title list | subreddit list | post_id list | score list | link_flair_text list | is_self list | over_18 list | upvote_ratio list | post_content stringlengths 0 20.9k ⌀ | C1 stringlengths 0 9.86k | C2 stringlengths 0 10k | C3 stringlengths 0 8.74k | C4 stringlengths 0 9.31k | C5 stringlengths 0 9.71k |
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[
"Help tutor needed"
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"math"
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"lw7jif"
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2
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""
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true
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false
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] | null | Hi, I think you are not at the right subreddit. This is usually where advanced (university)level math, and the process of studying is discussed. If you need help r/learnmath can usually help you out with a problem. You might find a tutor here, or there, but I'd suggest looking on the internet for something near you. Or... | do you have concrete examples of things you struggle with? | Yes, a problem like R=0.67log(.37E)+1.46 So what would the magnitude be if there were 15,500,000,000 kilowatt-hours of energy. | I see, so I agree with what u/newnimprovedaccount . You can probably benefit from a tutor but I believe that changing your mental approach first will be more beneficial. You can definitely do it. For example, in the problem you mentioned a good starting point is the following. Since you need to find the magnitude a goo... | U of t eng grad here. PM if ur interested |
[
"If the square root of -1 is i, what’s the square root of i?"
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"math"
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"lw5dkk"
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"Removed - post in the Simple Questions thread"
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0.43
] | null | I answer this since this is in my experince the most common misconception of all among first year university students after I have taught that group for 6 years. It's not meant to be picky, it's just that it is so massively widespread. No, although (-i) =-1 it is not the square root of -1. √(-1) is always i just as √4 ... | You halve the argument once more, hence 1/sqrt(2)+(1/sqrt(2))i | 1/sqrt(2)+1/sqrt(2)*i First, it's important to know that complex numbers can interchangeably be written either by: [real part]+i*[imaginary part] Or by: Distance to (0,0) [is that called magnitude? English is not my first language so I'm not sure but I'll call it magnitude from here on] and angle toward the positive re... | Magnitude is correct, but when talking about complex numbers we specifically call it the complex modulus. | I’m not expert enough to confirm, but I’d say yes you are right magnitude can be used in any context in which you mean “size” or “distance.” Here they gave the gave a complex one a specific name for some reason |
[
"I understand Real Analysis, but I struggle with exams. What do I do?"
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"math"
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"lvydox"
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"Removed - post in the Simple Questions thread"
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0.72
] | null | While I am not a big fan of RE, I got an A+ in the course and can offer the following advice: You can study pure math at the higher level even if you don't excel in every single math course. I am interested in getting a masters myself and hate "continuous" math (am more interested in number theory/graph theory). You ... | Thanks a lot! Super helpful advice. Especially (4) - I have never tried to solve proof-based problems in a time limit, but now I think I really should get started. | When I was still in college, I had a similar experience. I had been solid A or A- student and pretty confident in my abilities. Then I got to one class where I knew the content was more challenging (RA) and still felt pretty good even though I didnt feel mastery quite like I had in other classes. It all come out on the... | Not a math major, but something that has really helped me was going through the book "How to prove it: A structured approach". The pandemic had given me a lot of free time, so I read it from cover to cover and now questions to prove are much easier and I am not afraid of them. I had always struggled with Real Analysis... | Yeah, there's no other way but spamming unless you are a genius, and I am definitely no genius. |
[
"I'm building a website that will produce quotes based on sqft. I'm trying to get an equation that will produce prices based on exact footage. But can't seem to find a way to do it. I have a chart of current prices based on 1000 sqft. And the other is an excel sheet that I was trying to find slope..."
] | [
"math"
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"lwm6e4"
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"Removed - see sidebar"
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0.57
] | null | The line appears to be what OP is asking for. Like, how to get the in between prices based on in between footage. Unless I've misunderstood the problem. | That's why I mentioned a linear regression. I'm assuming the price changes linearly with square footage, give or take random fluctuations. If it doesn't, then the approach should be to graph the data and see if it looks like a curve of some kind instead. | But when they did that in excel it filled in the gaps linearly, not stepwise. This isn't a complicated problem. Linear regression? | The ft were your inputs. "For some number of square feet, we have that number times the price per foot." Problem is you have a step wise function, not a linear function (which is why the slope excel is spitting out is wrong. Since you arent building infinitely large buildings, it's not unreasonable to just manually set... | The general slope equation for a line is: y=mx + b m is the slope. You may have already found that correctly, but if you want to try another way, your can take your first data point and subtract its footage and price from the last data point. This is like shifting the line left and down to where it starts at the origin... |
[
"Classical field theory and the Euler-Lagrange equations: a mathematician-friendly introduction"
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"math"
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"lwba2x"
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38
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""
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0.88
] | null | I wish someone could write an article that explains the Euler-Lagrange equation without using ANY abuse of notation. It's quite difficult for someone who doesn't understand the E-L equation to decipher the abuse of notations. | The books Structure and Interpretation of Classical Mechanics and Functional Differential Geometry (pdf is under the Open Access tab) by Gerald Sussman and Jack Wisdom are designed to address this exact issue! Sussman is a renowned AI pioneer and co-inventor of the Scheme programming language, and Wisdom is a prolific ... | It is Standard notation. What I meant by abuse of notation is that you are taking some notation, and writing things that aren’t logically consistent with the rules of the notation, usually for short hand or to express some idea. For example, it’s common to write dL/dx’. In truth, you cannot take the derivative of a fun... | I tried to be completely upfront about the abuses of notation and discuss them at some length, but did use them for two reasons: 1) everyone does, so you have to learn to use the notation everyone uses, and 2) I fear that actually writing everything out without any notational abuse would result in a notational nightmar... | actually writing everything out without any notational abuse would result in a notational nightmare that would be even harder to decipher You only have to do that once, so people can get a better sense of what the shorter notation is doing. |
[
"Fast Factoring Integers by SVP Algorithms"
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"math"
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"lwf0t5"
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109
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0.96
] | null | The short version is they have a lattice based factoring algorithm which seems to work better than the number field sieve or quadratic sieve (the two best current factoring algorithms). This is not a polynomial time factoring algorithm, but if this is correct, this may be the biggest breakthrough in factoring in the la... | This destroyes the RSA cryptosystem. I haven't read the paper, but this is one helluva claim. I'm not a mathematician nor do I know anything about modern cryptography, but I believe that RSA is still widely used. | That's because whoever uploaded it to IACR which appears to not be Schnorr added that sentence. Edit: It looks like it was uploaded by him and he did put in the sentence which is just weird. | Once upon a time, I was a factoring researcher. The last thing I did before I left was worked on the record factorisation RSA-768. I did not get coauthorship because I left early, but they acknowledge my contributions in the paper. I tell you this to give myself some credibility to talk about this stuff. I have not ... | I have some questions for anyone who can understand and has time to read the paper, as I am interested but not entirely educated on such matters. What is the computational complexity of this algorithm in big-O notation? What exactly is the largest number factorised using this algorithm so far, and how long did it take?... |
[
"Wikipedia definitions sometimes makes me squirm."
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"math"
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"lwb0av"
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""
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0.11
] | In the definition for ), one finds: In mathematics, a function is a binary relation between two sets that associates of the first set to exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers. To me, that should read . Anyone else think ... | I don't think there's a problem with the current wording, but "each element" would also be fine. "each and every" is redundant (and not in a way that's positive for usability, just in a pointless and wasteful way) and/or causes a careful reader to think about why both words are there and if there's some special purpose... | I think it's clear enough as it is written. | "Each and every" is one of the redundancies that lawyers like to use that add no information. | Ah, yes, after reading the comments and re-reading the definition, I see what OP is on about. It is a sort-of agreed convention to say things like "every dog has exactly one tail" in mathematical writing, to mean "for all dogs D, it is the case that the dog D has one tail," rather than they all have to share one. It's... | I doubt anyone would have been confused about this, but I agree the wording was slightly ambiguous. It's literally just two clicks to change it so I just did that for you. I'm content to voice my warnings about Wikipedia math content here. You're being a bit dramatic here, aren't you? Like, if you dig through wikipedia... |
[
"Commutative Algebra Textbook Recommendations"
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"math"
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"lw79wz"
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4
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0.83
] | Hello math reddit! I’m a first year graduate student taking my first commutative algebra course this semester. We are using Eisenbud, but I personally find it dense and somewhat difficult to follow. I was hoping to find other references to help me because I am really beginning to struggle with this class. If you guys c... | Atiyah and MacDonald is a good introductory resource imo. It's lighter and really more of a survey of the material, but a good precursor to a more dense book | Geometry, geometry, geometry! Much of commutative algebra’s development was motivated as the machinery of algebraic geometry, so it’s very hard to learn the subject without acknowledging the geometric insights behind the algebra. Miles Reid’s two books “Undergraduate Algebraic Geometry” and “Undergraduate Commutative A... | atiyah macdonal is a great book!! I learned the basics from it | Great fucking book, its pretty hard to read doe since it is so concise. The exercises are so fucking great | Agreed |
[
"I read about noncommutative geometry and I would like to code a renderer to visualize it, how would I go about this?"
] | [
"math"
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"lw5fne"
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0.8
] | I watched a video about it and at the end it displays this example formula x * y != y * x for space coordinates, and I try to wrap my head around how this would look like and if it can be rendered to a 2D screen. any suggestion is welcome! :D EDIT: for my background, I wrote 3D renderer and raytracer before, so im firs... | I don't know that it's something you can really visualize that easily! Contrary to the name, noncommutative geometry is not particularly "visualizable." I'm going to try to give an expanation of what's going on when they talk about noncommutative geometry, but I think there's a point at while I'll be forced to use mat... | Disclaimer that I'm not an expert, but the great difficulty of noncommutative geometry is that you don't have local models. In the commutative world, manifolds, schemes, etc. are built by gluing together local models of a well-understood form. For manifolds the local model is Euclidean space, for schemes it's affine sc... | first off, thanks for your time and detailed answer. please excuse my stupid assumption below, but I come from a coding background so im used to numbers aswell as theoretical math (rule systems in compilers, chomsky hirarchy, etc)... well I assume any of these collection has infinite functions inside them? also there a... | Noncommutative geometry is "geometric" in the modern sense of the word: modern geometry is the study of any mathematical structure using geometric techniques, and geometric techniques are any techniques that "feel" geometric. The fact that noncommutative geometry can be studied by using strong analogies to DG at every ... | Yes, exactly, everything you say is right. There are pictures you can draw of objects that come up when you are studying C* algebras and noncommutative geometry, but you unfortunately cannot really visualize a "noncommutative geometry" What do you practically actually do? Uh..... well, this stuff is pretty much only... |
[
"What are some almost-Millennium Prize level problems that can be stated in such a way as to be understood by an average young person?"
] | [
"math"
] | [
"lvvorv"
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7
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false
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1
] | I'm trying to brainstorm problems in advanced mathematics and/or any contemporary research that can be stated as a question or phrase simple enough to be understood by a child (or, perhaps more broadly, someone without an education beyond the basic high school curriculum). An example might be, "Can a computer always fi... | Quite a few number theory conjectures satisfy that condition. Twin prime conjecture: Are there an infinite number of pairs of primes that differ by 2? Goldbach conjecture: Is every even number greater than 2 the sum of two primes? Perfect cuboid problem: Is there a cuboid whose edge lengths, face diagonals, and space d... | It's not millenium, but collatz is another good one. It could probably be understood even by a grade-schooler. | Ramsey numbers in general but specifically the exact value of R(5,5) | The statement of the Collatz conjecture doesn’t even need you to know what a prime number is. | D'oh, knew I was forgetting one of the well-known simple ones. |
[
"How do I compare signals and group them (for an AI)?"
