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"[crosspost] We are an international group of leading physicists (including many Nobel laureates) assembled here at Case Western Reserve University to celebrate 50 years of “the most successful theory known to humankind”… and explore what the next 50 years might hold! Ask us anything!"
] | [
"math"
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"8nrxlz"
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208
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""
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true
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false
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0.95
] | Hi Reddit! In honor of the 50th anniversary of Steven Weinberg’s world-changing publication, A Model of Leptons, the work that solidified what we now call “The Standard Model of Physics”, Case Western Reserve University is hosting a once-in-lifetime symposium this weekend that features talks from many of the most famou... | Can you guys prove for me that the core of the Sun does not spin, please? It'll settle a long standing bet I have with myself. | Why is notation in physics so atrocious? Why did anyone ever criticize quantized gravity? Can Cooper pairs be formed by groups of more than two particles? | You gotta click the link above to get to the AMA :) | It rotates. | You should click the link above to visit the AMA :) |
[
"Simple Questions - June 01, 2018"
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"math"
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"8nt491"
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20
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""
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true
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false
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0.84
] | This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread: Can someone explain the ... | Assuming all the events are independent, you cannot guarantee success after a finite number of attempts. The probability of zero successes after n attempts is 0.99 , and that's never zero for any n. | Interesting question! The effect you have noticed is real. If you choose a real number x uniformly (say, between 0 and 2*pi), then sin(x) is more likely to be near 1 or -1 than it is to be near 0. For a concrete result, notice that sin(x) is more than 1/2 when x is between pi/6 and 5pi/6, and this happens with probabil... | Consider the function f:[0,1) --> S defined by f(t) = e . (I'm thinking of S as the unit circle inside C). | No, this statement has nothing to do with the axiom of choice and you can prove it quite straightforwardly without it. For instance, suppose f:A-->B is bijective. Then for any b in B, there is an a in A with f(a) = b (since f is surjective). Since f is injective, this a is unique. Hence we obtain a well defined functio... | There's lots of little ways (many of which are closely related) in which it behaves differently than other primes, which can cause all kinds of issues in number theory. To name a few (I'm sure I'm forgetting to mention some things): One big one is the fact that [;(\mathbb{Z}/p^n\mathbb{Z})^\times\cong \mathbb{Z}/(p-1)p... |
[
"what is a good blogging site that one can post his notes and other things on mathematics and others see and leave comments?"
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"math"
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"8nrauv"
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13
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"Removed - ask in Simple Questions thread"
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true
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false
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0.76
] | null | Maybe medium? https://medium.com/topic/math | I've never been on Medium much before, except when Reddit links to articles there. Anyway, one of the first things that I stumbled upon was a discussion of cumulative advantage, i.e. the Matthew effect. From the article We like to think in America that most things come down to hard work, but a few lucky (or unlucky) br... | Does Medium have a good way of including LaTeX? | For math explicitly, I doubt anything like that really exists unless you generate interest (like Terry Tao's blog does). You could make your own subreddit or blog page and advertise it with a post here (I'm fairly sure that's within community guidelines), but ultimately if you're looking for comments and discussion, yo... | Reddit. The arXiv. |
[
"Combinations of Sweets"
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"math"
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"8nqnvw"
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1
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"Removed - try /r/learnmath"
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true
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false
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0.66
] | null | Since there is at least 1 of each color we can remove one of each to simplify the calculations. Thus we have 11 sweets that can be in three different colors. Let's order the sweet with all in one color first then all of another and so on. And let's place a little wall between the colors. Now we have 13 objects (11 swee... | I see how I made that confusing. The idea is that if you move the walls you change the color of the sweets. The sweets left of wall1 has one color, the ones between wall 1 and wall 2 have another, and those to the right of wall 2 have a third. Does that make sense? I'm basically rephrasing the problem in terms of walls... | Thank you. I'm a little unclear on the function of the "walls" though as they don't change state. Edit: Forgot to check my working. | Gotcha. | Check out the Schaum’s Outlines. Pick your poison.... |
[
"Any good books or websites full of math problems to solve?"
] | [
"math"
] | [
"8npmyz"
] | [
7
] | [
""
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true
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false
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0.88
] | I'd love it if there were a series of books full of maths problems that go from basic (long division, long multiplication etc) to really advanced stuff that you'd do in university. I dont know if theres such thing as that but thats what I'm looking for Alternatively a website with the same stuff would be good too but i... | I quite enjoyed Professor Povey's Perplexing Problems. Has Maths and Physics problems (still mainly mechanics though) and lots of good probability problems. | https://imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf Edit: wtf why is this so hard to find? There are thousands of books that might fit your criteria. A web search turns up tons of relevant stuff. What part in particular is hard to find? | It isn't really what you requested, but the Moscow Puzzles are quite fun. | Try going to Math Counts or other math competition websites for practice problems. | Project Euler maybe? But it might be to advanced for what you are looking for. |
[
"Yet another question on frequentists and Bayesians"
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"math"
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"8npkqx"
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7
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""
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false
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0.78
] | First, let me take a brief detour through quantum mechanics. There you have a formalism (Dirac's) for calculating and predicting the outcomes of experiments. This uses Hilbert spaces, operators, wave functions, and the Schrödinger equation. Adhering only to the formalism and asking no further questions labels you as a ... | I appreciate your detour, but I don't think it's as similar as you put forward here. Both are based on Kolmogorov's axioms, but (sometimes) do different calculations to answer different questions that in the end attempts at answering a similar overall question. define point estimators While bayesian stats can be done a... | AP Stats is definitely more frequentist than Bayesian | p(model)=1 for that experiment I might be misunderstanding you, but no. If that was the case, you could do the same data collection, test a different model and have two models with 100% probability each => 200% probability total. That's not allowed for probability. Or think about it in a different way: there would be n... | ... Confidence intervals and classical hypothesis tests are based on frequentism ... are ways of getting at a probability p(model | data) ... In a frequentist interpretation the probability is a limit of a repeated process, so p(model | data) is limit rate of some process producing a model provided the sample data is t... | ... p(model | data) (really a shorthand for something like p(parameter >= threshold | model, data)) Ah, I was confused by that shorthand, since the model is generally not treated as the result of a random process. "p(parameter >= threshold | model, data)" still doesn't really make sense to me, but it makes a whole lot ... |
[
"Proof-Based MOOCs?"
] | [
"math"
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"8np76a"
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16
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""
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true
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false
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0.9
] | Hey all, I have some free time this summer I wish to spend supplementing my studies. While I have found many interesting courses on edX and Coursera (such as one on complex analysis), and while they do mention being proof-based (at least in lectures), are the examinations as well? I ask, mostly, as I am unsure of how t... | Notes/HWs and lectures for abstract algebra taught by Benedict Gross at Harvard. | EdX has a linear algebra course called LAFF that does its best to be proof based. At the end of the day though it’s tough to pull off in that environment and the questions boil down to guessing if something is never/always/sometimes true. Still a good course though if you’re interested in implementing LA algorithms in ... | There's http://nptel.ac.in/course.php It's a collection of online courses from some pretty good universities in India, all in English. I used their mathematical stats for the first half a semester because my lecturer was useless. | The Galois theory course on coursera is proof-based. The lectures consist mostly of proofs being presented. In most weeks, you just have multiple choice questions, but there are some assignments where you have to write proofs, too (these are peer-graded) in addition to some optional ungraded exercise. The course goes d... | I enjoy testing environments - it sort of keeps me in tune for the Summer months so it won't be in much of a shock when I return to classes in the fall. |
[
"More efficient way to calculate a satisfying model for a 3CNF propositional formula"
] | [
"math"
] | [
"8noj51"
] | [
0
] | [
""
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true
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false
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0.5
] | I've been working on a way to deal with logic models more easily and I came up with this solution. Because this is an NP-complete problem, I feel like I missed something, but I can't find any errors in my math or logic. Please let me know if you see a mistake! The algorithm to calculate the model works by breaking down... | If you don't backtrack it will be pretty easy to find a counterexample by just running enough random instances of the problem. If you backtrack, then complexity cannot be polynomial (at least not with what you showed here) | Your approach isn't complicated at all. Essentially you just rewrite each x or y or z into several (not x) and (not y) => z clauses. Each table entry is just one or a few such clauses, and the "trying" strategy is still naively finding one applicable clause and deduce something, and repeat the process. It seems there's... | Code it up and try to beat survey propagation on a large problem. In the very unlikely event this works, post the code to github with some runtime stats and ask here again. Much more likely profiling your code will answer why your approach breaks | There is no backtracking, so it keeps this from combinatorially exploding there. That’s what everyone’s been telling me, “if you throw enough at it, I’m sure there’ll be a counterexample.” No one has been able to actually show a flaw in my logic that would allow a counter example to exist. That’s the holy grail I’m lo... | It's you who are underestimating the difficulty of the problem. Unless you can prove that your algorithm is not missing a solution in any case (i.e. means your algorithm wouldn't report opposite result on satisfiable CNF). Otherwise we don't care complexity on a wrong algorithm - in the problem P vs NP, algorithm has t... |
[
"Gergely Szűcs and Søren Galatius, \"The Equivariant Cobordism Category\" [1805.12342]"
] | [
"math"
] | [
"8np23k"
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4
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""
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true
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false
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0.67
] | null | Sure, there are a few motivations that I can think of, but to me it's interesting for its own sake, and I thought about motivations afterwards. I've been curious what the correct genuine equivariant analogues of principal bundles, tangential structures, cobordism, the Pontrjagin-Thom map, and Thom spectra are, and this... | I think I can sort of understand the abstract but Im not familiar with this area so I cant really see what are the implications or connections with anything else. Do you think this is somewhat explainable? I understand (some of?) the motivation comes from TQFT's and the nlab has convinced me that, for example, the cobo... | Rather than TQFTs or the cobordism hypothesis, these authors are primarily interested in understanding diffeomorphism groups of manifolds, specifically homological stability results. You can see how this works in the cited paper GMTW09 or the pioneering paper MW02 , where the non-equivariant story is told. | Was thinking of the same thing for [;Z_2;] and reflection positivity. The [; M = \bigsqcup B \Sigma_A ;] doesn't look to bad to actually compute concretely. | You're welcome! Thanks for your interest in this stuff! |
[
"Are Princeton Lectures in Analysis a good idea to use as an introduction to analysis courses?"
