a crazy conjecture: they postulated that there was a certain type of structure (a monster module) whose dimensions corresponded to a certain way of measuring values of the -function. (This sounds kind of unclear, because I'm leaving a bit out.) What Borcherds did was use a lot of work from string theory, involving exotic algebraic structures like to prove that there existed this so-called monster module. I am not intimately familiar with the work, but it was certainly a , and in addition to resolving this very strange conjecture it also opened up these interesting connections between several very discrete fields - in particular, it shows the existence of a string theory (describing a universe very different from our own) whose symmetries are the monster group. Anything else, and you'd have to ask a real expert on his work. | Yeah, fractals are weird too, but the Mandelbrot set (for instance) is self-similar to an infinite level of detail. If you could find smaller and smaller copies of the Mandelbrot set as you zoomed in, and then they suddenly stopped at a scale factor of 10 or something, that would be much more bizarre. | Yeah, fractals are weird too, but the Mandelbrot set (for instance) is self-similar to an infinite level of detail. If you could find smaller and smaller copies of the Mandelbrot set as you zoomed in, and then they suddenly stopped at a scale factor of 10 or something, that would be much more bizarre. | As a computer scientist, the existence of the monster group (and the rest of the sporadic groups for that matter) is probably the weirdest, most implausible fact I've ever encountered. | To me it's not really the fact there is a group so large, but that there are only 26 of them. I could totally see having an infinite number of sporadic groups - there's not a priori reason why they should have to be limited - but the fact that there's such a small number of them, and that the largest one is so large is to me what's so compelling. |
[
"Math problem that needs solving. Math puzzel winner gets a pizza sent to there house."
] | [
"math"
] | [
"fzysz"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.3
] | 10/10/10 in base 12 October 10, 2010 garnered a lot of attention because of it's representation as a calender date by 10/10/10. Suppose instead that we represented month, day and year base 12. Thus, in base 12, December would be indicated by 10 because 10 base 12=12 in base 10 Determine which year(s), if any, during the 21st century will have a 10/10/10 date, where each "10" is the base 12 representation. First person to submit the correct answer, I will send them a pizza to the address of his/her liking. Good luck | 2016 ...now show your work. I don't want your damn pizza. | I must be confused by the question. Wouldn't it just be December 12th, 2012? Further, since you require that the date be "10/10/10", and limit the answer to a single century, then the year must be unique, thus we already know that there cannot possibly be more than a single answer. | here goes nothin...2028? | 10/10/1210 base 12 So December 12th, 2028 1110 base 12 doesn't work. Number is less than 2000 in base 10 1310 base 12 is greater than 2100 base 10. Only one possible solution | Correct, send me your address and get ready for some pizza |
[
"After 2.5 years of being a Statistics major, I'm seriously considering throwing in the towel."
] | [
"math"
] | [
"fzkwf"
] | [
8
] | [
""
] | [
true
] | [
false
] | [
0.75
] | Mathit, have you ever almost thrown in the towel? What kept you going? I feel as if I'm no longer cut out for the curriculum. I'm currently an Accounting and Stat double major, and sometimes wonder if I should just drop the Stat. I'm current in my universities Math Analysis II course, and its hitting me hard. I've always been extremely good at math and an overachiever of sorts, but C's and D's are getting me extremely frustrated, along with professors who look down upon me (female, sorority girl, played collegiate sports...i've always felt like I had to PROVE myself worthy of a professors time). I know there are a lot of questions out there probably regarding this, but I'd like some personal stories of triumph or that analysis was your hardest class. Something to keep me going for the next year! | Analysis is hard. Seriously hard. At this stage of the game, you can't just attend lectures and expect to understand things. I recently got my Ph.D. in statistics and I had a hard time in analysis as an undergrad. I spent about 3-4 hours of prep work for every hour in class. If you are working your ass off already, then you might not be cut out for it. If you aren't at that level of effort... step it up because this subject isn't easy for . Edit: If you haven't made friends in the class, you should. Study partners help a great deal because you help teach each other and two brains are better than one. This isn't leeching off of other people, but rather attacking the problems from different points of view. Math really should be thought of as a social activity. :) Edit2: I've done my fair share of teaching and my best students were split about equally between males and females. The smartest students I've been in class with have been women, and I'm working as a post-doc under a female adviser. Don't ever let anybody tell you girls aren't cut out for math. Individual people might or might not be, but certainly not a gender. | Every professional mathematician I have talked to has experienced a moment where math suddenly became hard and they questioned if they were cut out for the profession. | My experience is that without having to try. It comes as quite a shock when they realize they have to seriously work. Wow, I somehow forgot about that. That's worth repeating.; it's probably a big part of the OP's problem. My first three semesters were so easy, even taking upper-level math courses, that I loaded up on courses the spring of my sophomore year and promptly went insane. | I've seen a number about computers, but no I can't find one about math, specifically. I did find one which was arguable. It was a rant. Don't take it to seriously. I hope you're with me as far as these two points are concerned: Placing the burden of proof on women to demonstrate their legitimacy belonging in technical programs is bullshit, especially when men in similar situations are considered competent until proven stupid. There's a time and a place. The OP is struggling with subtle (or maybe not-so-subtle) sex bias on the part of her professors, and complaining that some stereotypes hurt men is a distraction. | I spent about 3-4 hours of prep work for every hour in class. This is normal. Being a full-time student means taking about 15 hours of classwork, which means about 60 hours of work a week. It's tough to be a student. (Which is to confirm, not dispute, what you said.) Math really should be thought of as a social activity. :) This is so true. Also, being study partners with people who are better at the subject than you helps them than it helps you. You're doing them a favor. The smartest students I've been in class with have been women I haven't found this to be true, since in most classes I have taught (well, TA'd, anyway) and other advisory roles I've been in, there were considerably more men than women. But there was certainly no gender correlation. |
[
"What are your favorite examples of deep theorems being used to prove much easier things?"