] | [
"math"
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"lvvncv"
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8
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""
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0.84
] | Hello all, I'm currently working on an AI project (as a software dev). My math skills are limited, particularly as this problem seems quite complex. I have signals coming in from appendages. The signals are number streams with a maximum length of 10. I need to match those signals together - i.e, slight differences betw... | i wish i had a better answer but i dont. it seems like you are looking at an unsupervised learning problem. there are many approaches to these problems so you will have no shortage of methods to choose from i still dont quite understand what you are applying this to but it seems pretty complex. fortunately, many algori... | it sounds like the problem is more general than you think. unless you are looking for something really specific, there are a lot of classic, easy-to-implement methods that can answer your questions if you have labeled data ie swaths of predictor data that includes a target or outcome then the problem is easy. i would t... | Okay, thanks so much for the help! | youre welcome :) good luck while youre at it, look up DBSCAN. its a clustering algorithm that can pick up on shapes that arent just normally distributed or symmetric about their mean. i just have this feeling that the "first choices" of clustering algorithms such as gaussian and k means arent gonna be sufficient for yo... | The data is not labelled, but it follows the same format. For example A: 10, 5, 6, 8, 9, 10 B: 10, 4, 6, 8, 9, 11 C: 20, 2, 7, 3, 3, 5 A and B should belong in one cluster, while C should not. This is because A and B are quite close together. Before starting, I do not know what the appropriate 'distance' between signal... |
[
"Sequences that seem to infinitely repeat but do not"
] | [
"math"
] | [
"lw5cv7"
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6
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true
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false
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1
] | Could somebody please tell me the name of number sequences that seem to be infinitelly repeating but somehow aren’t? For example, I saw whose products (or something else, I’m not sure; whose results) were 1 1 1 1 and so on thousands of times and then suddenly a different number, maybe 154266189. This specific example h... | I don't think there's a specific term for this sort of thing, though. Law of small numbers. https://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers Most def worth a read is the original paper, full of amusing and amazing examples of patterns that hold for a long time, until they don't. https://www.ime.usp.br/~rbrito/... | This SE post of patterns that eventually fail is neat. I don't think there's a specific term for this sort of thing, though. | Not exactly what you are looking for, but here is an example for the count of platonic solids (regular polytopes) in each dimension: 2: Infinity (all regular polygons) 3: 5 (tetrahedron, octahedron, icosahedron, cube, dodecahedron) 4: 6 (hyper-tetrahedron, hyper-octahedron, hyper-icosahedron, hypercube, hyper-dodecahed... | let f(n) equal the number of ZFC proofs of Con(ZFC) with a Godel numbering strictly less than n fite me | It appears to not repeat infinitely, but then it does. |
[
"Sign function that returns only 0 and 1?"
] | [
"math"
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"mu6vu9"
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0
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"Removed - post in the Simple Questions thread"
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0.5
] | null | https://en.wikipedia.org/wiki/Heaviside_step_function | I'm actually fucking dying right now | If you want weirder and weirder 'sign functions' then you can normally set such a thing up as a gross linear combo of Heaviside functions, btw! | I mean, it's still annoying it isn't integrated into Desmos. But I'm disappointed that I didn't find it. | (x + abs(x)) / 2x for x ≠ 0 does the trick, use 0 or 1 as needed for x = 0. I don't know Desmos so I can't help you there... |
[
"I've forgotten calculus after doing proofs for a year"
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"math"
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"mu4ogo"
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16
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"Removed - post in the Simple Questions thread"
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0.77
] | null | I haven't used calculus for over than 10 years. If I am to use it now, I'll have to look at a Schaum's book for solved problems or just use sympy/Mathematica/octave to evaluate the integral. I believe there shouldn't be any shame in using a PC to compute stuff. That's why they are called computers. | I haven't really done any calculus in a long time, but yea I'd imagine I'd have a hard time remembering how to do a lot of the trickier problems, because when you don't practice something you lose it. It's normal. If you look through some examples and start practicing the problems again it will come back to you. | Most of the computational stuff that you do in calculus does not really generalize in such a way that you need to be able to do it yourself rather than having software do it for you. But some exceptions exist; for example, integration by parts is an actual important tool in analysis especially of linear PDE. But calcul... | I agree with you, but this may be our bias towards computational math taking over... | There are relationships that you may miss if you do everything by computer. I say this from experience :(. |
[
"I recently realised this weird duality about mathematical modeling and I'm wondering if it's just my misunderstanding or is it actually something"
] | [
"math"
] | [
"mu312u"
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0
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"Removed - not mathematics"
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0.1
] | null | Mass is inertia to motion. You apply a force to an object with mass and it undergoes an acceleration. The ratio between force and resulting acceleration is its mass. It doesn't matter if the object is conventional matter or a box containing energy. I didn't need energy in the definition of mass. So can you give a real... | What about mass of proton? What about electrons Huh? A proton and an electron satisfy F=ma. The mass of electron and protons were measured due their deflection due to electric fields (which produce known forces when charge is known) | In quantum mechanics, momentum and position are complementary uncertainty pairs Energy and time are complementary uncertainty pairs. Mass and Energy are not such pairs. | Alright but then you can take shape and size as example | You can't determine its acceleration in the first place how are you going to use F=ma? Also idk what it will even yield |
[
"\"A Pathway to Equitable Math Instruction\" and white supremacy in math"
] | [
"math"
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"lw808o"
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349
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0.83
] | has been getting some attention recently. The document people are more inclined to quote is , which is the one I've read or skimmed. I was initially going to post by Sergiu Klainerman, a professor at Princeton, but he calls wokeism more harmful in education than communism, a foot I didn't want to lead with, whether it'... | I recently heard the term "conceptual overreach" and it has stuck with me. It describes when a concept grows so large that it becomes bloated and almost meaningless. For example, if you mark every task you have to do as high priority then none of them really take priority over the others and the concept is stripped of ... | I read the Dismantling Racism booklet (well, most of it anyway) and while there is plenty to criticize within the content itself, that's not my biggest problem with it. The biggest problem I have with it is that it offers no discussion about the definitions of the terms it uses. It uses "racism" , "white supremacy" and... | Honestly it feels to me that what they're referring to is the white middle class bias that is present in many education systems (this is not unique to the US in any way). However for reasons that I cannot comprehend they have chosen to refer to that in a way that they surely must have known were incendiary and therefor... | Arguing about definitions, you can tell we're math people. | Sure, but all the things you're talking about are reasonable pedagogical points. There's definitely something messed up about a pamphlet supporting its pedagogical stances by suggesting that not doing so supports racism. |
[
"if pi contains all numbers, does it eventually contains squere root of 2 or other irrational numbers?"
] | [
"math"
] | [
"mtuf7i"
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3
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"Removed - post in the Simple Questions thread"
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0.71
] | null | If pi contained √2 as a substring it would follow that pi = 10 (m + √2), for some integers n, m which can't be true since pi is transcendental. | It's an unproven hypothesis, so we don't (yet) know. | Let me give this a shot: Assume that pi contains the entirety of √2, that is, at some point all of the digits of pi are the same as those of √2, off to infinity. Let's say the nth digit of pi is when this happens. Then pi*10^n would be some stuff before the decimal place, and then after the decimal place it would exa... | We don't know whether pi contains all strings of numbers | it would follow why |
[
"How’s Carnegie undergrad math program"
] | [
"math"
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"mtlsl8"
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0.54
] | null | As a grad program it's very specialized, but for an undergrad that's not an issue. | You mean the program at CMU? If so, it’s quite good and well respected. edit: though i should probably note that cmu does have a fairly strong skew toward applied math, so you may want to look into other places if you’re deadset on going into pure mathematics | I don't want to discourage going to a good state school, since that's also a good option, but I don't know what your basis for thinking such a program is better "math wise" than CMU - the CMU math faculty is excellent. | I go there and study math so feel free to DM me | Speaking solely from my observations, I find doing okay at a top undergrad is better for graduate admissions than doing phenomenal at a low ranked school. |
[
"How different is calc 2 from calc 3?"
] | [
"math"
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"mtv3w7"
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1
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""
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true
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false
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] | [deleted] | I've never heard of a computational calc class. Is it specifically for CS students or something? | I've never heard of a computational calc class. Is it specifically for CS students or something? | They mean calc classes where the focus is on finding numerical solutions to problems, as opposed to something like an analysis class where the focus is on proving propositions | Oooooh I see, mine is definitely way more computational based. | Thats typical, analysis classes almost always have calc 1 and 2 as prerequisites |
[
"Is there a software that takes approximations and tries to change them to original numbers?"
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13
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0.88
] | null | http://www.ramanujanmachine.com/ | Try Wolfram Alpha: https://www.wolframalpha.com/input/?i=+0.33333333 (See under "Possible closed forms") Also a relevant XKCD https://xkcd.com/1047/ | A standard piece of software for this is the inverse symbolic calculator , though you might have to input more digits for the simplest result to rise to the top. | There are a whole bunch of methods and software for doing this. Here is a pretty exhaustive overview by David Stoutemyer (one of the creators of the Derive computer algebra system which was also used in TI calculators) of various ways to do it: https://arxiv.org/abs/2103.16720 | First you round the number to the precision you want, and show the decimal number in a fractional form, e.g. 3.1416 = 31416/10000. Simplifying the fraction would need to find the GCD of 10000 and 31416. You can use the Euclidean algorithm for it. Use GCD function in Python. So numerator will be 31416/GCD(32416, 100... |
[
"Moderately challenging non-textbook book on math"
] | [
"math"
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"mtw3tq"
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5
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""
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0.79
] | I‘m a 2nd semester engineering student with a passion for reading and for mathematics. I‘m looking for an intriguing book on interesting mathematical concepts that is not trivial as I‘d say I have beyond high school level understanding of many topics and don‘t want to be bored. But obviously I‘m also not a math major, ... | by Douglas Hofstadter is a classic. | The trilogy "a mathematical gift". https://www.amazon.com/-/es/Kenji-Ueno/dp/0821838598/ref=mp_s_a_1_1?dchild=1&keywords=mathematical+gift&qid=1618839731&sr=8-1 | A couple of possibilities: "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics" by John Derbyshire. "Euler: The Master of Us All" by William Dunham. | thank you! | "Euler: The Master of Us All" by William Dunham. Dunham has a few books like this, they're all gems presenting Euler's various contributions to mathematics. |
[
"What are some cool and exciting topics/research concerning Linear Algebra? I need some inspiration.."
] | [
"math"
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"mtkuko"
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6
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] | I'm in a small yearlong math degree program (degree is inbetween a bachelors and masters degree) and just took 2 calculus courses in the fall/winter. I struggled a bit, however I genuinely find the subject of calculus inherently fascinating--be it in more advanced research studies, real-world applications or the phil... | Indeed, but many people do find it cool and interesting which is why I suggested it. Weird reply dude | Machine Learning is very linear algebra focused | One of the more fundamental problems in Applied Linear Algebra is that of low rank matrix factorization . Finding a "low rank" representation of a matrix is analogous to finding a low-dimensional representation of a dataset. That is, looking to see if your dataset actually lies on a line or plane (i.e. linear regressi... | Statistics is essentially using linear algebra to reverse engineer randomness, which I think is super neat. Functional analysis is, in many ways, an extension of linear algebra, and it's basically the foundation of modern applied math (optimization/control theory, PDEs, nonparametric stats, etc.) Linear algebra is one ... | One of the first moments where I thought linear algebra was awesome was this one: after learning about eigenvalues and the diagonal form, our teacher casually taught us how to find the explicit formula for the Fibonacci sequence (look up Binet's formula if you're curious). Later that year I found out how those same pri... |
[
"Cool Geometry/Geometrical Patterns Book"
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"math"
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"mtsibp"
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4
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""
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true
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false
] | [
0.84
] | Hi! I am looking for a fun visual (but deep) geometrical patterns book for my bookshelf. I am a mathematician myself so I am not looking for something high school level. For example, a book that has wallpaper groups or topology with beautiful visuals. Thanks a lot! Edit: It doesn't necessarily have to be patterns, any ... | Hmm, if it weren't for the "deep" requirement, I'd have suggested Beautiful Symmetry: A Coloring Book About Math , but it's fairly elementary group theory... | Your bookshelf might like "The symmetries of things" by Conway, Burgiel, Goodman-Strauss. Also it's a different kind of patterns but "Algorithmic beauty of seashells" by Meinhardt is really nice. | Tilings and Patterns by Grünbaum and Shepard is a classic | Symmetry, Weyl https://www.amazon.com/Symmetry-Princeton-Science-Library-Hermann/dp/0691173257 | Thank you! Will look into it. |
[
"When do you have the feeling that you really understand a mathematical concept?"