] | [
"math"
] | [
"8nobj9"
] | [
5
] | [
""
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true
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false
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1
] | I'm planning on taking an Intro to Real Analysis class in the fall along with Fourier and wavelet analysis and I am thinking of purchasing these books to study over the summer. Is it a good place to start? | The first book starts with Fourier analysis rigorously, but I would recommend starting analysis the traditional way (construction of , sequences, series, continuity, basic integration etc), and then moving on to Fourier Analysis, etc. Maybe since your Fourier class does not have an analysis prereq, it is more of an app... | Err, definitely not. All the books presume you’ve had a first course in analysis. | No. especially because it appears that you are not at top 10, 20 university, so a first course in real analysis would not be nearly demanding as any of the Stein-Shakarchi books from Princeton. Abbott's is an excellent and mild introduction; but of course, if you wanna impress and stand out from your peers, you can pro... | Personally I like Abbott’s explanations better than any other analysis book, but Rudin has more interesting (and difficult) exercises. If you just want to get a basis, Abbott will probably more than suffice, but if you’re up for a challenge then Rudin (“like drinking from a firehouse”) is the way to go. Good luck! | Weren't they written as a first sequence for undergraduates at Princeton? Obviously they're maybe more on a graduate level, but they are books meant for undergraduates. |
[
"What is the largest number you know, and can you please explain it in layman's terms?"
] | [
"math"
] | [
"8npckp"
] | [
0
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""
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true
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false
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0.42
] | I know Graham's number is very large, but there are much larger numbers that I'd love to know. I have a fascination with huge numbers, because they blow my mind. What's a huge number that you've come across that you can explain to the general audience? Edit: a number that is used in a proof, not something arbitrary lik... | Well if they're busy they probably won't show up. | It might be more illuminating to consider fast-growing functions defined on than to consider any given natural. Rather than discuss Graham's Number, we can consider Knuth's up-arrow notation. Rather than discuss BB(4), we can consider the Busy Beaver function. Rather than discuss TREE(3), we can consider the Tree fu... | Shannon's number, 10 , is a conservative estimate on the number of possible chess games. | The largest numbers I know of that are used in proofs come from the field of reverse mathematics: how little math can you get away with and still prove some proposition? The mathematician Harvey Friedman came up with some propositions that depend on very powerful systems (ZFC+LCA) to prove them, and most of those are a... | Here are some big numbers: Ramsey number Skewes' number hyperoperation Knuth's up arrow notation Conway chained arrow notation Graham's number Ackermann number Fuse number TREE(3) SSCG(3) Busy Beaver number Rayo's number Those are all finite numbers, at least. There's also a long list of really large (infinite) cardina... |
[
"Respect the parallelogram - brutal take down of a stupid math sign"
] | [
"math"
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"6xaqks"
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17
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""
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false
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0.75
] | null | I swear some of these people could probably be given a key, stood in front of a door, and be handed a piece of paper that says "the key you were given works with the door and behind it are riches beyond your wildest imagination", and they would spend the entire time complaining about how they never received any instruc... | They could have a god damn diagram of how keys work, and they'd still complain that nobody taught them how to use the key. First, unless you're rich -- at which point you should hire an accountant -- taxes are stupidly simple. They're made so that every person can do them. They're simple to the point that the majority ... | First, unless you're rich -- at which point you should hire an accountant -- taxes are stupidly simple. It’s more like if you have a salaried job, few dependents, and no other financial dealings taxes are stupidly simple. If you are a private contractor, own your own business, take stock from a startup, live outside th... | I would like some instruction about how riches work. | That's fair. I inaccurately equated complicated income with being rich. |
[
"Does this method work?"
] | [
"math"
] | [
"6x6lt8"
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1
] | [
"Removed - try /r/learnmath"
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true
] | [
false
] | [
1
] | null | But he didn't say he was looking for the limit of f(x,y) as (x,y) -> 0. He said he was looking for the limit of f(x,y) as xy -> 0, and it is absolutely fine to do the substitution that he described to find that limit. The fact that the function has multiple variables is irrelevant if you're just interested in its behav... | Try r/mathhelp or r/learnmath or /r/cheatatmathhomework | you're right. i didn't read carefully enough. | Thanks for the help:) | no that's not the limit of the function. even if that limit u to 0 exists it doesn't mean f(v -> 0) gets where v is the vector (x, y). |
[
"Via /u/paolog, a list on Math.SE of \"'[o]bvious' theorems that are actually false\""
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"math"
] | [
"6x6tzz"
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39
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""
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false
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0.93
] | null | Surprised not to see "If all partial derivatives of a function exist at x, then the function is differentiable at x." | I feel this statement needs enough knowledge to understand that almost everyone who understands it knows that it doesn't hold. | I don't think that this is obvious in the context in which it fails. In fact I think it is fairly clearly false if you understand what a topology is and what a limit is. | [I] have to wonder what's the [o]bsession with ensuring that all [w]ords are correctly [c]apitalized. | Previously submitted and discussed here three years ago , but i felt it worth resubmitting for those who didn't see it then, to demonstrate why we need rigorous proofs in maths. |
[
"Go Yamashita has published a 300 page summary on Mochizuki's Inter-universal Teicmuller theory."
] | [
"math"
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"6x9wsw"
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174
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"PDF"
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false
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0.94
] | null | That's probably because of the Greek letters. | Footnote on pg 6: The author hears that a mathematician (I. F.), who pretends to understand inter-universal Teichmüller theory, suggests in a literature that the author began to study inter-universal Teichmüller theory “by his encouragement”. But, this differs from the fact that the author began it by his own will. The... | get fucking real at least 95% of phd students would look at this like it's chinese unless they are in a very specific field | Worth mentioning that "I.F.", which presumably refers to Ivan Fesenko, is the author of widely publicized articles on IUT (see here and here ), was the co-organizer of two international workshops on IUT, and has made the claim "I expect that at least 100 of the most important open problems in number theory will be solv... | After learning the preliminary papers, all constructions in the series papers of inter-universal Teichmuller theory are trivial (However, the way to combine them is very delicate and the way of combinations is non-trivial). After piling up many trivial constructions after hundred pages, then eventually a highly non-tri... |
[
"I'm taking real analysis in the spring; what can I do to prepare?"
] | [
"math"
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"6x6zxx"
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7
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""
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0.73
] | I did got B/C+s in my linear algebra and differential equations classes, and As in calc. These were at a community college, and most of the classes were focused on computation rather than theoretics. The reason I didn't do as well as I would like is my poor study habits, not doing my homework to completion, and general... | Stop being lazy. Start learning how to write proofs. https://artofproblemsolving.com/articles/how-to-write-solution | Clear the decks in the rest of your life. This is a and requires 20 hours of work outside of lecture per week. Take a light course load, cut back your hours on your part time job, etc. Do whatever you can to enable yourself to make this class the #1 priority in your life. If you don't know how to do formal proofs, lear... | The hard part of Real Analysis isn't so much the material (which is, after all, mostly the same material you already learned in calculus), it's that you have to write proofs and understand quantifiers. Get good at those things and you should have little trouble. | Second this. Also, trying to go as far into Spivak's Calculus as possible. If money is a pressing issue, there's always http://libgen.io . | I would suggest Velleman's as well. It is a very good book, and less expensive. |
[
"Each Constitutional Value Not Let"
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"math"
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"6x5f0t"
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0
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""
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false
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0.36
] | null | I don't know how to tell you this, but nobody can understand a single thing you say. You might have a disorder that causes you to have unorganized speech. Please seek professional help. | There was/is medical corruption tied to courts/with them also with areas's crimes against children, and against elderly, too, blaming others for their failures with English, and as recorded criminally ill stewards of medicine, and of database relationships to our areas, and to all. | Yes, your opinions are manifest in relationship to lie progression coverup styles with much recorded uncharged originally/still. | I'm sorry if what I said sounded like a personal attack. I am just a little confused with what you're trying to say. | I'm saying that people saying they are confused was/is being used to not let databases crimes recorded from being reported. And we've recorded sick natures with our kids. |
[
"Math paper shows large animal populations can quickly go extinct"
] | [
"math"
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"6x5a8c"
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14
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"Image Post"
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true
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false
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0.69
] | null | This happens when people are willing to spend a lot of money to eat rare species. It is extinction via a homoclinic orbit, for which the http://www.sciencedirect.com/science/article/pii/S0022519317302916 | For some reason i dont have access to the articles. What are the differential equations this is generated from? And how are they modelling populations with what looks like a second order differential equation? Everything I see in population ecology is 1st order. | Hurrah for the arXiv and open-access math preprints (paper is mostly unchanged between the peer-reviewed one and the preprint) https://arxiv.org/abs/1703.06736 | I'm paranoid that the article is somehow watermarked, so I won't upload the full thing, but here is the model: http://imgur.com/a/jjrec | Plot doesn't show what seems like the most interesting feature in this context (since OP mentioned "quickly go extinct"), namely the behavior as t increases and population goes to zero. Is there any finite time for which population = zero? |
[
"Why is the Reddit math community so hostile?"