] | [
"math"
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"g00p0"
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16
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""
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true
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false
] | [
0.86
] | Some of you might recall the thread posted a while ago about coloring a certain type of island with three colors, that gets blown into triviality by the Four Color Theorem. What are your favorite examples of high-level, difficult proofs being used when they don't really need to be? Some of mine: Euler's proof of the infinitude of primes follows from the fact that the zeta function has a pole at z=1. Using Bertrand's Postulate to show that the nth Harmonic number is never an integer. Any use of the Feit-Thompson Theorem. | Relevant question on mathoverflow. | Fermat's last theorem to prove that the cube root of 2 is irrational. | For those who don't look at the MO answers, the follow up to this is "Unfortunately, Fermat's Last Theorem is not strong enough to prove 2 is irrational" (apparently due to W. H. Schultz). | incomplete! | Proving anything with the Graph Minors Theorem. |
[
"AskMath: I need your creative help."
] | [
"math"
] | [
"fyput"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.56
] | [deleted] | Mathematical thought class? What is that, math for poets? | It means that you can find a bijection from the natural numbers to the rationals. That is, you can put the two sets in one to one correspondence. There are several ways to do this. Here's a common example. The path traced out by the arrows will hit every positive rational number. Then you just assign a natural number to its place on that path. It's difficult to tell what the bijection is in this case, but there are more explicit maps as well. | hahaha kind of, it's just a class where we discuss more abstract particulars of math as opposed to just learning formulas and whatnot. | What level is your course? There is an astounding amount of interesting mathematics out there. What about a classification theorem? Maybe the classification of closed surfaces http://en.wikipedia.org/wiki/Surface#Classification_of_closed_surfaces or the classification of the 17 plane symmetries (the so-called wallpaper groups) http://en.wikipedia.org/wiki/Wallpaper_group | How about a demonstrative project on the Tower of Hanoi game? |
[
"How do you find eigenvectors from a row-reduced matrix (A-(2)I)=0 that results in an identity matrix?"
] | [
"math"
] | [
"fys78"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.57
] | The 3x3 Matrix A is: -2 1 0; 1 -1 -1; 1 3 -3 eigenvalues: -2, -2+i, -2-i (A-(2)I)=0 ===> -4 1 0; 1 -3 -1; 1 3 -5; ====> 1 0 0; 0 1 0; 0 0 1 Does this all seem correct? | Eigenvectors. | Try posting this in r/learnmath or r/cheatatmathhomework . btw, 2 isn't an eigenvalue, but -2 is. | As a matter of fact I do not. I don't even have this class tomorrow. | no worries, checking on students? | Do you happen to know how I could find the row-reduced matrix that precedes the eigenvector for lamba = -2? |
[
"Triangle fit inside another triangle"
] | [
"math"
] | [
"fyq3i"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.82
] | I saw this posted online 10+ years ago, and at the time they mentioned it was still unsolved. I'm wondering what the current state is now? Given six numbers, representing the side lengths of two triangles, what are the necessary and sufficient conditions such that one triangle can fit inside the other? | Still open as far as I know. If the triangles are right triangles then it is known: http://www.math.grin.edu/faculty/Jepsen-fitting-right-triangles.pdf | Solution here: Triangle in a triangle: On a problem of Steinhaus . I'm afraid I couldn't find the pdf publicly. | Yo dawg, I heard you like triangles... Sorry. | (Croft, Falconer, Guy) in section B1. | Do you have any reference to where you found the problem before? Otherwise, I'm somewhat skeptical of this claim... |
[
"Forget ladders, this question features cows and has had me stumped for 20 years!"
] | [
"math"
] | [
"fys0o"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
0.76
] | [deleted] | Someone posted a slightly more general version last week. The answer is in the comments. | I believe you are correct. The ratio of silo radius r to rope length pi*r is no coincidence - it's exactly half the circumference of the silo, and half the rope is 1/4 of the silo. I think the area would look much more like this . | I think you're wrong in saying the shaded blue region ought to be a cycloid. Imagine the cow is pulling straight up (in your description) on either side of the silo. It's maximum height would be r + pi*r/2... (half of the rope would be wound around the silo, the other half in a straight vertical line). I made a parametric equation which could solve it... but I feel like there must be a simpler way. | I think you're wrong in saying the shaded blue region ought to be a cycloid. Imagine the cow is pulling straight up (in your description) on either side of the silo. It's maximum height would be r + pi*r/2... (half of the rope would be wound around the silo, the other half in a straight vertical line). I made a parametric equation which could solve it... but I feel like there must be a simpler way. | Am I right in assuming that the area of the silo itself is not grazeable? |
End of preview. Expand
in Data Studio
YAML Metadata
Warning:
empty or missing yaml metadata in repo card
(https://huggingface.co/docs/hub/datasets-cards)
Prompt-Reply Objects from Origin to March 2023 with top 5 Comments
Source Data
The data for this project was compiled from three main sources:
Pushshift Reddit submissions dataset, which includes the following fields: "title, post_id, over_18, subreddit, link_flair_text, self_text" BigQuery, where the Pushshift data was uploaded and queried for submissions from the r/math subreddit A web scraper (https://github.com/P1ayer-1/Reddit-Convo-Tree-Builder) used to extract updated post content, including any replies to the original posts In cases where the updated content was not available (e.g., because it was deleted), the title or self_text from the original Pushshift submissions was used to create a more comprehensive dataset.
Output Data
The output data is in JSON Lines format and includes prompt-reply objects for posts from the r/math subreddit, along with the top 5 comments for each post.
license: cc-by-4.0
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