] | [
"math"
] | [
"mu37gn"
] | [
10
] | [
""
] | [
true
] | [
false
] | [
0.82
] | Sometimes I just don’t get the feeling to have fully grasped something even though I’ve don a lot of exercises and understand every important proof regarding the topic. | You guys are understading things? | I usually try to explain things to my colleagues or girlfriend. If they don't understand or ask a question I can't answer I address the problems and try again. | I never really do. | It takes a lot of time. I was talking to one of my professors and he mentioned that one of his former colleagues, who's a pretty big name in algebra, said that it took him 1.5 years to understand what tensor products are, and that the more he thought about it the more he realized how little he really knew about it. So ... | For me it's counterexamples: given a definition, it's natural to think of objects which satisfy the definition, but I also find it helps to think of some which do not. Given a theorem, think of cases where the theorem works, but also of cases where the assumptions aren't met, and whether the theorem holds in those case... |
[
"How to incorporate coding/computational aspect in linear algebra?"
] | [
"math"
] | [
"wtj3b6"
] | [
45
] | [
""
] | [
true
] | [
false
] | [
0.85
] | This semester I’m taking my second linear algebra course. My first one was just all matrix operations focused. We talked about vector spaces, but it was mainly just computing eigenvalues and eigenvectors by hand and doing matrix multiplications. The second class I’m taking is all proof based, kind of like linear algebr... | I need some time to compile resources, but I just thought I'd point out that it's not just statistics; linear algebra is in computational mathematics. From the Fast Fourier Transform, to Van Der Monde matrices and finite difference methods, to Markov Chain Monte Carlo, to Jacobian-based nonlinear optimization, and on a... | You'll want to look at either Demmel's or Trefethen and Bau's book of the same name | My first coding language I learned was Python, then I learned MATLAB and C++, then a bunch of others like R and fortran. I mostly use those three though, whichever best suits what I'm working on. Right now that's mostly Python, since I'm mostly doing machine learning stuff. I'd say that MATLAB is the easiest to go from... | You may look into python and SciPy. https://scipy.org/ | Actually, I’d need it especially for MCMC and optimization. So that’s good to know. I’ve heard tho that often coding this stuff isn’t as direct as the formulas. For example, some decomposition methods I’ve heard may have the inverse in the formula, but it may not be computationally efficient to actually calculate an in... |
[
"How to introduce knot theory to late high school students featuring concrete proofs?"
] | [
"math"
] | [
"mthqci"
] | [
18
] | [
""
] | [
true
] | [
false
] | [
0.88
] | I am asked to introduce knot theory to late high school students featuring concrete proofs but have no idea on how to do that :cry: | Presumably you know something about knot theory which is why they are asking you, so I would recommend thinking about what initially got you interested in the subject, and how you can relay this through simple examples to students. Personally, I would just ignore what they ask about “rigorous proofs”. | I work at the Los Angeles Math Circle and we did exactly this last year: https://circles.math.ucla.edu/circles/search_handouts.shtml?query=knot Feel free to use our handouts for ideas, but I'm not sure if our admin would be comfortable with other people directly teaching from them without modification. | Not sure if it's the right level, but I found these notes ("Knot Knotes" by Justin Roberts) helpful: http://math.ucsd.edu/~justin/Papers/knotes.pdf There's also Colin Adams's For a specific topic, definitely show them tricolorability | I had fun with a group of middle schoolers talking about knots and braid groups. I think the idea of "arithmetic" but not with numbers is very cool to students. I ended with a proof that IF there is a left-order on a braid group, then the group has no idempotents. I.e. you can't undo any braid by repeating it. | I'll add that to my Watch Later list. In the meantime, there's also this lecture by Prof. Jessica Purcell https://www.youtube.com/watch?v=b4WA3-tZgcc |
[
"What Are You Working On? April 19, 2021"
] | [
"math"
] | [
"mu3sfb"
] | [
8
] | [
""
] | [
true
] | [
false
] | [
0.85
] | This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on this week. This can be anything, including: All types and levels of mathematics are welcomed! If you are asking for advice on choosing classes or career prospects, please go to the most recent . | Anything can seem difficult when you first come across it, it's totally normal. I remember really struggling with the definition of a function in my first term of uni. Is there anything specific you're struggling with? | Reading by Birkoff and MacLane. Got stuck on some of the harder problems. I want to get up to Galois theory. Put some finishing touches on a paper I wrote awhile ago, but I found out later that the results I proved were already known, so I can't publish it. Oh well. Also tutoring my nephew who is visually-impaired and ... | I'm at Maths in Moscow... it's my second semester. Semester 1 went ok. Semester 2 is extremely challenging with Algebraic Number Theory and Rep Theory. I just dropped linear algebra. I feel as though I didn't learn anything in college. And that's why I'm having these difficulties now. I don't know if I should take a st... | not easy for me :/ | Why not use matplotlib to create the plots? Gnuplot ain't bad itself, but I prefer matplotlib. Ofc, gnuplot is easier to use, comparing to coding a python script to plot your data via matplotlib. That said, you might enjoy Mathematica for the plots. It's the most intuitive CAS program out there, with an intuitive langu... |
[
"How do I find the numbers that make up an average?"
] | [
"math"
] | [
"o4mq91"
] | [
1
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.57
] | null | Unless you have some more info, it’s impossible. They could be anything from 1 and 37015, to 18508 and 18508. Or if negative numbers are involved, there’s infinite options. | All you know about the numbers is that a+b / 2 = 18,508, or that a+b = 37,016. Unless more info is given, you can't solve for both at the same time. | Okay, thank you | Well if you have one of the numbers then it's really easy otherwise I don't think you can | One equation, two unknowns - for the case you mentioned. In general, taken over many numbers, you will have one equation with as many unknowns as the numbers for which you have computed the average for. Final answer: not possible! |
[
"You can grow Into a math person"
] | [
"math"
] | [
"mttltg"
] | [
1034
] | [
""
] | [
true
] | [
false
] | [
0.97
] | There’s this idea in the air that you’re either a math person or you’re not; moreover, people often assume that you have to be very intelligent to do math. While there is a lot of intelligent people in mathematics I’m certain that a lot of people who think that they’re not smart enough for math or people who have faile... | Lol I’m doing my PhD and nobody has figured out I’m dumb as fuck yet. It’s a matter of blind persistence, not raw intelligence. | Lol I’m doing my PhD and nobody has figured out I’m dumb as fuck yet. It’s a matter of blind persistence, not raw intelligence. | Someone should make an r/math circlejerk subreddit | I still remember reading an article about how dull math education at high schools could be due to ruining the thrill of discovery (I guess it was from some link that was posted in some post here at the comments). And I'd say that may play some part as well into that fear of being bad at math for not being good enough t... | Like only "intelligent" people can play chess The best chess players I've personally met are sharp in that they really don't have a lot of breadth to their intellect. I think quantitative reasoning subjects have a 'clout' factor to them, kind of perpetuated precisely by the 'you need to be a natural' type of mentality.... |
[
"Coffin Problems: These deceptive problems have elementary statements and solutions, but are actually extremely difficult. They were used to discriminate against Jewish students in the 70s and 80s."
] | [
"math"
] | [
"mtgsww"
] | [
89
] | [
""
] | [
true
] | [
false
] | [
0.92
] | [deleted] | 41: Find sin 1 . What are they even expecting? It's an irrational number. Do they want a decimal expansion? Do they want an approximation (sin x = x)? Do they want a Taylor series? I feel like for whatever answer someone might have given for this question, they could always think of some reason to say that the answer i... | Isn't this literally one line if you use sin(x) = (e - e )/2i? | Isn't this literally one line if you use sin(x) = (e - e )/2i? | Yup. Professor Edward Frenkel of UC Berkeley even mentions this in one of his interviews. Incredibly Sad to hear how this was a practice used in Russia. | Did you read the whole original post? If your goal is to be an antisemitic asshole, and unfairly deny Jewish students acceptance to your math department while maintaining plausible deniability, these are a great tool... for the reasons you outline. |
[
"Does Godels Incompleteness theorem apply to physics?"
] | [
"math"
] | [
"o4jauw"
] | [
4
] | [
"Removed - incorrect information/too vague"
] | [
true
] | [
false
] | [
0.57
] | null | This question depends closely on what you mean by applies to physics. There are problems which are of physical interest which are known to be undecidable. For example, it turns out that the spectral gap in a very general form is undecidable , but arguably that's closer to the Turing halting theorem than Godel (although... | Problems in physics can be undecidable in the computational sense, but the incompleteness theorems apply to axiomatic systems, and physics, being a natural science, is not axiomatised. | You appear to be talking about limits on the physical universe. That's a different question which doesn't really directly talk about issues like Godel's theorems in any obvious way. I'm not also sure that whether the universe is closed in the technical, thermodynamic) sense has much to do with the topic at hand (and I ... | As an aside, there are incompleteness theorems associated with Gödel : (The "sufficiently powerful" criterion is critical: Presburger arithmetic , for example, which doesn't have multiplication, is complete.) | https://redd.it/o3p3f0 ? |
[
"How to learn statistics well?"
] | [
"math"
] | [
"o4h4r8"
] | [
3
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.8
] | null | Added it below | Added it below | Yeah, it's not clear exactly what topics OP will learn in the class. I'd assume entry level stuff by default, but it's best if they provide some outline of the curriculum. | Fair. Textbook is Modern Mathematical Statistics with Applications, Second Edition (Devore, Berk), we're covering chapters 5-12. So Joint Probability Distributions, Statistics and Sampling Distributions, Point Estimation, Statistical Intervals Based on a Single Sample, Inferences Based on Two Samples, the Analysis of V... | r/statistics |
[
"Can I get good at math?"
] | [
"math"
] | [
"o4e3xm"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.67
] | null | *I never listen in class, I dont do my homework and I dont study* do the first one boom C do the first and second one woah maybe a B do all 3 hmmm might hit an A there u have it | Start studying, doing your homework, and paying attention in class. If you find holes in your knowledge, use Khan Academy to help patch them | So is my goal achievable? | Yes of course as long as you actually put in work. By your own admission, you've put in 0 effort. | I haven’t been putting any effort in for years because I hated my math teacher and math itself. I just studied maybe like 3 hours in total before the test, but that obviously isn’t nearly enough, especially after not paying attention and not doing any homework. But I want to change! |
[
"Is there a real life example for \"minus plus, minus\"?"
] | [
"math"
] | [
"o4cblm"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | null | for everyone confused i believe OP is referring the rules for how signs interact with multiplication for OP: i think the confusion is because the formatting (at least on mobile) is horrible and doesnt show anything on the left hand side of the equals sign except for a single dot. also referring to this as “the four rul... | i havent thought of a super clean answer but if you buy that displacement = velocity*time, we can do the elementary physics mechanics version. on the side of a freeway looking at cars traveling left and right, define signs: then these results follow from (velocity)(time) = distance: substitute numbers as needed | There is no absent student in class, equals Everyone is present. This isn't a very good analogy for signed multiplication, since you can't "multiply" two absent students to get a present student, nor two present students to get an absent student. All you're effectively saying here is that "present" is the opposite of "... | xD Yeah I didn't think about the wording there...also I noticed the problem with signs and tried whatever i could and nothing worked | i wouldn't say it's just -(-2) = 2, since it would be an excellent example for ∀ and ∃. but you're right that it's definitely not what OP is going for |
[
"Does topology care about materials?"