] | [
"math"
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"6x5pos"
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0
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""
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true
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false
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0.41
] | null | Plus all mathematicians prior to the 19th century including Gauss and Euler did mathematics without knowing the epsilon-delta definition of a limit. Yes, becuse those tools where not avaliable to them at the time. That is like saying we should not build houses using electric power tools becuse those were not around whe... | I see /u/duckmath has an alt. | You say that most mathematicians know nothing of physics. Even if they remember very little, almost all will have learned at least basic physics at some point in their education. The parallel you draw between basic math and Latin is not valid - today, Latin is an esoteric, dead language, while math is necessary to unde... | seems intolerant to any opposition to the idea that everybody should know math i've not observed this, personally; but granted, i certainly don't read every thread. Could you please link to a few recent examples? math is one of the best majors i've not observed this either, but then i would hardly be surprised by peopl... | Yet mathematicians REQUIRE 18 year old international marketing majors to memorize and learn epsilon-deltas This is a lie. Mathematicians don't set degree requirements for international marketing majors. If business colleges are requiring their students to take analysis, that is on them, not on mathematicians. |
[
"Necessary and sufficient criteria for the geometry of the gear?"
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"math"
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"6x5qvv"
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24
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0.95
] | In this post you can see that some shapes of the first gear are allowed, and some are not. Can the allowable shapes be characterized? That is, criteria on the first gear so that there exists second gear that will turn smoothly with it? Certainly convex is sufficient but not necessary. My next thought was star-shaped, b... | I just want to say I love this question. | Certainly convex is sufficient but not necessary Eh? A circle is convex but makes for a shitty gear… Also I’d have guessed that not being convex was necessary, because you’d want some teeth and those will break convexity. | You're right. I guess we need to define what "works" means. I agree that if you want to actually rotate the other gear, the first must be nonconvex. I was mostly thinking of situations where the first gear would not turn. I guess there's two versions of the problem, now. | Consider if there was really high friction on the second gear, such that the second gear does not spin if the first gear is not touching it - a rectangle wouldn't work there. I think the criterion you really want is that it can 'pass' the second gear from tooth to tooth. Not that that's definitely impossible with a r... | Y… One question seems to concern the ability to simultaneously rotate without mutual obstruction and the other concerns the possibility to transmit force. If you don’t want to transmit force, convex shapes work fine. But as soon as you do, I think you need at least 3 teeth… Also a rectangle is convex… I guess you could... |
[
"Why is calculus a required subject?"
] | [
"math"
] | [
"6x58sk"
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0
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""
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true
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false
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0.33
] | null | What schools require art history majors to take calculus? | Lmao any engineer will tell you they use every bit of math they learned on a daily basis, also if you are going to ask why does everyone need to have a basic understanding of math then you also have to ask why we have art and history classes forced from 1st-12th grade as most engineers don't need to know what alexander... | Please don't feed the trolls. | Go away | Didn't even think about it, you're right |
[
"Constructing a musical rhythm from successive golden sections."
] | [
"math"
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"6x4vvj"
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0.78
] | null | Hi Boykjie! Thanks for the note. I would post to r/listentothis but it's against the (stupid) rule that you can't post your own material. You're more than welcome to if the spirit moves you. Have a great weekend! | I was expecting something underwhelming, but this is actually quite musically interesting, could really be developed! Maybe not exactly the kind of stuff for /r/math though. Maybe /r/listentothis ? | Nice ! For my taste, it's a little bit all over the place. Maybe 2 second as a base unit interval is too long and 1sec would be enought ? Also, have you tried using it as a pitch ratio ? the g-ratio is approximately a sixth, and it's enharmonic inverse is a third, between the minor and major (6/5 and 5/4). I believe it... | I actually built a four note scale using Golden Sections of an octave. The cent values ended up being: 0 cents, 283 cents, 458 cents, and 742 cents. You can hear the scale at work in a track at http://williamsteffey.com/2017/08/08/what-it-sounds-like/ I know there is another popular way to express Phi as 833 cents. I ... | I know there is another popular way to express Phi as 833 cents. Yeah, its the one I had in mind I beleive. 2 is close to Phi. And 2 / 1200) is close to 2/Phi. The thing is, the golden ratio is the least approximable by an integer ratio, which are consonnant. Phi in music is precisely the opposite of harmony : dissonan... |
[
"Lecture notes for an introductory course on algebraic topology given by John Baez and Derek Wise"
] | [
"math"
] | [
"6x3jh0"
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37
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""
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false
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0.94
] | null | They're cousins! | Shit's about to get real in the weekly topology reading group | Definitely read that as Joan Baez and had to do a double take | thats so cool | *Handwritten notes from the blackboard. YMMV but this is probably not the kind of stuff for independent learning. |
[
"Anyone know the equation to predict the twists of a mobius strip when cut with just information about how many twists the intial strip had"
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"math"
] | [
"6x4ac5"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.81
] | null | I sort of ignored this question when I first saw it, but then decided to think more about what it is asking. I think you're talking about a Moebius band implicitly embedded in three space, i.e. either knotted or unknotted. If you do not care about the embedding, a moebius band with a 1/2 twist is unaffected by twisting... | Cut it thou the center here is a pic | Cut it thou the center here is a pic | https://youtu.be/wKV0GYvR2X8 | Tadashi Tokieda cuts various combinations of loops and Mobius loops - with surprising results. |
[
"Trouble with proofs"
] | [
"math"
] | [
"6x3pi5"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.38
] | Hello dear fellow Mathemagicians, over the last couple of years I have spent a lot of time trying to prove pretty much everything that was shown to me. During school that was often no problem, although I often lacked an idea to start with. Since being in the University, trying to proove any theorems, axioms or just som... | I took a course called "Introduction to Mathematical Rigor." It was very helpful. https://www.math.uri.edu/~tsharland/MTH307/MTH307.html The textbook is free online: http://www.people.vcu.edu/~rhammack/BookOfProof/ Check out: https://math.berkeley.edu/~hutching/teach/proofs.pdf | What courses have you taken so far in University? Generally discrete maths, abstract algebra, or apparently real analysis are the first real intro to proofs courses that most people are exposed to. | Taking a couple hours to devise a proof for a random statement is not necessarily unreasonable. If you're just going through a curriculum, the nontrivial theorems often took years (if not lifetimes) to produce in the first place... Textbook exercises should (usually) be solvable in less time, but that's because textboo... | If I'm having trouble with proving something in particular, and I'm confident I understand all of the relevant definitions, first stop is working with examples. If I'm trying to show structures of Form Y have Property X, I find it useful to come up with a standard example and an example where I think there's no way it ... | Thanks a lot man, I will check that out, hopefully it helps! Have a nice day! |
[
"Favourite Math Youtubers?"
] | [
"math"
] | [
"6x3khw"
] | [
32
] | [
""
] | [
true
] | [
false
] | [
0.87
] | Just looking to get more math videos in my life. Doesn't have to be how to's either, just based on math in someway | Mathologer , 3blue1brown or whatever it is, standupmaths , minutephysics and Looking Glass Universe | What everyone else already said, and I also love blackpenredpen and PBS Infinite Series | numberphile and standupmaths are my fav | James Grime/singingbanana . He is just the cutest! Oh and I guess his videos are also interesting. Dr Peyam also made a channel very recently and his videos on blackpenredpen are really interesting | adding to what's already here...MIT opencourseware videos include full lecture series on calculus, linear algebra, discrete stochastic processes, financial math, etc...Harvard has lecture series on probability, abstract algebra There's a site called mindyourdecisions that does quick math and logic puzzles. THe puzzles ... |
[
"Norbert Blum Has Acknowledged His P vs NP Paper Was Flawed"
] | [
"math"
] | [
"6x5c6v"
] | [
818
] | [
""
] | [
true
] | [
false
] | [
0.96
] | null | It's good that he's finally acknowledged it. I wonder what effect this'll have on the talk he is scheduled to give? | He said it will take a while to formally write up the flaw so I would imagine it will be canceled. | The paper isn’t “fake”, it’s “mistaken”. The author did not intend to mislead | At the very least it will show that this particular approach will not work, which will be useful for further research. | The whole approach is doomed. |
[
"Please i an so frustrated is this not the same thing? I have been right at the correct answer for so long."
] | [
"math"
] | [
"6x3dzu"
] | [
0
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
0.43
] | null | /r/learnmath It is definitely not the same thing. Multiply yours out; you will see that it is different. | Wrong subreddit, /r/learnmath would be better suited for this. However, expand out your answer and you'll see they're not the same. | Ive gotten tons wrong because ive typed 1x and 1y instead of x and y. I hate this. | Thank you. Ill check it out. | Your answer is (y-1)(14y+2) = (y-1)14y + (y-1)2 = 14y - 14y + 2y -2 = 14y -12y - 2 which is not the same as 14y + 27y -2 |
[
"I wonder that Europe and America have private institutions for preparing Olympiad"
] | [
"math"
] | [
"6x1v2d"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.86
] | I always curious about preparing Math Olympiad in Europe and America. Our country has a lot of private academies for Math Olympiad. So, the students who want to enter these academies must finish entire middle school and High school courses during elementary school(I did once. but when I was in middle school, I gave up ... | In America students who participate from the IMO come from schools all over the place. They qualify by taking the USAMO and are trained in a summer program called MOP at CMU. In Hungary a lot of the IMO participants come from a high school called Fazekas Mihály Gimnázium | I am an American student. I competed in the USAJMO (US olympiad for 10th graders and below) twice and the USAMO (US olympiad for 11th and 12th graders) twice, so I think I can answer this. There's no dedicated math olympiad schools (that I know of). Olympiad training mainly comes from buying your own books (although so... | Also, about IMO selection: We do it weird. The current procedure is you take something called the TSTST while at MOP. The best people on the TSTST get invited to take TSTs. The people who got the highest combined score on the TSTs + some other olympiads (including USAMO) get invited to IMO. | alpha af | Thanks! You have a good day too. |
[
"Where to find this article by Hartmanis?"