] | [
"math"
] | [
"o4dqci"
] | [
0
] | [
"Removed - incorrect information/too vague"
] | [
true
] | [
false
] | [
0.24
] | null | One could argue that the point of topology is to study the properties of objects that remain no matter the choice of “material” I’m sure you didn’t mean it, but it is profoundly arrogant to suggest an enrichment to a subject you don’t know much about | How is this related to the question of what material is an object made of? You don't sound very nice and are not listening to what people are telling you in pretty much every comment. Your question basically makes no sense. | No, in topology there aren't any materials or textures. The shapes are just, well, 3D "clay like" models. If there was materials involved in topology, then topology wouldn't make sense anymore for example, if a torus mug were to be made of glass, it wouldn't have the capability to morph into a donut torus. Since I'm gu... | Well I agree with them in that I think you've misunderstood what topology is. I just don't understand how commenting that with no further explanation is helpful; just discourages someone clearly interested. | don't bother with nlab if you know very little math. you won't understand a single thing |
[
"Is mathematics invented or discovered?"
] | [
"math"
] | [
"o3yt7i"
] | [
0
] | [
"Removed - not mathematics"
] | [
true
] | [
false
] | [
0.33
] | null | I have never heard a definitive answer to this and I'm not even sure if there is one. | Kinda both. We invented a way to describe what was already there | Invention is a form of discovery. | Yup. The more mathematicians I try to engage about these things, the more I find it's not that they hold some deep cognitive dissonance about "existence" it's that they just. don't. care. Sometimes/often they've literally can not recall ever having questioned what "existence" means, mathematically. They generally lack... | I think many do not like to talk about it because it is a moot question whose answer is essentially irrelevant. You seem to have a lot of preconceptions about mathematicians. |
[
"Complex polynomial roots not making sense"
] | [
"math"
] | [
"o4gszv"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
1
] | [deleted] | Why doesn't that bother you with the 17? After all, 17 has two square roots, and then there is the plus-minus sign! It comes down to: what do you think that plus-minus sign ? | A complex number has two square roots, like a real number. Why don't you think the same reasoning you used above applies to a real polynomial like x - 3x - 2? | Because that has 17 in the root, which has two roots- with one being the negative of the other. But -6i-8 has two square roots, and then there is the plus-minus sign. | The way the standard quadratic formula is written is for polynomials with real coefficients. Thus you will be taking the square root of a real number which has a positive and negative answer. This results in the plus/minus sign in the formula. What you are really doing is adding both square roots though. Thus when you ... | When you find the two square roots of a real number, the square root symbol/function only gives you the positive one, which is why the plus-or-minus is needed to indicate both solutions. Notably, square roots of a positive real number always come in positive/negative pairs, which is why the plus-or-minus gives you both... |
[
"MATLAB For People in Hurry - Free Course From Udemy"
] | [
"math"
] | [
"o4fcso"
] | [
35
] | [
""
] | [
true
] | [
false
] | [
0.8
] | null | Pretty sure there is a free course on the MathWorks website as well | Ease of use, way better documentation, quick plotting, no need to fret about imports… It’s a tool for a different job than most software engineering, but it’s quite good. There are probably thousands of biologists who would never want to learn to deal with even something as accessible as python, but matlab is tolerable... | There's little reason to use Matlab instead of Python nowadays, unless you're dealing with legacy code. | Numpy code is actually quite annoying to write in my experience. Or at least i found it more annoying than dealing with the quirks of matlab | Simulink is one big reason. Python has no equivalent. |
[
"Sine function using floor function"
] | [
"math"
] | [
"o4a4zn"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.45
] | [deleted] | The approximation is fun but surely f(x) is more honestly defined as cos(pi floor(x)/2) :P | ////////// EDIT: As some people have stated, some of the formulas shown in the image can be written in a better way. Since I can't change the image, I will write the modifications here. To sum up, I'm changing "f", "h" (now called "hₙ") and "rₙ₊₁" functions: f(x) = cos(π/2•⌊x⌋) hₙ(x) = | f(2 x - 1/2) | rₙ₊₁(x) = rₙ(x) ... | True, I know, it is just that I didn't want to use sinusoidal functions at all to make the aproximation | True, I know, it is just that I didn't want to use sinusoidal functions at all to make the aproximation | Wouldn't it be f(x) = 1,0,-1,0...? Probably an errata |
[
"The Volume of a Sphere - Numberphile"
] | [
"math"
] | [
"o45s6p"
] | [
325
] | [
""
] | [
true
] | [
false
] | [
0.95
] | null | The cross sectional area of the cone varies as r and r varies linearly with z, so the cone has a cross sectional area proportional to z The sphere, when cut into slices, is a series of circles with r=sqrt(1-z ) (assuming unit sphere). The area is then proportional to r = 1-z Sum the cross sectional areas of the sphere ... | Could anyone help me out - what am I missing here? @1:05 The idea that the same height cross sections always add to a constant cross section. That doesn’t make any sense to me. The double cone cross sections are varying linearly with height. But the sphere cross sections are varying non-linearly. I don’t see how a lin... | The animation was a bit misleading, because it showed 1-dimensional slices of a 2-dimensional vertical slice. I suspect the original presentation on paper may have been clearer. | Intuition: imagine the pyramid is made of clay or dough. You can always squish it to move the apex around without changing the volume of clay, as long as the base and height doesn't change. Proof: you can take a point-in-center pyramid, cut it off into multiple off-center pyramids, calculate the volume of each part sep... | I get how he proves the off-centre pyramid is 1/3 the volume of its enclosing cube, but how does that prove a point-in-the-centre pyramid is also 1/3 the volume of its enclosing cube? Also, what happens at 2:23? He says 'that is 1/3 the volume of that, so that is 2/3 the volume of that'. What are all these 'thats' that... |
[
"Why is hand-graphing still utilized in academic teaching?"
] | [
"math"
] | [
"o4ehvb"
] | [
64
] | [
""
] | [
true
] | [
false
] | [
0.8
] | I was wondering this the other day. I passed all my basic courses (Multi-variable/ODE) and am now moving onto Math Methods for Physics, and other upper level courses. My Engineering and Physics peers have never liked hand-graphing. They're long and tedious problems that end up bleeding time on exams, and they can easil... | Graphing is really useful for getting intuition about how a function behaves qualitatively. For example, how fast does it grow, does it "spin", etc. You see this most in lower division classes so you build those connections. Then in upper division classes, when you see a function you can visualize how it behaves and re... | You want to know that a student can visualize basic recurring shapes from their formulas. That they know what a quadratic looks like, what it means that its vertex is at a given position, etc. You need some way of making them externalize their understanding so that you can check if it's correct. I can believe that ther... | The functions should be your friends and graphing them by hand is how you invite them over for tea. | Nhm. To add to that, learning how basic transformations (ie a*f(bx-h)+k for any f) affect the shape of a graph is super important to developing intuition for function composition. | Not the same effect. With desmos (or whatever) you'll key in the function, glance at the graph, say "yup, that's cool", and move on. |
[
"Is the Eigenvectors for identity matrix always just going to be i, j, k, and so on vectors respectively?"
] | [
"math"
] | [
"tf9p0y"
] | [
1
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.67
] | null | Those are eigenvectors of the identity matrix, but they're not the only ones. Every vector is an eigenvector of the identity matrix, and there's nothing special about those ones. | Unfortunately, your submission has been removed for the following reason(s): /r/learnmath books free online resources Here If you have any questions, please feel free to message the mods . Thank you! | You mean, you found that a vector v is a 1-eigenvector if and only if Zv = 0, where Z is the zero matrix? That's correct, and all vectors v satisfy that, not just i, j, and k. | You mean, you found that a vector v is a 1-eigenvector if and only if Zv = 0, where Z is the zero matrix? That's correct, and all vectors v satisfy that, not just i, j, and k. | That's a bit confused. If you want to find the eigenvalues of a matrix M, you find which values of λ satisfy |M - λI| = 0. If you do that with M the identity matrix, you will find that only λ=1 works. Then to find the actual λ-eigenvectors, you look for vectors v such that (M - λI)v is the zero vector. With M = I and λ... |
[
"How much self study is enough?"
] | [
"math"
] | [
"o4av7v"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
0.88
] | null | I feel bad that nobody answered you, so I'm gonna give you what little words of wisdom a first-year undergrad can offer. I'd be worried about you burning yourself out doing this. A PhD entails a highly non-trivial quantity of work and it's in the same subject as what you're proposing to do in your downtime. I don't kno... | I'm sorry. I know what it's like to feel worthless, so I empathise. | I'm sorry. I know what it's like to feel worthless, so I empathise. | maybe I'm putting too much self-worth into my mathematics because a large part of my motivation to do this is down to feeling not good enough Mathematics isn't the be-all and end-all of anything except mathematics. Your worth isn't measured by the quantity of your mathematical knowledge, or indeed by the quality of you... | maybe I'm putting too much self-worth into my mathematics because a large part of my motivation to do this is down to feeling not good enough Mathematics isn't the be-all and end-all of anything except mathematics. Your worth isn't measured by the quantity of your mathematical knowledge, or indeed by the quality of you... |
[
"What is your favourite function name except 'f' and/or your favourite variable name except 'x'?"
] | [
"math"
] | [
"o4h0l0"
] | [
449
] | [
""
] | [
true
] | [
false
] | [
0.94
] | null | g y | Thread over. Love these easy questions. | R is for Real C is for Complex Q is for Quotient (makes sense since R is already taken) N is for Natural Z is for Zinteger | Well, obviously, the second best name choice for a function is 'x' and the second best variable name is 'f'. 😂 | Phi(g) Sort of confusing but a habit from learning Group Theory(g is used WAY to much, and Phi is ALWAYS an homomorphism) for rings I use r, fields f, and vector space v, modules m One of those conventions that actually makes sense |
[
"Are there equations that create infinite loops"
] | [
"math"
] | [
"tf311r"
] | [
0
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.29
] | null | Yes, sometimes you can't simplify an expression as far as you'd like to. | Not sure what you mean, but if you map ever real number to the pair (cos , sin ) in the plane, you wrap the real line around the unit circle endlessly. Is that the kind of thing you mean? | No, i don't think so | Any equation can pretty trivially be made a tautology. But it's a lot more likely that you're just using a technique that only reorganizes the equation in a way that isn't useful. If you're simplifying a + b + 2ab = N and it simplifies to itself, that's not a tautology - you just haven't found a way to simplify it. | I think i understand this.. Thank you |
[
"Generating sequence using prime numbers"
] | [
"math"
] | [
"tey14l"
] | [
0
] | [
"Removed - incorrect information/too vague"
] | [
true
] | [
false
] | [
0.46
] | null | Phrased in a more precise way, your question is the following: : Let p_1<p_2<... be the sequence of odd primes in increasing order. Given n≥1, what is the largest value of N for which there exists integers a_1,b_1,a_2,b_2,...,a_n,b_n such that for each 1≤m≤N, the congruence m = a_k or b_k (mod p_k) holds for at least o... | I'm getting downvoted but if someone can answer this quickly then go for it lol | Certainly a much better way to phrase it. Thanks. It’s a interesting question right? I would love to know the first 10 terms or so | Sorry. For the first example, each element in the set is “divisible” by either 3a or 3b, and since you can’t have 3 consecutive elements that are divisible by at least one of 3a or 3b the max is 2. For the next example each element has to be “divisible” by either 3a, 3b, 5a or 5b. Does that make sense? | Sorry. For the first example, each element in the set is “divisible” by either 3a or 3b, and since you can’t have 3 consecutive elements that are divisible by at least one of 3a or 3b the max is 2. For the next example each element has to be “divisible” by either 3a, 3b, 5a or 5b. Does that make sense? |
[
"What are the most effective ways to self-study Mathematics and to Excel at it?"