] | [
"math"
] | [
"6x1lg2"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.81
] | I want to read this article: Solvable Problems with Conflicting Relativizations by Hartmanis. But I can't find it. What is the best place to look for these things (when Google scholar doesn't show anything)? Its probably more compsci related but they don't allow text posts :( | Quick googling turns up many things that cite it. It appeared in the Bulletin of the European Association for Theoretical Computer Science in 1985. No evidence of that journal being online from that time period, so your best bet is to find a university library that has it and request inter-library loan (this assumes ... | Solvable Problems with Conflicting Relativizations by Hartmanis If you google that you will find several things that cite the paper by name. | Where was it referenced from? I can't find any evidence of a paper with that name ever being published. And it's Juris Hartmanis you're looking at right? | Non-Mobile link: https://en.wikipedia.org/wiki/ICanHazPDF /r/HelperBot_ /u/swim1929 | Cool! Didn't know this twitter trick. |
[
"Could someone explain me this? [text on comments]"
] | [
"math"
] | [
"6x0upl"
] | [
338
] | [
"Image Post"
] | [
true
] | [
false
] | [
0.93
] | null | Infinity is an attracting fixed point. | Here 's a good rundown. | So, I started studying dynamical systems and I am a bit confused after this post: I do get what both Julia and Fatou sets are. The Fatou set F(f) of a rational function f: Ĉ --> Ĉ is the greatest open subset of Ĉ (with respect to inclusion), such that if we restrict f to F, the iterates f form a normal family, i.e., ev... | You can realize infinity as a "real" number, at least for topological purposes, by embedding C into the riemann sphere (by the stereographic projection, say) and the image of C will be all of the sphere minus one point which you can take to be infinity. This is a geometric realization of the topological notion of one p... | I wouldn't if surprised if this post was written by a bot... |
[
"[Large numbers] I need some ideas for giving meaning to the significance of a number that is extremely large"
] | [
"math"
] | [
"6x0rxw"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | [deleted] | How did you calculate this? SHA-512 is from the SHA-2 family, which is a completely different algorithm than SHA-1, so it doesn't really make sense to compare them since I believe the Google researchers exploited some specific features of the SHA1 algorithm. A better way might just to be finding the how many hashes/sec... | "pretty small" is an understatement. From a computational complexity standpoint, it's barely distinguishable from 2. It doesn't even take special notation to represent. | Just say that with current technology (and foreseeable future technology), a hash won't be broken until (find the appropriate position at https://en.wikipedia.org/wiki/Graphical_timeline_from_Big_Bang_to_Heat_Death ). | 10 is approximately 2000 times larger than the number of chess positions 10 is approximately 120,000 times larger than the Monster group. | This is assuming protons decay in the first place |
[
"What are some tools/websites for learning undergrad&grad Maths. And also what are some things I can learn in 15 minutes that will prove invaluable."
] | [
"math"
] | [
"6wznws"
] | [
37
] | [
""
] | [
true
] | [
false
] | [
0.86
] | Hello. First of all, this might have been asked before, but after 2 hours of googling which bring close-minded results like "All you need is a good brain and a pencil", I had enough :). We're in 2017, there surely have to be some great hidden gems in the depth of the internet. So, here are the two questions I'm asking:... | I don't really think Khan Academy is good for any undergrad level math. His linear algebra and calculus courses are very basic imo. You might want to check out Evan Chen's Napkin. It's a project where he tries to explain a lot of different facets of undergraduate mathematics. It's not the best piece of literature on th... | If you're doing commutative algebra or algebraic geometry, the stacks project is incredibly helpful. For category theory, ncatlab . | I can understand that. The main issue is that he assumes readers have extensive contest experience. I did so I didn't notice that much, but glancing through again in the first few chapters he makes references to some olympiad problems and some techniques that very few people would learn unless (a) they don't need Napki... | Symbolab and Paul's online math notes are also good websites. | Honestly, if you're planning on learning undergrad and grad math, you're best bet is to read books. |
[
"I'm a professional software developer that wants to go back to college (dropped out) to major in mathematics. What am I in for?"
] | [
"math"
] | [
"6wz4rn"
] | [
3
] | [
"Removed - see Career & Education Questions thread on front page"
] | [
true
] | [
false
] | [
1
] | null | I major in mathematics and there's definitely some harder upper math classes. For me my probability and statistics classes were the worst. Of course it depends on your professors and some math courses just click more for certain people! As long as you put in the work you'll be fine. Good luck! | I'm wanting to major in math because I want to do research in AI (and would like to be prepared for the underlying mathematics) | I'm wanting to major in math because I want to do research in AI (and would like to be prepared for the underlying mathematics) | Why not just do a CS undergrad and take the necessary math/stats for machine learning? | I suppose that would be best |
[
"Everything about Model Theory"
] | [
"math"
] | [
"6wzs6z"
] | [
71
] | [
""
] | [
true
] | [
false
] | [
0.96
] | Today's topic is . This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week. Experts in the topic are especially encouraged to contribute and participate in these threads. Next week's... | My area of study is "homogeneous structures" which studies a very special kind of model, a Fraisse structure. I use model theory in a much more combinatorics focused way. At a high level, a Fraisse structure is an object defined using some number of relations with (countably) infinitely many points, and the object is "... | Did you mean to sticky this? Also, for topics like this where some of us regulars know enough to write a "one-page" summary, it might be better in the future to give us a heads up beforehand. I don't have time right now, but I'd have been willing to do a high-level overview of model theory. | Recently, model theorists have made tremendous breakthroughs in algebraic geometry (broadly defined). The work of Pila and Hrushovski definitely come to mind. I have seen several expositions which put the model theory in a back box. But then I am not a model theorist. Can someone explain precisely what makes model the... | The standard model of arithmetic is the usual natural numbers we all know and love. There's several ways it can be characterized. Let me give a few. is the unique model of arithmetic so that every element has finitely many predecessors. is the unique model of arithmetic so that its arithmetic operations are computable.... | I'd be happy to help. For that one, I think what I wrote a while back is probably enough of an intro. Finding it is easy, it's the only gilded post I have. And honestly, I think anyone would struggle with trying to write intros to such a variety of different fields on a regular basis. The last few, I would've had no... |
[
"When Pi is Not 3.14 | Infinite Series | PBS Digital Studios"
] | [
"math"
] | [
"6wzn7f"
] | [
11
] | [
""
] | [
true
] | [
false
] | [
0.68
] | null | Always, because pi is 3.14159.... You can't truncate a number and expect it to remain the same, right, /u/mybirthdaye ? | That is worse than what got linked to badmath. Wow. | That is worse than what got linked to badmath. Wow. | He's right though even though he's a crank. The quote above is incorrect. He said "many equations of physics" instead of "many digits". Pi appears so much partly because circles are so apparent in nature. Maybe that's still wrong, but I agree with that statement. | This thread. |
[
"Question on disk and washer method"
] | [
"math"
] | [
"6wyss0"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.6
] | I'm writing a paper on the volume of a torus using disk, shell, and washer methods and im a bit lost. What's the difference between the disk and the washer method in the case of a torus? When i use the disk method, the cross-sectional area is itself a washer and so i end up doing the exact same steps for both the disk ... | The disk method is inapplicable. Washers for shapes with a hole, disks for shapes without. | Hmmm that actually makes sense.. when i used the disk method i ended up getting a washer cause the cross section of the torus is just a circle with a hole in it, thank you man | I am not familiar with the disk washer method. But here is a rough idea. You take the torus and cut it into very thin cylinder. if A is the area of the cross section of each cylinder (probably this is the disk) and dx is the thickness then the volume is Adx. Now the total volume is \int A dx. integral over what? Well ... | Yes those steps i am familiar with. My problem is with the naming and the difference between methods. Thank you though | These aren't standard names. These are just terms that your teacher or textbook is using to explain what the cross-sections look like. |
[
"Highschooler looking for feedback/suggestions on a math essay idea"
] | [
"math"
] | [
"6wygmo"
] | [
12
] | [
""
] | [
true
] | [
false
] | [
0.78
] | [deleted] | I think you could definitely write a 3000 word paper on the construction of the reals, provided you talk about different methods and the history behind each one of them. Then, as you mentioned, you could write about how these constructions allow one to show \pi a real number, etc. Maybe even adding some discussion on t... | I'd totally go for your original idea. I mean, I tend to have the opposite problem - my essays always end up too short because I don't have enough to say. I envy you if you're worried about going overboard. the Eudoxus Reals. | You're not meant to actually talk about the history of whatever you're writing about for its own sake with the math EEs. Perhaps in passing but you are meant to really focus on developing the mathematical ideas. | The people who grade the essays have to pretend they know nothing outside the syllabus This is only a requirement for the Math IA--not the EE. Making an assumption of "nothing outside the syllabus" wouldn't work for the EE since there are people ranging from Math Studies to Further Maths. I personally did my math EE on... | The people who grade the essays have to pretend they know nothing outside the syllabus This is only a requirement for the Math IA--not the EE. Making an assumption of "nothing outside the syllabus" wouldn't work for the EE since there are people ranging from Math Studies to Further Maths. I personally did my math EE on... |
[
"Do stacks, sheaves, schemes, sites, toposes, and other fancy machinery have anything to do with nice objects like conics, cubics, and quadrics?"