] | [
"math"
] | [
"teqnz1"
] | [
1
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
1
] | null | Imagine saying you’d like to study history without specifying that you’re interested in Bronze Age Mesopotamia, Italy in Late Antiquity, China under the Song Dynasty, pre-contact Mesoamerica, Scotland during the Protestant Reformation, the Canadian Prairies during the Great Depression etc. Mathematics is no different, ... | Thank you for clarifying this as I did not know that. Well, I want to self-study Calculus and basically understand Calculus to the point where I know every bit of it. I love math but I do not how to effectively study it or to excel at it. | The understanding of why calculus works will come from a subject called Real Analysis. The process of learning analysis is likely a very different mathematical experience than you've been exposed to before, because it is all about reading and writing mathematical proofs, which is very difficult to do at first. On the o... | I'm still figuring this out but I guess studying within timeslots and dedicating that time slot to a section until it's mastered For example, if you didn't know how to do division you could take from 5-6pm every day to dedicate to reading on it and practicing it until you're into the "I can do this in my sleep phase." ... | Thats still a pretty big field. Is this a specific class or are you trying self learn a subject? |
[
"Sequence using double primes, excluding 2."
] | [
"math"
] | [
"tefdgb"
] | [
0
] | [
"Removed - incorrect information/too vague"
] | [
true
] | [
false
] | [
0.5
] | null | I don't understand the definition of the problem . Can you explain how fulfills the definition? What is n and which are these 8 consecutive numbers each divisible by 3, 3, 5, 3, 3, etc? | Don’t think in terms of which real integers fits the definition, since that’s impossible. What I’m trying to say is if you could theoretically have two distinct prime roots for 3 & 5, call them 3a & 3b, and 5a & 5b, then what is the longest chain you can build using those 4 terms (3a, 3b, 5a & 5b) where each term is d... | Is the question for the 33533533 example the following? And then for the next example you have sets 3a, 3b, 5a, 5b, 7a, and 7b? | That’s correct. Looks like the mods decided best to remove my post now :( | Probably because it was very confusingly worded - I think it was practically impossible to understand what you meant from only your initial post. If you ask again, try to explain more concretely what you want - use examples, and explain how they answer your question. |
[
"Linear Algebra"
] | [
"math"
] | [
"tf9zzq"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | null | They look like normal questions to me maybe you should look into alternative learning resources. | These questions look quite standard and easy.. I would suggest doing more practice problems and trying to understand the abstractness behind why certain methods work. Further, maybe try solving proofs behind the theorems. I know that helped me, particularly when my intro lin alg class at GT used the book “Linear Algebr... | Sometimes, I don’t even know what a question is asking me, it’s just a blob of random vocabulary of which I know little about. Then you are lacking basic definitions. Get more books (I studied LA 35 years ago not in US, so I can't help). Do more exercises (really a lot more, at the end almost all problems you'll find w... | The math program at Michigan is top 10 in the country, but grad students aren’t always the best teachers. The material looks standard, seconding other recommendations to use alternative learning sources e.g. Youtube. | University of Michigan Math Department is well known… but not for being a debacle. |
[
"I've finally enjoyed a Math Paper."
] | [
"math"
] | [
"tewhx3"
] | [
29
] | [
""
] | [
true
] | [
false
] | [
0.81
] | [deleted] | Yes, from my experience it seems to be characteristic of Indian English. | Yes, from my experience it seems to be characteristic of Indian English. | I would think this actually comes from British English then. | In Britain at least, yes, although we wouldn't use it like OP does. | That's great to hear! I agree with you, managing your time, especially during a test or exam, is hard. I much prefer when I'm given a couple of days to digest the problem. |
[
"To Keep Students in STEM fields, Let's Weed Out the Weed-Out Math Classes"
] | [
"math"
] | [
"teuidg"
] | [
703
] | [
""
] | [
true
] | [
false
] | [
0.84
] | null | Engineering departments also worry about calculus sequences driving attrition. In Ohio, Wright State University’s solution also involved revising math offerings. But rather than changing the content of the calculus course, they focused on preparing students for calculus by emphasizing “engineering motivation for math.”... | Asking engineers to write a math curriculum is how we get monstrosities like combined DE/linear algebra classes that do neither justice. Bonus points for the leveled up version that also includes shitty introductions to transform methods, Fourier series, and complex analysis in the same course. The article blames math ... | I feel like for students, they will just consider all math weed out classes. They literally call calculus of any level a weed out class. This just sounds like people want to lower standards. | I can see how the full calculus series probably isn't necessary for every degree encompassed by STEM. But from my experience as a math tutor at an engineering college, the students that really struggle with calculus are students that struggle with the algebra too. What I fear is if Calculus isn't an early weed out cour... | Doing integrals by hand isn't "doing integrals by hand" it's "understanding how and why integrals work by performing the process" so you can apply them in relevant situations that may not be immediately obvious to someone who isn't aware of that. You can't be clever without the tools for understanding Now, testing peop... |
[
"Sporadic Groups"
] | [
"math"
] | [
"tf3zvu"
] | [
8
] | [
""
] | [
true
] | [
false
] | [
0.91
] | I am not a mathematician but I am very fascinated by the classification of finite simple groups. In my understanding, mathematicians started this classification with some countably infinite families. Then Mathieu found some simple groups that don't belong to any of these families. After 100 years other sporadic grou... | Nobody declared "Those are the only sporadic groups" without the larger context of the known finite simple groups. The classification of finite simple groups is a huge proof by contradiction. If the list of known finite simple groups (certain infinite families and 26 additional examples) is not complete then there is ... | There are nonabelian finite simple groups larger than the Monster group, for instance the alternating group on 10000 symbols. If you mean finite simple group, then unfortunately we don't know , except for the fact that the proof tells us so. The revision, or rewrite, of the proof (aka the "second generation" proof) is ... | I thought the sporadic groups are only in the context of finite simple groups. However, thanks for the explanation but I still don't get it. What do you mean " a smallest finite simple group" ? What prevents the existence of a group larger than the monster? | The "sporadic" group are sporadic because they do not fit into known families. We don't have a strict mathematical definition of the property of "sporadic", other than just listing out what the groups are once the classification is known. Because of that, it's not possible to prove that there are 26 sporadic groups by ... | Dummit and Foote's discusses non-existence proofs in the context of the Feit--Thompson theorem that all groups of odd order are solvable (so there are no simple groups of odd order besides the cyclic groups of prime order). See "Remarks on the Existence Problem for Groups" in Section 6.2 and "Application to Groups of ... |
[
"Mathematicians, do you read through the proofs of results in papers or do you just care about knowing the the result proved"
] | [
"math"
] | [
"tf3jj3"
] | [
33
] | [
""
] | [
true
] | [
false
] | [
0.9
] | I understand that undergrads and grad students reading research papers should probably read through the proofs to better grasp/learn the material. But, do seasoned mathematicians care for understanding the proofs of results they need for their research? | It depends. Some papers you read because they have useful techniques. Others are useful as a black box machine. Edit: Some you also just read for flavor, because it’s interesting! | In combinatorics, the proof is almost always more useful & interesting than the "theorem". | Really depends on why I decided to read the paper and how far from my area it is | Sometimes you also need the result in a slightly more general case, so you have no choice but to open the black box and fiddle around. | As an example of this, I work a lot of with decision problems in group theory, and often I have to read proofs of 'existence' results to check that their construction is in some sense computable. For example, trying to change the statement "for x > 0 sufficiently large" into "for x > N where N is this computable value"... |
[
"Are there negative and complex bases?"
] | [
"math"
] | [
"texmiu"
] | [
10
] | [
""
] | [
true
] | [
false
] | [
0.7
] | How would they even work? | They work in the exact same way as the integer bases greater than 1. They are not particularly useful, though. | No, -5 would still be -5 in base -10, because the "ones place" would correspond to (-10) so it would still be the ones place. But now 15 in base -10 would also be -5 in base 10, so now numbers don't have essentially unique repesentations. | Base -1+i is also interesting, because it can represent all complex numbers using only the digits 0 and 1, and it is related to the dragon curve. | https://en.wikipedia.org/wiki/Quater-imaginary_base | Base -b can represent all numbers, positive and negative, using b digits and without a negative sign. So there's pretty much no point in using a negative sign in negative bases. |
[
"What's the most interesting intersection between higher maths and natural science?"
] | [
"math"
] | [
"tew46s"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.71
] | I'm not talking about branches of math that were developed specifically to solve scientific questions (e.g. Diff EQs/calculus in physics, etc). People talk about the "unreasonable effectiveness of mathematics in science", and I'm curious what applied mathematicians have run into. For example, I find the application of ... | There are a lot of applications like this! Two examples you could look into could be how group theory is used in mineralogy, specifically crystallography. You could also look into how some people are trying to topologically classify different proteins through knot theory. Again there are a lot of things like this th... | Riemannian geometry pre-dating general relativity by several decades feels like a good example. Honestly the push and pull of math and physics development as a whole speaks deeply to this “unreasonable effectiveness”. | Petri nets in biological modeling. Swarm robotics concepts in modeling group motion in bacteria. Both of these often boil down to "differential equations with coupling defined by a graph" Game theory in population dynamics (again, this usually couples game theory with differential equations) | Your first example is something that blew my mind in undergraduated. Essentially there are only 7 1D infinite repeating patters up to group isomorphism 17 2D ones and some 300+ 3D one which you can use to classify all possible forms of crystals thst could exist. So fucking cool But the 2D are the shit. I was (and am) ... | I'm coming from a limited perspective as an undergrad but I find the complex numbers and their use in physics an amazing example of effective math |
[
"Is there a better algorithm than lattice points to draw aesthetically pleasing circle approximations from line segments?"
] | [
"math"
] | [
"tet87w"
] | [
16
] | [
""
] | [
true
] | [
false
] | [
0.93
] | I have a spare-time project that's essentially a . Basically, you can draw straight lines between any two intersections on the grid. I have three kinds of drawing tools for the application. The first two - to draw a single line and to draw a box, are simple to implement, but I have been having some trouble making a cir... | This seems somewhat similar to making a circle in minecraft. Perhaps you can adapt the techniques used there to get nicer circles. I believe you can take the convex hull of the points where x +y < r | How are you choosing the points to connect? Ideally you'd only choose vertices that actually lie on the desired circle. Your problem spots are where consecutive vertices have significantly different distances from the center. | Create a "convex hull" around the points you have. This should remove all pointy out bits. There are algorithms for this online if you search the term. | I don't have a good suggestion right now, but any approach that produces concavities should be immediately rejected imo. | I get the X and Y values of 64 * r equally spaced points on the circle, and if those values both differ by less than the "fuzz rating" (in my case, 0.3) from integers, I use those integer values as a point on the circle. Then I connect all the points found this way. |
[
"Properties that apply to pi but not e"
] | [
"math"
] | [
"tesb41"
] | [
157
] | [
""
] | [
true
] | [
false
] | [
0.87
] | Does anyone know of any interesting properties that apply to pi but not e (or e but not pi)? Obviously there are simple things like pi > 3 but in terms of interesting qualities they appear to be very similar, both irrational and transcendent and computable and conjectured but not proven to be normal. I recently learned... | The continued fraction of e has a simple pattern, but pi’s does not. The irrationality measure of e is 2, which is as low as it can be for an irrational number. The irrationality measure of pi might also be 2, but we only know that it’s no greater than about 7.1. Edit: I changed my opinion and no longer think this make... | pi > 3 Engineers: o.O | Most properties of pi do not apply to e, given that they are different numbers | Name a mathematical constant you can discuss with your girlfriend but not your boss | Sort of. The rationals are dense in the reals, so all irrational numbers are equally well approximated by rationals in the sense that there exist arbitrarily close rationals to that number. The irrationality measure is more about examining the growth rate of denominators in a sequence of approximations. My opinion is t... |
[
"What’s a fun branch of math to self-study?"
] | [
"math"
] | [
"teg9dp"
] | [
262
] | [
""
] | [
true
] | [
false
] | [
0.97
] | I’m a math hobbyist with not much formal education in math so far, but I’m heavily interested in concepts like Abstract Algebra/Group Theory and Real/Complex Analysis. However, as far as I’m aware, these are typically really hard subjects to self-study. So, do any of you recommend any subjects that don’t require a teac... | Graph theory can be very interesting and useful. Maybe you could give it a try. | Complex analysis (aka "geometric function theory" or "holomorphic functions of a single complex variable") is very much worth studying, for two reasons: It is hella useful outside of pure math. For example, the mathematical tools used in digital signal processing (series and transforms) are complex analytic in nature. ... | Linear algebra. | Combinatorial game theory. I self studied with "Winning Ways" by Berlekamp, Conway and Guy during my PhD. I think the fun of it kept me going through the slumps and slogs of doing a PhD. Unfortunately it's pretty expensive to get all four volumes... | Seconding, it also doesn't have prerequisites (but does bring in many other things eventually) |
[
"i just measured my gfs ass cheek....somethings not right here..."
] | [
"math"
] | [
"vk6scd"
] | [
0
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
0.35
] | null | bruh cool it, if you post something and it gets removed by 3 different subreddits it might not be a good idea to keep posting it | This behaviour suggests his girlfriend is probably imaginary… | Ass cheeks are not perfectly round. Instead get a container of water, dip her ass in that and see how much the level rises from that you can gauge a much more accurate measurement of volume | https://www.reddit.com/r/math/comments/vk5uj4/i_just_measured_my_girlfriends_ass_something_isnt/?utm_source=share&utm_medium=ios_app&utm_name=iossmf | Cause humans are very good at gauging 3 dimensional objects without maths... |
[
"i just measured my girlfriends ass.... something isnt right here. help"
] | [
"math"
] | [
"vk5uj4"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.42
] | null | Someone take to Matlab to solve this man's problem! | Your girlfriend's ass measures from starfish to cheek peak? That seems small to me. Edit: "awfully" meaning "very", not "sMaLL bUtT bAd" or anything. | I mean, butts tend to be more elliptical, so you’d probably do better with a vertical measurement too | That's just 1 cheek player. | Applied… math? |
[
"How fast would you have to drive?"
] | [
"math"
] | [
"vk5mb5"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.41
] | null | The speed you have to drive at is the distance you have to drive divided by the time you have. Can you work out those two quantities? | Yes, you will need to deal with timezones, because you're going to need to find how long there is between a sunrise (which you probably have in one time zone) and a sunset (which you probably have in another one). | Not exactly a brain-buster. But there are lots of variables. For example, which East Coast city you start on and which West Coast city you end at. Which time of year you are making the trip as well. It's 2,789 from NYC to LA. Sunrise in NYC is at 5:26 (as of writing this). Sunset in LA is 8:08 PDT, which is 11:08 ... | More like 192.3mph | Shouldn't it be 17.5 hours? 23-5.5 The record is 25.7 hours , but it was set during the 2020 lockdowns and started at night to avoid the worst traffic. |
[
"logic math books and using negations"
] | [
"math"
] | [
"vk376j"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.88
] | null | It's not entirely clear what you're asking about. Pretty much every introductory logic text will introduce a negation connective in the first chapter; it's fundamental to traditional (non-constructivist) presentations of logic. Can you give any examples of what you're looking for? | Some background: Syntactic derivations in second-order logic based on the Comprehension Axiom Schema and Axioms of Choice are very much like syntactic derivations in set theory. In neither case would a working mathematicians write all the details of the argument but would resort to shorthand notation. In both cases—sec... | Negations and proofs by contradiction/counterexample are used everywhere in math. | Perhaps fuzzy logic op? | Yep, a bit. The basic idea is that to consider the negation of something we may be able to conceptualize the structure better. I posted a little follow up with some background but basically, I was curious if any books use such methods more generally and in a more explanatory structure. |
[
"An introductory book to quaternions"
] | [
"math"
] | [
"vjr4ed"
] | [
11
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.87
] | null | Try reading "Naive Lie Theory" by Stillwell! | I think Geometric algebra is even cooler and more general. There’s a few good books on that. | He covers Algebraic Geometry, which shouldn't be confused with Geometric/Clifford Algebra. | Thanks, I'll give it a try! | Good advice |
[
"An embarrassing theorem back in high school"
] | [
"math"
] | [
"vjnmt4"
] | [
1
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.55
] | null | if you 'fold out' the path of the light into a straight line then this is just the statement that in a right triangle the length of the adjacent side is equal to cosine(angle) times the length of the hypotenuse | First, congrats on having thought through this yourself. Coming up with both a mathematical question and an answer to it is something to be proud of. As far as originality goes, you should not have high hopes here. I don't know if this result has been stated before in exactly this language in terms of light bouncing be... | Snell-Descarte law ? | Now that I look back, yeah, it seems so! Did notice that, but it's just basically calculating the hypontenuse of a base L, except by parts. Weird how it's just now I notice it. | You reading are correct, since the light travel in straight line (ignoring the effects of gravitational field) accordling to the Huygens principle. Also you are assuming that the light bounces only by reflextion, similar to happens on optic fibers. Still I need to read carefully your formula. |
[
"After about 20 hours, I think I solved the legendary Problem No.6 of IMO 1988. Am I missing something? Please let me know in the comments."
] | [
"math"
] | [
"vk4xo6"
] | [
215
] | [
""
] | [
true
] | [
false
] | [
0.91
] | null | What are x and y in your theorem 2? You claim they are arbitrary positive integers, but the first line of your proof states "It is evident that y >= x," so you must be putting some hypothesis on them that your theorem 2 omitted to state. What is k in the theorem? I can't really understand what you are trying to say. Yo... | What are you talking about? | Interesting proof! I don't think anything important is missing, with the key pieces coming from theorems 3, 4, and 6. Though a few things that seem out of place are: 1) Theorem 2 doesn't hold for the trivial case of x = y = 1 2) It is unclear what k is in Theorem 5 when you are assuming f(x, y) = m 3) You assume monoto... | Theorem 2 is still a bit unclear. You make a claim involving k before defining what k is. | It was the assumption made in the Introduction part. WLOG, since f(a,b)=f(b,a) we can swap the values (a,b) such that a<=b without changing the value of f(a,b)=f(b,a). About the first part of Theorem 2, you are right, that was a mistake. This part of the theorem is actually not important, but nevertheless I've updated ... |
[
"Ideas for bachelor’s thesis (Algebraic Topology)"
] | [
"math"
] | [
"vjnthj"
] | [
8
] | [
""
] | [
true
] | [
false
] | [
0.65
] | null | this should be a question for your advisor, shouldn‘t it? | Three courses in point-set topology is a lot! Especially for undergrad. How did that work? | Definitely talk to your advisor about this. Also, talk to any topology faculty because they might have an idea and would possibly be a thesis advisor (assuming your academic advisor doesn’t have to be the same as your thesis advisor). From my own experience, I pushed do a thesis as well but years later found myself wis... | There's a lot of work left to do in the field of (quantum) knot invariants if you're interested in low-dimensional topology. Some of it could be considered low-hanging fruit as well, if you're getting used to the field. | three courses in point-set topology and one introductory course in algebraic topology Four courses in topology on a bachelor level? Lucky you, we had only the one. What were the syllabi of all 4? |
[
"Marcus du Sautoy | The Creative Code to Thinking Better | Talks at Google with Timothy Nguyen"
] | [
"math"
] | [
"vjxejy"
] | [
29
] | [
""
] | [
true
] | [
false
] | [
0.79
] | Marcus du Sautoy, Professor of Mathematics and Professor for the Public Understanding of Science at Oxford University discusses AI, creativity, and mathematics in his recent talk at Google with host Timothy Nguyen. In addition, we discuss his books and as well as his forthcoming book on games. | To this day, Google's understanding of the subjunctive mood in my native tongue is worse than that of Microsoft Word's spellchecker in the late 90's. So, "AI is learning to think", my foot. | It’s learning very slowly 😉 | It learns something, but you are exactly right about how it learns: it just ‘averages’ existing usage. If you are a descriptivist about language you might say this is good enough! It can speak well enough to communicate. | It can speak well enough to communicate. Speaking well enough for what purpose? A five year old can communicate effectively, but generally their language skills are not what you would call top-notch. Really good prose and poetry in any language tends to make use of the full range of available wordage. | Of course. We are talking about whether AI has learned a language. 5 year olds have learned enough of their native language to communicate some things. Right? That’s all I’m saying. I agree there can be other measures of language use beyond ‘can you communicate basic thoughts’. |
[
"A question about alternate card shuffling methods."
] | [
"math"
] | [
"vk93w7"
] | [
12
] | [
""
] | [
true
] | [
false
] | [
0.94
] | I'm looking into making my own card shuffling machine, and would like to find a method that would approximate the randomness found from hand shuffling. I watched from Numberphile, that suggests that the reasonable number of shuffles by hand using the 'riffle' method is 7 to properly mix the deck, with any more shuffle... | The standard hand shuffle used by poker dealers is faster than the shuffle machines. They save time by shuffling the second deck while you play a hand with the other. | Just have the machine repeat whatever process you pick mulitple times. | To be clear, a 52-shuffle involves, for each card, choosing a random number between 1 and 52 and putting the card in that pile, and then stacking the final piles atop one another. The likely result of this procedure is that some of the piles are empty and some contain multiple cards. Piles that have multiple cards will... | If we forbid empty piles, the lemma still holds. And all outcomes now have equal probability. But the product of amount of piles can't go above 52 for obvious reasons. The lemma that an a-shuffle followed by a b-shuffle is equivalent to an ab-shuffle? I don't think that's right. Two 8-shuffles make a 64-shuffle, and in... | Sure, that's one way to do it, but it's also considerably more complex that what I'm after. |
[
"How can you say that imaginary numbers exist?"
] | [
"math"
] | [
"v08h9g"
] | [
0
] | [
"Removed - not mathematics"
] | [
true
] | [
false
] | [
0.29
] | null | It exists because someone says it exists. Math isn’t physical; you won’t find an imaginary number, pi, or anything else jumping around out in the forest. But by assigning it a definition it now exists as an abstract object. Of course, the fact that imaginary numbers have very real applications is another question. | Imaginary is just a name mathematicians have to some numbers that have a certain property. They demonstrably are a closed set and have other provable properties. Their use in the real world is also well established, in a way that describes relationships between things, not in a way that you are using imaginary num... | Well you can understand the idea of negative numbers, maybe in the context of directions, and debt, but they don't physically exist either, you can never have a negative number of things, similarly complex numbers are real because they can be understood in the context of rotations numbers and mathematical objects are r... | You can't. Numbers are not tangible things that exist. In math, we agree on a set of rules and then explore where these rules logically lead to. Generally, a lot of these rules have been inspired by the "real world" (we define the natural numbers because they match our experience with counting) and this is why math is ... | When people are first taught about the imaginary and complex numbers, it's usually stated as just "these weird things exist, just trust us and memorize it." But you don't have to take it on faith! The imaginary numbers (and their friends, the complex numbers) come from a clever way of adding and multiplying points in a... |
[
"How do you calculate bell curve percentages for standard deviations beyond 3?"