] | [
"math"
] | [
"6wxlg5"
] | [
46
] | [
""
] | [
true
] | [
false
] | [
1
] | I'm working through "Conics and Cubics" by Bix, and "Geometry: A Comprehensive Course" by Pedoe. I enjoy the concrete calculations that give me insight on beautiful geometric objects. For example, I am in awe of the fact that given two conics in different planes of the affine space with two common points, and a point n... | You're intrigued by classic geometry because you understand it and you haven't run up to its limitations yet. It's all new and sexy. But it's been done. Yes, it's useful under specific conditions, but those conditions limit the amount of novel work that can be accomplished. It's like seeking to make a physics career ou... | Modern algebraic geometry was ( and is ) inspired in the study of such objects, but for different reasons it has been necessary to develop more abstract and broad objects, and while the original super geometric picture might not be obvious, it is still present. People still do 'classical' algebraic geometry in some sen... | This is very true. I would add that on a personal note, I did not see the point of some of this abstraction a few years ago, and now I find some of it very interesting. A lot of these ideas are only interesting (to me) when someone shows you the right perspective on them, or the critical example that they enable you to... | OK here is another answer, the Bezout theorem in its simplest form says that two curves in the plane of degree m, n meet at mn points if you count multiplicity. But it is only true if you use complex coefficients and work in the projective plane. Now, you have to say, what is a definition of a curve in the projective... | The conic section is a great object to illustrate the purpose of stacks. A conic section may be characterized by its eccentricity. If e=0 you have a circle. If 0<e<1 you have an ellipse. e=1 is a parabola, and e>1 is a hyperbola. So the space of possible eccentricities is the real half line [0,∞). If we assemble all th... |
[
"Lost Turing letters just discovered."
] | [
"math"
] | [
"6wwxm3"
] | [
26
] | [
""
] | [
true
] | [
false
] | [
0.92
] | null | Interestingly the collection contains a papyrus scroll signed by Turing advocating the use of 60 symbols in a Turing machine tape alphabet. It makes sense because trigonometry was used a lot in the war. | Turing machines can't represent/operate on real numbers to full precision. NJW was right all along!!! | https://www.youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ | NJW ? | Will Numberphile do a video about these? |
[
"Irrational Number Part 1"
] | [
"math"
] | [
"6wxxhw"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.27
] | null | This video is wrong. Rational numbers are NOT exactly the numbers that have finitely many digits. For example 1/3 = 0.3333... is rational. The sum of two irrational numbers is NOT necessarily irrational. For example π and -π are irrational, but π + -π = 0 is rational. | "Closed minds"? You mean: "basic desire to be correct" | 4 pi. I don't doubt you taught, I spend the first month of every calc one class undoing the bullshit people like you do. | I am not trying to say the definition in the video. I know the definition. Buddy rational numbers are the ones where you know where the number ends. Clearly you know the definition, given that you've given an incorrect definition twice; once in the video and once in a reply stating that you're wrong, affirming that you... | Buddy rational numbers are the ones where you know where the number ends. No, that's not true. A simple glance at any good online resource would tell you that: In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator ... |
[
"Mathematicians, how important was math to you in gradeschool?"
] | [
"math"
] | [
"6wwkk9"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.89
] | I'm curious to know how math impacted your life at an early age. Did you have someone who ignited your interest, was it not even on your radar, what? I'm asking in particular because I have a 7 year old whose life is numbers. He's getting nothing but basic addition and subtraction in school, and every year I'm told tha... | I didn't fall in love with math until I was about 18, and I was only exposed to higher math because I needed it for my CS degree. You should do everything you can to help him pursue his passion. Math a big deal, and there's no reason to limit his potential (especially if he's doing well socially). It's not often that a... | No need to worry too much. Throw the following book at him and let him burn some hours. https://imaginary.org/sites/default/files/5to15_en_gb.pdf | I'm sure those teachers are wonderful people, but they're part of the reason the US is 38th in math . Whether they think it's important is irrelevant. Is it important to your son? | You could try looking for math circles in your area. Those are social events where someone with math knowledge leads a group discussion about some interesting math with kids. They're very interactive and very social, as group work and discussing solutions is a big part of the circle. I attended them in high school, alt... | Schools can be tricky with gifted kids. Out of all my friends from high school (most of which attended gifted schools) who I know from math, none of them felt satisfied with their school's way of doing math. These were kids from different different states and cities, too. The standard approach by school's is to just pu... |
[
"Why is this wrong?"
] | [
"math"
] | [
"6wwhx0"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.42
] | I had the following thought 9 is the largest 1 digit number 99 is the largest 2 digit number 999 is the largest 3 digit number This trend holds true for all multiple digit numbers, no matter how many digits 99<99.1 99.1<99.9 99.9<99.91 99.91<99.99 This trend holds true no matter how many decimal places are added Ergo, ... | You are working with garbage if you start throwing an infinite strings of digits to the left of the decimal point. Every real number lies between two integers, so once you start writing stuff like ....999 (infinitely many 9's to the left as some kind of "limit" of 9, 99, 999, and so on), you are NOT working with real ... | Yeah, of course. You can't just write down a definition and assume it's well-defined without proof. If ...999.999... is a number, and place value arithmetic works the usual way, then we can subtract .999... from it to obtain ...999, which should also be a number. You can verify yourself that it's the additive inverse o... | As such, infinity is capable of being defined as 99(repeating infinity).99(repeating infinity). Gonna need a proof of that sir | A proof for a definition? | Repeated nines after the decimal point has a definition in terms of limits. Repeating left doesn't (unless you work with padics but then it will be finite and repeating after the decimal won't make sense). |
[
"Scaling a Timeline"
] | [
"math"
] | [
"6ww710"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.8
] | I want to make a timeline of world history for my kids to add events to as they learn about them, I have a crazy idea to have it wrap all the way around the inside of my house: going in and out of rooms, the whole works. As I started to measure and think about what bit of wall would represent each year I realized somet... | You probably want to use something roughly like a log scale, though maybe you want to at some point switch to a constant scale for the most recent events. First you need to figure out how much total length you have total and what kind of scale you want for the earliest and latest ends. Then you can try to fit an approp... | https://xkcd.com/1017/ You could do something like this. | Wow, there is an xkcd for everything, I'll try it. It even links to a spreadsheet I can mess with! | The total length shouldn't matter though right? I figure once I get the proportions right I can fit it to any length, and if I can't get proportions to make sense, then I don't need to waste the time measuring my whole house. I thought what I was doing was roughly a log scale (each year equal to the last year times a c... | Image Link Mobile Backward in Time People tell me I have too much time on my hands, but really the problem is that there's too much time, PERIOD. Comic Explanation This comic has been referenced 7 times, representing 0.0042% of referenced xkcds. xkcd.com xkcd sub Problems/Bugs? Statistics Stop Replying Delete |
[
"How is SHA-256 not reversible? I.E. Why couldn't you find all acceptable values for bitcoin hashes by reverse-engineering the starting bytes?"
] | [
"math"
] | [
"6ww6lh"
] | [
12
] | [
""
] | [
true
] | [
false
] | [
0.88
] | null | Hashing algorithms are not unreversable, just often designed to be computationally expensive to reverse. In most cryptographic situations, the gold standard is that the algorithm is designed in such a way that no technique to attack it is better than a straight up brute force search—which is computationally expensive a... | /r/crypto is probably better suited to this particular question, however let me give it a whirl. You're right. You could. It would take multiple universes to do it though. SHA-256 has (ostensibly) 256 bits of output, which means there are 2 different possible outputs. 8x GTX1080's can perform about 23012MH/s, which ... | If I understand your confusion correctly, you're asking why you can't just do each step of the algorithm in reverse to reverse the entire algorithm. If I start with A, do 10 computations, and get B, why can't you, given B, undo the 10th one, then undo the 9th one, and so on until you undo the first one and recover A? A... | Thanks for the clarification. How is it possible to design an algorithm with no method faster than brute force? Is O(n (algorithmic computational difficulty) vs. O(2 (brute force difficulty) for values of n less than 997 a valid structure in which to create a "gold standard" algorithm? Is my thinking along the right t... | When SHA256 is computed, the input message is first expanded from 16 32-bit words to 64 words. All the bits in the first 16 words have some influence on the bits in the later 48 words. So now you have this very large internal message. Each word of this expanded message is iterated over with a function that has a 256-bi... |
[
"Help me screw with my buddy"
] | [
"math"
] | [
"6wvpfa"
] | [
0
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
0.44
] | null | Weak cheese. /r/homeworkhelp | Back in my day, we used to have to pay real money to cheat! You know, find the kids playing Magic cards and pay those bastards! This a poor attempt at getting a problem solved, youngin' | Not really, it should just be -11cos(x) - 8ln(cos(x)) | Oh man, thanks. Just out of curiosity, is this a hard question? | I ain't lyin boss. Honest to god. School isn't even starting for me yet! I tried putting it in wolfram alpha and I have no idea if it's the right answer or not, embarrassing to say https://imgur.com/gallery/lOTvK here's some proof. |
[
"What's the point of memorizing a bunch of integration techniques if most models/functions that describe real world phenomenons can only be integrated numerically?"
] | [
"math"
] | [
"6ww69i"
] | [
18
] | [
""
] | [
true
] | [
false
] | [
0.83
] | null | Integration has a lot of uses in areas other than numerical models. Most of (theoretical) physics, for example, uses a wide range of integration techniques. | But when OP is not interested in theoretical physics why the heck do they still teach these things to him ??? He will learn something which he will never use. And as we all know, learning things is bad for your health! | Even in numerics, understanding methods of integration can be useful in making an algorithm faster. What I have found to be less useful is methods of solving differential equations (which is similar in nature). | To a mathematician, u-substitution, integration by parts and whatnot aren't just techniques to integrate specific functions, they're general and powerful theorems. For a very simple example, consider how you'd go about verifying that gamma(n+1) = n*gamma(n). | Pretty important for the theoretical aspects as well. In PDE and functional analysis the definition of the weak derivative is done through integration by parts. |
[
"Question about convergent improper integrals."