] | [
"math"
] | [
"v07mq7"
] | [
0
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
0.33
] | null | Unfortunately, your submission has been removed for the following reason(s): /r/askmath /r/theydidthemath If you have any questions, please feel free to message the mods . Thank you! | Assuming by "bell curve" you mean the pdf of a Standard Normal distribution N(0,1), it is the integral of said pdf over the interval [-7,7]. However, that integral cannot be calculated explicitly, but you can get numerical solutions to any degree of precision computers can achieve, and the result is very close to 1, yo... | I'm not trying to give financial advice, I was just implying that the Cauchy distribution is particularly intractable. In fact, it is not even L¹ (let alone L²), which means that it doesn't have a mean and, therefore, not even a standard deviation. Reversion to the mean is a tried and tested strategy in Quant Finance,... | I'm not trying to give financial advice, I was just implying that the Cauchy distribution is particularly intractable. In fact, it is not even L¹ (let alone L²), which means that it doesn't have a mean and, therefore, not even a standard deviation. Reversion to the mean is a tried and tested strategy in Quant Finance,... | https://en.m.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule |
[
"“Both real and imaginary numbers have exactly the same logical status. They are human concepts that model reality, but they are not themselves real.” - Professor Ian Stewart"
] | [
"math"
] | [
"vkdrkt"
] | [
937
] | [
""
] | [
true
] | [
false
] | [
0.97
] | I’m reading Professor Stewart’s Incredible Numbers and came across this quite. I’m a Maths teacher and I’ll be using this when introducing and teaching imaginary and complex numbers. I just liked the quote and thought I’d share it. | Platonists in shambles. | Consult your physician to find out if intuitionism is the right thing for you | You could argue that nothing is “real” other than the fundamental subatomic particles. Anything else is just a human abstraction to describe patterns of those subatomic particles An alternative Platonic view would be to consider basically every coherent concept as “real” in some way | Math Prof CRUSHES ancient Greek wide-boy | Well, fundamental particles are better explained as excitations in quantum fields, so we can go deeper anyway :D |
[
"Question about a lever"
] | [
"math"
] | [
"uzox5r"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.5
] | null | Unfortunately, your submission has been removed for the following reason(s): /r/learnmath /r/homeworkhelp /r/cheatatmathhomework /r/math If you have any questions, please feel free to message the mods . Thank you! | The road to riches is paved with homework. | The road to riches is paved with homework. | This sub is not for homework help, try elsewhere. | It’s not homework. It’s a real world application. I’m using it for something on my airplane. At least hint to me a way of calculating it. Physics from 2 years ago is long gone out of my brain |
[
"Does the claim \"mathematics is hierarchical and needs to be taught in a specific order\" stands the ground?"
] | [
"math"
] | [
"uzkdhu"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
1
] | null | I mean, some things are hierarchical in terms of understanding required, so those should be taught in a certain order, while some others are not. An interesting example is teaching probability. You can start teaching the basics of probability without a lot of advanced knowledge required. You can even teach some very i... | Have you done any advanced probability? Learning it without measure theory is painful, and in some cases impossible. In fact the kind of measure theory you get in advanced probability/stochastic analysis is far beyond what you'll see in a general first course. | I've seen some things, but it's not my area at all. Yes, of course, I fully agree with you. My comment was restricted to structuring thevteaching of mathematics up to the undergrad level. My bad for not making that clear. | I can second that entirely. I tutor adolescent children (~14-18 yo.) and interestingly about the curriculum are two topics, combinatorics/stochastics and vector geometry because BOTH can be done at any point in those 4 years and different teachers have different prefrences. Right now I have a young man learning about v... | It's absolute rubbish. Math "starts" with sets nowadays. Sets were only invented in the 19th century. And people did math before that. |
[
"Trouble with the journal Combinatorial Theory"
] | [
"math"
] | [
"v02yb1"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.54
] | [deleted] | Math journals are terribly slow. I have never had a positive response in less than three months and usually it takes much more than half a year. I have experienced rejections after two years. So what you say about CT does not seem to indicate anything out of the ordinary, your behaviour on the other hand could possibly... | May I ask what your experience is with publishing generally? The hassle is not a good sign, but some of these timelines don't appear terrible to me. Maybe it's different in combinatorics, as I gather people publish quicker there, but I had a paper at a good journal take 7 months to get a referee. Aanother paper rejecte... | I don’t think any of this will hurt the journal. I do think it’ll hurt the chance of acceptance of your paper. Withdrawing the paper before all reports are in will not lead to acceptance. Asking for a decision 1 month after submission is bold strategy. | Math journals are slow in part because they can be. arxiv.org is the actual "journal" of record, and the other journals are basically curated subsets of it. The slowness of journals does not inhibit the dissemination of knowledge, so it is considered acceptable. Yes, it is annoying that they are slow. However, spamming... | In mathematics, people generally only withdraw a paper from a journal if there's something wrong with the paper, or there's been a massive failure of process at the journal. Neither of these have happened here, so it does come across as lack of confidence in the process or your paper, especially if you aren't a known n... |
[
"Can at least one statement from every single math field be axiomatically proven?"
] | [
"math"
] | [
"uzye2s"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.17
] | [deleted] | I get the feeling you haven’t completely learned it the | What is a non-axiomatic proof? A proof always follows from axioms or other theorems whose proofs follow from axioms. | I mean, maybe Italian algebraic geometry (like the kind done by Severi)? | Yes, and kind of. There's no universally accepted set of axioms for performing mathematics. ZF has gained popularity, because set theory is exceptionally powerful, but it's far from the only acceptable axiomization. You could, if you wanted, take as an axiom whatever you want to prove and claim it to be an axiomatic pr... | Well, ZFC is just ZF along with the axiom of choice which is the de facto standard for mathematicians. There is a growing mass of us who use IZF or CZF (intuitionistic or Constructive) ZF. Similar to classic ZF, but we approach mathematics through a purely constructive lens. https://plato.stanford.edu/entries/set-theor... |
[
"Neil Calkin deletes previous tweet, labels news of a short proof of the four-color theorem as “premature”"
] | [
"math"
] | [
"v059tr"
] | [
617
] | [
""
] | [
true
] | [
false
] | [
0.98
] | null | Fair play for explaining a redaction. Many would have just left it at that. | One thing people seem to be getting wrong: Neil Calkin never claimed a proof. He was stating two other mathematicians, David Jackson and Bruce Richmond, claimed a proof. More pedantically, David Jackson claimed the two of them had a proof. | If you really think you've cracked something then the excitement can be quite overwhelming, and leaves one liable to do things like post tweets before a really thorough amount of checking has been done. Absolutely fair play for the deletion, totally natural and human to post the tweet the first place. No hard feelings. | Yes, and for all we know, they may still think they have a proof. Maybe it's just that they want to make the announcement themselves (and are not ready to do that just yet) rather than have someone else spill the beans on Twitter. | Although, to be clear, the he never claimed had a proof—he claimed that he had heard that two others had a proof. |
[
"Why can more general problems — paradoxically — be easier to solve or prove? (from maths codidact)"
] | [
"math"
] | [
"uzy7ny"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.65
] | null | Generality focuses on big picture attributes without getting bogged down in the noise of the particulars. For example: To prove that sqrt(x + 5 sin cos(x-3)) is continuous you are drawn to look at the properties of that particular function. A lot to get bogged down in there. To prove that the composition of continuou... | 3b1b’s recent cube shadow video is a fantastic look at general vs specific problem solving | It can be like being given a Where's Waldo where everyone's blurred out except for Waldo. (Such a picture generalizes all possible photos that disagree only in the blurred portion.) | Often the context happens to be the context of the problem. | Using statistics to answer mathematics . Interesting XD Thanks! |
[
"Currency with pictures of mathematicians"
] | [
"math"
] | [
"v01yl0"
] | [
85
] | [
""
] | [
true
] | [
false
] | [
0.97
] | I recently discovered that, before Germany adopted the Euro, . That led me down a rabbithole where I found a . Of course, this raises the obvious question - which other mathematicians have been immortalized as the portrait on some national currency? Is there a CFA frank with a picture of Grothendieck? An Iranian coin w... | Alan Turing | The UK previously has had Newton (on the £1 note in the 70s) and Faraday (on the twenty in the 90s). | Just google "mathematicians on currency". The page http://matheminutes.blogspot.com/2011/11/mathematicians-on-money.html shows currency with Newton, Descartes, Pascal, Gauss, and Euler. (Ignore the last image on the page, which is fake.) If you do an image search on that you find a few more: Cahit Arf on Turkish bankn... | 10 Frank note had Euler: https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Euler-10\_Swiss\_Franc\_banknote\_%28front\_and\_back%29.jpg/927px-Euler-10\_Swiss\_Franc\_banknote\_%28front\_and\_back%29.jpg?20061001134651 | There's still a Newton quote on the £2 coin. Edit: it turns out they've now changed the design, but I've not seen any of the new ones and I'm not sure if they're circulating yet. It seems they stopped minting them for a while when the new £1s came out. |
[
"Modified Laplace transform?"
] | [
"math"
] | [
"v00mez"
] | [
14
] | [
""
] | [
true
] | [
false
] | [
1
] | Hi everyone, I'm currently taking a classical controls system course and have been learning about the Laplace transform. The way I understand it, the transform works by multiplying your signal by a specialized function e and integrating over time. The function e can be expanded to e such that each axis represents eithe... | Similar to typical R functions on a given domain can be given a vwctor space structure. Just like you can apply a change of basis to a normal vector space to make some problems simpler, you can do a similar thing for these function spaces. The Laplace transform and Fourier transform are basically doing just that. In pr... | Okay, so in essence you CAN, but finding some basis that is useful is another matter entirely. Thank you! | To add to the previous commenter, you may want to look into wavelet transform . They describe such change of bases in such function spaces (more precisely, the Hilbert space of square integrable functions on R ). By choosing different wavelet bases, you can extract different information. Specifically, look into the pri... | Seems to be a question for u/Academicoveranalysis | Wavelet transform In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. |
[
"Good linear algebra/representation theory based intro to QM other than Woit?"
] | [
"math"
] | [
"uzwdnf"
] | [
66
] | [
""
] | [
true
] | [
false
] | [
0.94
] | I'm looking for an "QM for math students" text that takes an algebraic approach at the college senior/first year grad level. Woit's "Quantum Theory, Groups and Representations" initially seemed ideal, but after skimming the book I worry he's too talkative and loose with his proofs. Are there similar books? I should not... | There is Hall's "Quantum theory for mathematicians". | I wouldn't say it's very algebraic. There is a lot of functional analysis in that book. | Definitely not lol, sakurai probably mentions representations once or twice and is hardly rigorous | Here is the book | I was not attentive in my reply to the "algebraic approach" part of the OP, but only to the "something besides Woit and still aimed at mathematicians" part. |
[
"Please tell me math gets more interesting after Calc 2"
] | [
"math"
] | [
"m11u4s"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.6
] | null | Good luck to you. Everybody who has gotten a university degree had to push him/herself through all kinds of classes that they absolutely hated. It is inevitable. But it also builds character. If employees see you took all this math they won't only think that you know quite a lot of math and are pretty smart, but they'l... | I really don't recall my Calc 2. My linear Algebra class was the worse class I ever took in college. The instructor was horrid. I love math but he did terrible things to my love of math. Sorry about your Calc 2. | Damn, that doesn't sound like fun | I guess you're a chemistry major. I can't promise you math gets more interesting after calc 2. Maybe your classes are very heavy on memorization and plug/chug. Your future classes might be like this too. I can tell you there ARE more interesting classes after calc 2, but as a chem major you probably won't take them. Bu... | Well actually it's 4-5 classes, calc123 linear algebra and maybe vector analysis. I guess if I change my mindset I'll get myself through it. Can't take pchem without all this math. |
[
"Where to start as a beginner."
] | [
"math"
] | [
"m0u9cy"
] | [
7
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.89
] | null | Nah I’d keep pluggin on khan if it’s working for you | Khan academy is a good place to be! If you want some fun things to fit in with the simple stuff look up math circles or competition math for the grade range u are in. | Don't be afraid to spend some time on the simple stuff. The simple stuff is the foundation for the interesting stuff, and you need to know it well so you don't get stuck later on. A common cause of problems in maths is not having the fundamentals down. Be patient: maths, like most worthwhile things, takes time. | Im doin Master's in Pure Math and if there's so.ething ive learned is that there's no shortcuts. | aops (art of problem solving) textbooks are pretty solid for content and have some interesting problems, some of it may be overkill though |
[
"How do Physicists handle the overwhelming facts that they know about reality?"