] | [
"math"
] | [
"6ww1jn"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.76
] | Suppose you have an improper integral evaluated at zero and infinity with an integrand f(x) that is convergent. Again suppose that there is another convergent improper integral evaluated at zero and infinity with an integrand g(x). Let f(x) = g(x) at most a countable number of points. Is the above information enough t... | We are speaking of integrals, not numbers. It's not always true that Int f(x)g(x) dx = Int f(x) dx Int g(x) dx, in fact that's very rare. | That won't fix it. Explaining in symbols is messy, but just think of the functions 1/sqrt(x) and 2/sqrt(x) on [0,1] and then on [1,2] make them smoothly go down to zero then stay zero from 2 on. The only fact like this I can think of that is always true is that if f(x) and g(x) are functions so that Int |f(x)| dx and ... | No. Consider f(x) = 1/\sqrt{x} for 0 < x < 1 , and 0 otherwise. Let g(x) = 2/\sqrt{x} for 0 < x < 1 and 1/x^2 for x \geq 1 (and 0 at 0 ). Then these functions are only equal at 0 , but their product is 2/x on the interval 0 < x < 1 , which is not integrable. | /u/trent1inventor , if you want to learn more about this, I recommend looking up "integration by parts". It's a useful trick that tells you how to integrate the product of two functions, and its derivation/proof is pretty damn clever. Succinctly, integration by parts tells us that for functions u and v, Int u * dv = uv... | What if we add the requirement that both functions must be continuous along the entire domain of integration? |
[
"is their a modernized version of Euclid’s Elements?"
] | [
"math"
] | [
"6wvcra"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.67
] | My math class is reading it and going over it in class. I'm having a bit of trouble reading the text in the propositions. any links and or recommendations are welcomed. Thanks. | Part of the problem is that some of the proofs in Elements are wrong/have hidden assumptions, as in the conclusions do not follow from the postulates. An example of this is discussed here . | If you don't mind a Java-based version, here's a nice interactive version: https://mathcs.clarku.edu/~djoyce/java/elements/elements.html | Wasn't the assumption at the time that the reader would actually draw the construction on a piece of paper? I get that it doesn't meet modern standards of rigor, but it also wasn't really trying to. "You are doing this on a piece of paper" doesn't even have the form of an axiom... but it does mean that that point is go... | I think I saw an expensive Kickstarter version as a thread on here some time back - it's pretty nice but I can't find the link E: Found it lol https://www.kickstarter.com/projects/1174653512/euclids-elements-completing-oliver-byrnes-work | Not quite what you want but this is a YouTube channel going through the Elements. |
[
"Great videos for a third grader who loves math?"
] | [
"math"
] | [
"6wv7s7"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.67
] | Hey guys, I'm having a bit of a tough time and I'm hoping someone who is an educator or just loves teaching children about how cool math is can help out. Since I just got my degree in mathematics recently I've been the 'math guy' at my job (which has nothing to do with math) and we just brought on a woman whose child i... | Maybe look through the videos by Numberphile and ViHart. Not everything on those channels is appropriate for elementary schoolers, but some of them would be. | PBS kids show Cyberchase. Enjoy! Ps. Gilbert Gottfried voices the bird! | Donald Duck in Mathemagic land. Pretty old but sparked my interest in math when I was young. | This was my favorite show as a child! I still enjoy watching it (though it does feel quite childish). | Thanks! I love the stuff from Numberphile but I will definitely have to sift through it a bit. Stuff like the rock paper scissors video though I'm definitely going to add. And ViHart has some great ones as well! |
[
"Are there any applications of combinatorial Game theory?"
] | [
"math"
] | [
"6wv1rt"
] | [
16
] | [
""
] | [
true
] | [
false
] | [
0.79
] | I am intersted in Combinatorial Game Theory as it is offered in my university but I have looked through the Web and haven't really found other applications besides computer science and games (like board games and such). Are there other applications? | Construction of the surreal numbers. | Ehrenfeucht–Fraïssé games and pebble games are used in mathematical logic to show that certain properties of mathematical structures cannot be expressed as formal sentences. For example, you can use them to prove that no sentence in first-order logic can distinguish connected graphs vs non-connected graphs. | I still don't get this. | Lexicodes are a class of error correcting codes that were derived from combinatorial game theory. They were developed by Conway and Sloane, among other game theorists. | Basically the surreal numbers are the part of the objects manipulable under combinatorial game theory that behave like the real numbers (for the most part). This is a gross simplification (it's possible to extend addition and multiplication to the full collection of games, but - for example - you can't guarantee that e... |
[
"Don't Fall for Babylonian Trigonometry Hype"
] | [
"math"
] | [
"6ww2n9"
] | [
393
] | [
""
] | [
true
] | [
false
] | [
0.92
] | null | But what about 1/4? That’s 0.25, which terminates, and yet Mansfield doesn’t consider it an exact fraction. And what about 1/10 or 2/5? Those can be written 0.1 and 0.4, which seem pretty exact. How does she figure this? As far as I can tell Mansfield never anywhere claimed or implied that such decimal fractions aren’t... | I like this paper demonstrating that a Sumerian document calculates (4/3) for the purposes of compound interest. The English in the paper isn't the best though. | That reminds me of the medical researcher who "invented" the trapezoidal rule for estimating the area under a curve. It was discussed in this subreddit , stackexchange , and doubtless many other places a few years ago. | Wildberger (co-author of the paper) is a known crank. I don't understand why journalists who report on this don't take the five minutes it takes to research his name. | One of the problems in all this is that people who can read cuneiform don't typically know much about trigonometry. I once collaborated with a friend (now deceased) who was an Egyptologist. He was trying to decipher a math papyrus, with examples eerily similar to those found in middle school textbooks. (It dealt with s... |
[
"Wtf"
] | [
"math"
] | [
"6wua1h"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.14
] | null | Because of the reason already given to you. Go to /r/learnmath . This is not a homework forum. | IT was asking for a simple calculation. Please see the sidebar, copied below. Homework problems, practice problems, and similar questions should be directed to /r/learnmath , /r/homeworkhelp or /r/cheatatmathhomework . Do not ask or answer this type of question in /r/math . If you're asking for help learning/understand... | Did you read the sidebar? | It's either could or could , but never could . See Grammar Errors for more information. | It's either could or could , but never could . See Grammar Errors for more information. |
[
"I made a complex function grapher - please tell me what you think!"
] | [
"math"
] | [
"6wubc1"
] | [
39
] | [
""
] | [
true
] | [
false
] | [
0.87
] | null | Just use the Taylor expansions :) | I guess it doesn't do sines, cosines, exponentials, or logarithms? | Not yet, but I am planning on adding support for those functions. I wanted to get some feedback on the basic functionality before going any further :) | Could somebody please explain this to me? I'm an engineering student, my only math courses have been calculus through multivariable, and an ODE course. I know what complex numbers are, can do arithmetic with them, yadda yadda yadda. What I'm confused about is what the variable z means in this context. I assume it's a c... | Each complex number z corresponds to a point on the plane. If you do something to each point (i.e. if you f(z)) then you get another set of values. These may represent a 3d surface (e.g. a wave ) and if you don't want to plot a 3d graph you can represent the vertical displacements with shades and colours, like a contou... |
[
"Rationalizing radical fractions"
] | [
"math"
] | [
"6wtrsq"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.4
] | Hey reddit math people, maybe somebody here knows the answer to this. In a review of some old stuff (reviewing for calculus) I ran into this question: Rationalize the expression and simplify: (root(4+h) - 2)/h The answer here was given as: 1/(root(4+h)+2) Anybody know why the bottom expression is considered rational an... | Go to /r/learnmath . Also, probably a typo, I've never seen a source prefer radicals in the denominator. That said, it doesn't really matter so long as you understand how to manipulate fractions like that, and how to go from top to bottom or bottom to top whenever needed. | In Calculus you'll evaluate the expression as h goes to 0. In the first expression you get "0/0" as h->0, which can't be determined. In the second expression, you can see the expression goes to 1/4 as h->0. | It’s not the “best final version”, it’s just a particular way of normalizing the expression, which can sometimes make things easier or sometimes harder, depending on what you want to do with it afterward. As far as I can tell the main reason to always normalize such expressions in a class setting is so that teachers ha... | You'd want to go the other way, so that the numerator is irrational and the denominator is rational. The key observation is that if you have x +a, you can multiply it by x -a and remove the square root. Do this to numerator and denominator and you can get square roots in only one of them. It's just a manipulation tr... | "Rationalizing" an expression, at least in high school math textbooks, does typically mean to rewrite the expression with the irrational part in the numerator. |
[
"Anyone know any rigorous books that revisit elementary arithmetic/algebra?"
] | [
"math"
] | [
"6wtk6u"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.79
] | [deleted] | The first few chapters of Tao's Analysis I. | grundlagen der analysis by Landau | Mathematics for Elementary Teachers by Beckmann | Are there any prerequisites? Or is it like Number Theory - not many prerequisites but insanely hard? | Are there any prerequisites? Or is it like Number Theory - not many prerequisites but insanely hard? |
[
"I need help understanding the series I created."
] | [
"math"
] | [
"6wrfmo"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
1
] | [deleted] | Your sequence (not series) only includes numbers with a finite decimal expansion. This misses a lot of rationals, not to mention every irrational. | 0.333... will never appear in your sequence. Nor will sqrt(2). Your sequence contains numbers with as many digits as you want, but none that actually has infinite digits. | It's all good. As long as you don't title your post "why Cantor was wrong" people will usually help you. | It's doing all the numbers n*10 then n*10 then 0.1+n*10 ... can't that hit every number at aleph 0? | Yeah, true. Sorry for wasting your time. |
[
"math for research in machine learning"
] | [
"math"
] | [
"6wqo9w"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
0.85
] | [deleted] | ML is mostly applied statistics, so that's probably the most important. Algorithms and Complexity is also useful, as it informs what is and is not learnable in various contexts. Numerical analysis/numerical linear algebra is also important, as the implementations of most ML algorithms boil down to doing computations ... | Advanced classes in Optimization, Statistics and Numerical Analysis | Manifolds (which I'm assuming is some kind of differential geometry course) and functional analysis aren't totally useless in machine learning, but their relevance largely comes from the areas where they intersect topics like probability, statistics, algorithms, complexity, and numerical analysis. If you've already co... | Advanced classes in Optimization, Statistics and Numerical Analysis Doesn't functional analysis also play a role in the theory of ML ? | so taking manifolds and functional analysis (something I'm quite interested in) won't be very useful? |
[
"Why more physics can help achieving better mathematics"
] | [
"math"
] | [
"6wqc9o"
] | [
45
] | [
"PDF"
] | [
true
] | [
false
] | [
0.85
] | null | When linking to arxiv, please link to the summary page and not to the pdf. It would be greatly appreciated. | Abstract for the PDF avoiders: In this paper, we discuss the question whether a physical “sim- plification” of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these simplifications often lead to worse mathematical pr... | https://arxiv.org/abs/1708.07735 | I rather like this paper, we are always taught to use the simplest model possible but I hadn't considered that using higher order terms lead to more rigorous and perhaps broader solutions. Thanks for this, quite an interesting read. | Thank you for saying it. I really wish people would do this, especially since arxiv has such a useful landing page for each article. |
[
"What is a proof?"
] | [
"math"
] | [
"6wq01a"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.64
] | null | A proof is a proof. What kind of a proof? It's a proof. A proof is a proof. And when you have a good proof, it's because it's proven. Former Canadian prime minister Jean Chretien | And that's the point of the article, so much for reading the link before commenting on it. | You beat me to it. Obligatory video: https://www.youtube.com/watch?v=TLmUJCCKBTk | I'm pretty sure Youtube truncates when a video doesn't end perfectly on a second rather than adding a few milliseconds of silence. Really annoying because all of these short quote videos cut off the last couple of words. | It's okay, I did make the joke because it sounds like he's talking about proofs. I should've given context, it's one of the most famous blunders by a Canadian politician in recent history so I'm used to people around me knowing it (I'm Canadian). |
[
"twin numbers and the relation with number 6"
] | [
"math"
] | [
"6wpytd"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.58
] | I have found a new characteristic of twin number that the sum of the twin number minus the sum of next twin number is always divided by 6 not only the number between the twin prime is divided by 6 , this applied to all twin numbers except numbers except of 3 - 5 and 5 - 7. example: 5 + 7= 12 and 11 + 13= 24 24 - 12 = 1... | This kind of stuff is so exciting until you take an intro number theory class and learn modular math lol | If p, p+2 are prime and p > 3 then p is odd and congruent to 2 mod 3. So p is congruent to 5 mod 6. So p + p + 2 is always congruent to 5 + 5 + 2 = 12 mod 6. | Modular math is awesome though. They reveal extremely deep relationships between numbers. | Take some number p, it can be written as the sum of a multiple of 6 and another number, so p=6k+a, where 0<a<6. If a=2, then p is even, so it is not prime, If a=3, then p is a multiple of 3, so it is not prime, If a=4, then p is even, so it is not prime. So a prime is either 6k+1 or 6k+5. Thus, twin primes are always o... | All primes other than 3 and 2 are of form 6n ± 1. Thus, if you happen to find twin primes, one is 6n+1 and one is 6n-1. 6n+1 + 6n-1 = 12n. Six divides 12n. |
[
"The ultimate sequence / function"
] | [
"math"
] | [
"6woc9q"
] | [
0
] | [
"Removed - ask in Simple Questions thread"
] | [
true
] | [
false
] | [
0.41
] | null | Well, it looks neat, but I gotta say I don't understand what it is you're trying to do with this. What does this function express? What makes it an "ultimate" function? | Can you figure out how to make it use e instead of cos? Do you know what the difference between a function and a sequence is? "Sequence" has a defined meaning, and I don't think it applies here. | It could be this: https://en.m.wikipedia.org/wiki/Euler%27s_formula | Non-Mobile link: https://en.wikipedia.org/wiki/Euler%27s_formula /r/HelperBot_ /u/swim1929 | It's a function that can combine other functions together, you can combine many of them if you alter the function. Many more sequences can be generated through this method of combining sequences. The general term also doesn't include any imaginary numbers and whatnot I think that this make making functions a lot easier... |
[
"3,700-year-old Babylonian tablet shows Greeks did not invent trigonometry - \"not only contains world’s oldest trigonometric table; it is also the only completely accurate trigonometric table\""
] | [
"math"
] | [
"6wogm2"
] | [
0
] | [
"Removed - repost"
] | [
true
] | [
false
] | [
0.3
] | null | Oh for fucks sake. Can we please stop posting this bullshit? | Discussion post: https://www.reddit.com/r/math/comments/6vu0ty/new_research_shows_the_babylonians_not_the_greeks/ | You go ahead and feel free to not post links you find interesting, which have never been posted to this subreddit before. THAT's the way to improve the Internet! You've nailed it; congratulations. | There have been posts about this twice since friday, just the telegraph's version wasn't posted. It is also not the "only completely accurate trigonometric table," that's really misleading. | twice since friday hooooly shit that's more coverage than cnn gave muh russia |
[
"Clarity regarding wind speed, geometric growth,. exponential growth"
] | [
"math"
] | [
"6wjzk9"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
1
] | [deleted] | The way I understand it: Geometric growth corresponds to the growth of a geometric sequence or series. As you may see, this looks like exponential growth, but it is typically used in discrete settings (though it's not unheard of to use it synonymously with exponential growth). Quadratic or polynomial growth in general ... | Is your Google broken? | To really get at your question, though, consider how the wind applies some pressure (force/area) proportional to its speed across the sail. | You need r/physics or someplace that specializes in aerodynamics. | The force is an extremely complicated phenomenon arising from the different possible behaviors of air as it flows around an object. However, for relatively high speeds, the force is approximately proportional to the square of the speed, i.e., it increases quadratically. An exponential (or geometric, which is the same t... |
[
"What Are You Working On?"
] | [
"math"
] | [
"6wkd5c"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
0.94
] | This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on over the week/weekend. This can be anything from math-related arts and crafts, what you've been learning in class, books/papers you're reading, to preparing for a conference. All types and levels of ... | LPT: killing the kids outside your classroom is just as illegal. | Getting ready to pass my last two required courses for the bachelors tomorrow. It'll all be over in 15 hours, so I'm a bit nervous. | Not killing the kids in my classroom. | Trying to solve some exercises on Algebraic Topology. I'm struggling a bit (an understatement, I'm afraid). In one exercise, you need to prove a property of a direct sum of groups in which one of the terms is a quotient between the kernel of a group homomorphism and the image of another homomorphism, but those homomorp... | Writing up proofs for a couple combinatorial identities. ( These ones but generalized to noncommuting x'es.) |
[
"Equation for simple math problem"
] | [
"math"
] | [
"6wjv2s"
] | [
0
] | [
"Removed - ask in Simple Questions thread"
] | [
true
] | [
false
] | [
0.25
] | null | thanks for the instruction. I was on a mobile and didn't see the sidebar. I have posted to ask /r/askmath | Read the sidebar. | Don't understand your reply. What sidebar? | Maybe you're on mobile or similar and cannot see the guidelines. Among those: If you are asking for a calculation to be made, please post to /r/askmath or /r/learnmath . | The sidebar of this sub. |
[
"Algebra read left to right"
] | [
"math"
] | [
"6wke86"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | h ( g ( f ( x ))) : x then f then g then h ( b – a ) : from a to b ; in vector spaces the vector going from a to b ( b / a ) : again from a to b ; in complex plane the scaling and rotation mapping a to b Essentially that is how I've come to read my equations upon deciding it insane to keep on the old way where everythi... | The notation "f(x)" seems to come from the way we say (in European languages, at least) "the f of x" rather than "x's f" or "of x its f". This is a quirk of natural language, not of mathematical notation. People have tried turning the order of composition around (and writing xf or x instead of f(x)); it only ended up c... | Image Mobile Standards Fortunately, the charging one has been solved now that we've all standardized on mini-USB. Or is it micro-USB? Shit. Comic Explanation This comic has been referenced 4776 times, representing 2.8623% of referenced xkcds. xkcd.com xkcd sub Problems/Bugs? Statistics Stop Replying Delete | Herstein? | The most annoying thing is that commutative diagrams get written in the opposite way from the algebraic notation. | And thus, not wanting to meddle with how it is written, i thought of limiting myself to the way it is read. And reading right to left here and there would merely be a habit to form. I think it helps and that's that. |
[
"Do you visualize maths in colour?"
] | [
"math"
] | [
"6whgmc"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.6
] | When you guys visualize graphs, shapes and such in math, are they in colour? For me personally it's completely colourless, like not even grayscale; it's as though the colour "information" just isn't there. Would be interested in the different answers I get. | No. | Well when doing analysis I usually don't see green, but algebra has always had a distinctly not-red to it for me | Would you care to expand on that? How exactly do you not see math in color? What sort of colors do you not see? | I do see abstract things in color. For shapes, it's really any color as long as it's filled. For numbers though, there's a specific color for each going as follows: 1- black/dark blue, 2- beige/yellowish, 3- bright red, 4- blue, 5- bright orange (think Home Depot), 6- beige/gray, 7- brown, 8- yellow green, 9- black, 10... | As someone who is interested in graph theory, I visualise some graphs with colored vertices. This is because χ, the chromatic number of a graph, is very important. I have certain special cases, like the 3-coloring of the Petersen graph, memorised. So I always picture it in that color configuration. Other graphs, no. |
[
"An interesting question about additive subgroups of R^(n)..."
] | [
"math"
] | [
"6wh7sg"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.58
] | Show that if any additive subgroup of R contains any non-degenerate interval (meaning the end points aren't the same), the subgroup is all of R. : State and prove, in as much generality as possible a similar result for R ; that is, a result of the form: "If an additive subgroup of R contains X, then it is all of R ." T... | There is also a generalization of this to structures other then R . Namely, the following is true: Any connected topological group is generated by any open neighborhood of the identity. | You can actually get that a connected topological group is generated by any open set just by translating. | Take a Q-basis B for R . Let B'={k/n : k ∈ B, n ∈ Z\{0}}. Call such a set a Z-basis for R . If an additive subgroup G of R contains a Z-basis, then G=R . | Is this an iff condition? | I think the converse statement should actually be: If G generates R then G contains a Z-basis. G need not be a subgroup. I don't think this is entirely obvious? |
[
"I never understood fractions or decimals as powers until today, it was very simple but no one explained them to me"
] | [
"math"
] | [
"6wima9"
] | [
402
] | [
""
] | [
true
] | [
false
] | [
0.88
] | so like lets say 5 is easy it's 5×5×5, but I always wondered how would I expand 5 it turned out I do this 5 × 5 × 5 × 5 which is 5 × 5 × 5 × √5 so it's simple 5 × 5 × 5 × √5 this maybe very simple and stupid to many but this is a life change to me, I hope that if someone had the same problem like me someday will find t... | If you ever plan to move to more advanced maths I suggest dropping the "power as repeated multiplication" idea as soon as possible. Don't get me wrong: it's really useful when starting off, but it quickly becomes very limiting, just like with multiplication which we start off thinking as repeated addition. Yes, it migh... | 3Blue1Brown is a gift to humanity! I especially love his linear algebra playlist. | All right. And from here how does one proceed in actually calculating √5? What about 5 Let alone 5 | The pedagogical point is that once you have a notion of "nth roots" and "exponentiation is repeated multiplication" there is only one sensible way to define exponentiation of rational numbers. Once you have "exponentiation of rational numbers" and "exponentiation is continuous" there is only one sensible way to define ... | 3.5 = 7/2 , so 5 = 5 = √( 5 ) |
[
"3d Vector to orientation"
] | [
"math"
] | [
"6wfxb2"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.67
] | So I was thinking the other day about rotation, and I thought of a way to convert from a vector to an orientation: rotate around the axis of the vector by it's magnitude, for example, say you have a vector[0,0,1], you get a rotation of 1 radio around the z axis, because the vector goes along the z axis and has a magnit... | what you're doing is something like "take the cross product with the vector [0,0,1]". It's true that picking a cross-product on R is basically the same as orienting it for the reason you've given. But remember that we could orient it the other way, e.g. use the left-hand rule instead of the right-hand rule. To put it... | I actually just wrote a little article today for my website on using quaternions to do rotations in R https://adamsturge.github.io/Engine-Blog/mydoc_rotations.html | https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula | By 1 radio do you mean 1 radian? Anyway, if you represent a rotation by a quaternion and then take the logarithm, you get basically this. But note that you probably want to use [0, 0, 1/2] as your vector to represent a 1 radian rotation, because the way quaternions are used for rotation is via a kind of sandwich produc... | Here's an example how this is widely used. OpenGL is industry standard for graphics and 3d modeling software. You typically have a coordinate system for the object of interest and then matrices to define the transformations needed to get to the screen point of view. http://www.opengl-tutorial.org/beginners-tutorials/tu... |
[
"TI-82 vs T8-84 for Algebra II"
] | [
"math"
] | [
"6wfl2q"
] | [
0
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
0.4
] | null | I have a TI-82, I don't know what this guy's talking about. It graphs, because it's a graphing calculator, though he might be talking about the Ti-82 , which I think doesn't graph. But you'd know if you were getting a TI-82 Stat. I took Algebra II last year, my TI-82 worked fine. The only thing my calculator didn't hav... | I have a TI-82, I don't know what this guy's talking about. It graphs, because it's a graphing calculator, though he might be talking about the Ti-82 , which I think doesn't graph. But you'd know if you were getting a TI-82 Stat. I took Algebra II last year, my TI-82 worked fine. The only thing my calculator didn't hav... | Most teachers don't allow phones during testing tho. | You can't graph with the TI-82. Ti-84, TI-89 or TI-nspire-cx are recommended if not required for Algebra II. | Is the graphing calculator mandatory? If yes, then I recommend getting a ti 84. When I was in algebra 2 we rarely used graphing calculators. Does your teacher have a class set? If yes, then then you don't need it, and at home for homework you can just use https://www.desmos.com/calculator I recommend a ti 84 if you pla... |
[
"Numbers where changing the base permutes the digits"
] | [
"math"
] | [
"6wfy77"
] | [
85
] | [
""
] | [
true
] | [
false
] | [
0.89
] | This shows that 238 changes to 283 when changing the base from base 11 to base 10. Are there any other numbers like this? Edit: I thought of a way to generalize this. You could have more than one permutation and more than one base change which would create a huge path connecting different numbers together. | For b>2, 21 base b is 12 base 2b-1 | Yes, there are 272 such numbers less than a million and 4808 less than 100 million, starting with 1 to 9, then 196, 283, 370, 1723, 4063, 7587, 8665, etc. There can only be finitely many such numbers in total though, because all sufficiently large numbers have more digits in base 10 than base 11. EDIT: corrected 238 to... | nice | are there finitely many still if you allow any combination of bases though? | You can just exclude the identity permutation and ask the same question. |
[
"Question about the Rubik's Cube"
] | [
"math"
] | [
"6wfllw"
] | [
35
] | [
""
] | [
true
] | [
false
] | [
0.83
] | null | Read this: http://mathworld.wolfram.com/PermutationCycle.html . Express the effect of a sequence of moves on a Rubik's cube as a permutation on the little squares. Take the cyclic representation of that permutation, and the lcm of the cycle lengths is the order of the permutation. | Proving that, eventually, repeating a sequence will return to its original state might be doable in the two weeks. What? I can do it in one line. There are finitely many Rubik's Cube states. If f is your sequence of moves, eventually f (starting position) will equal f (starting position). f is invertible, so take f of ... | Since there's only a finite number of positions, eventually you have to get a repeat. The harder part (but not too hard) is to show from there that the first repeat is the initial stage. | His second sentence addresses exactly that issue. In words, the idea is that if the starting point weren't on an orbit then there must be a point x later on that is the point in the orbit. But this contradicts invertibility of f, since x must be reached by both a point in the orbit and a point outside the orbit. | You don't need very much group theory to solve this. Write down the effect of the sequence in cycle notation, then computer the order of the element. PM me if you have any questions. |
[
"Advice on newbie tutor, who is about to tutor kids in middle/high school math."
] | [
"math"
] | [
"6wfbeu"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | [deleted] | Note, I'm not critiquing the original poster but I would like to mention that this is actually more important than you think, to those downvoting. When creating my advertisements for tutoring (on Facebook, fliers, etc). I've had numerous parents give me the following advice.. Most parents want a really good tutor for t... | I'm a college senior who has been tutoring for years! Some tips: Ask the student how they'd go about solving a problem, and talk it out together. If they REALLY don't know where to start, try referring to an example to show them a method, and then try that method together. Think out loud with the student. Say, "usuall... | I know you are 'Math' But you could start by using their, instead of there. Just saying. | Also don't forget to not talk too fast. If showing a method you are familiar with or you are excited to get to the end of a solution just remember to make sure to look and see if they are still following. Ask lots of questions. Instead of saying 'now we need to divorce by 5' say 'what do you think we should do with the... | I've tutored quite a bit. My advice is teach them how to problem solve, approach new problems, find information in their book, notes and online, study, and think about math in a way that will help them in future classes. Don't be a homework answer machine! Show them cool math stuff to get them excited. Have them follow... |
[
"Why aren't mathematicians able to each how do do mathematics?"
] | [
"math"
] | [
"6wctxj"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | null | I don't think this is true. There are a number of books aimed at teaching how to transition from plug-and-chug mathematics (up to, and including intro calculus and maybe intro linear algebra) to mathematical reasoning (proofs and such). Many university curricula include a course on mathematical reasoning. Some do it ... | I disagree. Someone who has worked through Rudin as well as a rigorous linear algebra brook should do fine on that exam. | I disagree. Someone who has worked through Rudin as well as a rigorous linear algebra brook should do fine on that exam. | A professional mathematician is, by definition, someone who is good at math whose been doing math for a long time. If you're good at something and you keep doing it you will get better. If a high school senior took an algebra 1 final, he'd pass it easily. A high school freshmen might find it difficult. Why is that? Bec... | There's books like "How to Solve It" by Polya which cover this. |
[
"Online graduate courses for credit?"
] | [
"math"
] | [
"6wd6q1"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.67
] | [deleted] | Beginning math graduate courses in the US are often undergraduate courses in Europe. Talk to faculty in your department to learn more about the differences and get advice from them. | Agree with /u/chebushka about the discrepancy between US and Europe. To answer your question, whether it's justified or not, most people would turn their noses up at an online graduate credit, if you can even find a reputable one. | I'd love to know the logic for a single one of those downvotes beyond people taking it as a dig at the US. | I can't speak about all areas of math, but its faculty in number theory is well known to people who work in number theory. Considering your username, perhaps that is helpful. | I can't speak about all areas of math, but its faculty in number theory is well known to people who work in number theory. Considering your username, perhaps that is helpful. |
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