] | [
"math"
] | [
"m0nqqf"
] | [
0
] | [
"Removed - not mathematics"
] | [
true
] | [
false
] | [
0.37
] | null | Hmm, I get the feeling that you probably want /r/Physics . | I think you're overstating the level of ignorance that we have about the universe. It's not an exaggeration to say that physics has completely explained the how and why of essentially everything that everyone experiences. (With the giant philosophical exception of experience , of course.) It's one of, if not the, most ... | Er, no, math is fancier than physics, so there's no way physics is fancy math. | Physics is just fancy maths | Physics uses only a small subset of maths, and is mostly interested in using it to develop laws and principles abouts "IRL stuff" with a vague hope of enlosing all the universe in a single equation (likely a differetial equation). So no, it's more like different flavors of icecream than icecream vs topping. (Which is s... |
[
"Solving differential equations without a rhumbus?"
] | [
"math"
] | [
"m06ynv"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.2
] | null | I don't remember using my rhombus in DE. | What is a rhumbus? | Google didn't help... What is it? | I like your showerthoughts | Uhhh...all you need is pencil and paper? |
[
"If several leading digits of pi repeat, why don't all of them?"
] | [
"math"
] | [
"m0mcs0"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.13
] | [deleted] | But it's a valid answer. all digits would repeat, then Pi would be a rational number. But we know that Pi is not a rational number. Thus, the numbers cannot repeat. It's a valid logical conclusion. | Why would you expect them to? Looking for a substantial and real answer, not "bc that's what fractions do". | Any sequence might repeat infinitely if pi is a normal number. There is no proof either way afaik. Secondly, think about a the Champernowne constant (0.1234567891011...) It is irrational, but any sequence will repeat infinitely. 3141592 occurs twice, as you have indicated. It doesn't in the same way rational numbers... | If pi is a normal number (as it "probably" is, though nobody knows for sure), then finite sequence of digits in its decimal expansion will occur infinitely often, though not necessarily at regular intervals. Although 3141592 occurs again, as you say, the next digit is 1, as opposed to 6 at the start of the expansion, s... | I doubt you can find a simple (kids?) answer in relation to how pi is calculated. Most of the times pi was calculated taking one of the many known series whose sum is pi and then computing a suitable number of terms. So what we calculate is always an approximation. This does not give any insight about the fact the digi... |
[
"Drew a Euler Circuit and a Summation this term!"
] | [
"math"
] | [
"m0vps6"
] | [
98
] | [
"Removed - not mathematics"
] | [
true
] | [
false
] | [
0.98
] | null | It’s the mental fog that is me learning summations lol | Would legit buy that second one dam nice job | Could you share some more details about what that is/how it's done ? | Totally! The first one is inspired by Euler Circuits; “In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex.... | What are my eyes look at? I can't make any sense of the second one. It's like you told a machine learning algorithm to take math notes. |
[
"Distribution of Primes Along a Hilbert Curve"
] | [
"math"
] | [
"m0u7yw"
] | [
1197
] | [
""
] | [
true
] | [
false
] | [
0.98
] | null | It seems far more homogenous than the random selection. | An explanation: What is a Hilbert Curve? A Hilbert Curve is a space filling fractal which has found use in a wide variety of mathematical and non-mathematical applications. Its traditional form is a two dimensional assortment of congruent connected lines forming a "curve" (a long connection of lines that has only two e... | In the light of this new find, I conjecture that there exists a space filling fractal whose properties are such that nodes with Prime numbered indexes define an unobstructed pattern. Not to burst your bubble or anything, but this is probably true of any subset of the integers. What would be really interesting is if you... | Probably is basically random noise. Although, the primes get more sparse with log(n) so I would think that you'd start seeing a larger black region develop in the lower-left corner if you took this out to extremely large n. | Visually to me at least it seems a lot like random noise, no? |
[
"On David Robert's blog: \"This argument of Mochizuki doesn’t make sense to me\""
] | [
"math"
] | [
"m11smn"
] | [
70
] | [
""
] | [
true
] | [
false
] | [
0.9
] | null | I thought what Mochizuki was belaboring was relatively simple: Scholze and Stix take two objects which are isomorphic in one context and use this to identify them in a different context. The example he uses could have been better rendered like this: “{0} and {1} are isomorphic as topological spaces, but not when consid... | I know it's been said before, and I don't remember whether it can be somewhat explained as a difference in the cultural use of emphasis in writing (?) (either between Japanese and English, or between my usual MathPhys and pure math), but to my eye Mochizuki's enormous over-use of emphasis is supremely tiring to read. I... | Hi, it's "the blogger" here. My argument is more that Mochizuki is using an absolutely misleading metaphor. In i) he is talking about identifying 𝛼 and 𝛽 (in the sense as considering as literally equal, via passing to a skeleton), and in ii) he is talking about identifying 𝛼 and 𝛽 as points (well, not quite this, ... | This should be upvoted to the top. I don’t really understand why the author of the blog post got the wrong impression that Mochizuki was trying to claim that we could identify an interval with a loop because we could identify two singleton spaces, as it is evidently contrary to what the excerpt was trying to say. Peop... | Hi, author here. It was abundantly clear that Mochizuki was not trying to claim that, but rather arguing against passing to an equivalent full subcategory by giving a really misleading counterexample. |
[
"Example of second order linear recurrence relation with constant coefficients"
] | [
"math"
] | [
"m0jj9g"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
1
] | Does anyone know of an algorithm where a linear second order recurrence relation describes the time complexity? I am teaching a class in discrete math and we teach how to solve these recurrences, but I am trying to come up with an example where it shows up. | Maybe we can cheat a little... Fibonacci numbers satisfy a second order linear recurrence. It is well known that Fibonacci numbers can be interpreted combinatorially as the number of ways to tile a board of length n x 1 using only monominoes (1x1) and dominoes (2x1). So, if the algorithm is "given n, count all the tili... | I suggest writing to CS faculty at your school and ask them how recurrence relations other than 1-term recurrences show up in CS topics the students study. You could tell your class that recurrence relations are as basic to CS as differential equations are to engineering. The recursive way programs run makes a familiar... | Why are you asking specifically about an application to time complexity, e.g., are you only teaching an audience of CS students? | Yes, pretty much. Or maybe any way a second order recurrence shows up in nature. | Thank you, I will do that and take a look. |
[
"Tips to learn mathematics from a visually impaired mathematician working at Google ~ T V Raman."
] | [
"math"
] | [
"m0cwh7"
] | [
101
] | [
"PDF"
] | [
true
] | [
false
] | [
0.97
] | null | Downloading to read later on today. I've been thinking about this exactly in the last few days, about whether and how I'd be able to adjust to studying anything mathematically related in the case of sudden sight loss. I've read accounts of a few programmers who had to tackle the problem in their domain, but mathematics... | One of the greatest topologists of all time, Lev Pontrjagin was completely blind from the age of 14. Topology is in a sense, the study of geometric shapes and certainly involves a visual component. | Also check this webpage. http://emacspeak.sourceforge.net/raman/publications/thinking-of-math/ | That's, of course, remarkable. But I wonder if it wouldn't be harder for OP than for someone who lost their sight starting higher education. If you learn all the basics by relying on diagrams and visual intuition and then you can't draw them anyone, that seems to me like it might be harder than having to learn everythi... | Incredible. His story is really inspiring too. |
[
"Announcement: /r/math's 14th Graduate School Panel's Call for Volunteers"
] | [
"math"
] | [
"m0md19"
] | [
15
] | [
""
] | [
true
] | [
false
] | [
0.88
] | Greetings, , So (at least in the US), many graduate schools have sent out or are starting to send out offers for Fall 2021 programs, and many prospective graduate students are starting to make their decisions about which graduate school to attend. However, lots of things have changed in response to COVID-19, including ... | I'm a second year phd student studying quantum algebra. I'll help out! Hopefully there will be some questions I'll be able confidently answer this time. | I've been offering to help for the last however many of these, but in the recent ones there haven't been a lot of questions I've been able to help on. I suppose people's questions have changed. Or I've grown more ignorant or more humble. I'll still offer to help this time, on the off chance that my ignorance might be u... | I'm a first year phd student in descriptive set theory in europe, I previously did a masters in Bonn, last time there were a few questions about Bonn so hopefully I can help out this time as well! | I would be happy to volunteer, and I've taken a non-standard path that may be of interest. I have a PhD in applied math from a top 5 school and work in industry. Between undergrad and grad I was at a mathematical consulting firm as a programmer and analyst. Since my doctorate I've worked in defense as a systems enginee... | Id like to help out, I'm a second year PhD student studying analytic number theory. |
[
"What's the most abstract / roundabout way of defining Euclidean space?"
] | [
"math"
] | [
"m06x5f"
] | [
66
] | [
""
] | [
true
] | [
false
] | [
0.97
] | null | A Euclidean space is a finite-dimensional Banach space over R in which the group of isometries acts transitively on the unit sphere. | Banach space over R - A vector space over R (meaning that scalars are real numbers and not e.g. complex) equipped with a norm, in which all Cauchy sequences converge (which basically means that there are no sequences which seem to concentrate but do not converge.) (The last thing is the Banach part). Isometries: Maps f... | The unit interval is the initial object in an appropriate category of bipointed spaces. https://mathoverflow.net/questions/92206/what-properties-make-0-1-a-good-candidate-for-defining-fundamental-groups/92223 | In the norm topology | Yeah, if you take a topological space X and construct Dedekind cuts of rationals in the internal logic of the topos of sheaves on X, then you get the sheaf C(-,ℝ) of continuous functions with values in ℝ, w.r.t to the euclidean topology on ℝ. At no point do you need to specify that you want to put the euclidean topolog... |
[
"Most important inequality in mathematics"
] | [
"math"
] | [
"m0yl5l"
] | [
244
] | [
""
] | [
true
] | [
false
] | [
0.96
] | One of my professors shared with me what he considers the most important inequality in mathematics: health > math Please learn from my mistakes. If you begin to feel burnt out from math, take it easy and do something else you enjoy for a while. Withdraw from a class if you have to! There was a time that I was so invest... | Cauchy–Schwarz? But seriously, yes. Burnout is real. Math will still be around next year, you've got to make sure you are too. | I couldn't agree more and remind my students of this daily. Thank you for posting it :) Also I reduced for you: hel > m | I was about to say Cauchy-Schwarz Inequality until I read the body. | Most important equality : Im(burnout)=0 | Even after reading it I was still debating between Cauchy-Schwarz and triangle; the health thing might be third, but I think Cauchy-Schwarz still wins. |
[
"Is there a platform that you plug in a mathematical statement to be proven and software does it for you?"
] | [
"math"
] | [
"m0er7m"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.64
] | Wolfram Alpha can do this and a few other websites claim to. I found at least one website that can prove things but only for logic, not math. I am currently working on elementary number theory in my math class. Is there any technology I can use to help me or check my proofs? | There are interactive theorem provers, and automated theorem provers. Using either is its own skill, as you need to prepare a representation of your theorem in formal language and understand the representations for anything you use. Automated provers can't prove very much but interactive theorem provers can with some w... | To verify proofs you need to have formalised all the definitions, theorems, lemmas etc that you’re using. It takes a lot of time to build it all from the ground up. There is a big community effort to do these things in Lean, I think Kevin Buzzard’s blog is a nice place to get a feel for what’s going on. | If you're doing number theory best thing is to just write your own python script that checks your answer | If you have no friends/acquaintances that can help you then the typical way you get your proofs checked is that you submit them for marking or submit them for publication :-). If you're lucky you might get useful comments back as well! | The point of taking a class is to develop the capability to know when what you’ve done is correct, and the capability to communicate with your classmates about each other’s ideas and work. It’s actively harmful to use software to do this. You’re not going to asked anything that won’t yield to thinking about it for a we... |
[
"What Are You Working On?"
] | [
"math"
] | [
"m0k74t"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
1
] | This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on this week. This can be anything, including: All types and levels of mathematics are welcomed! If you are asking for advice on choosing classes or career prospects, please go to the most recent . | Trying to not crumble under academic pressure. I’m also coming to terms with some past abuse, so yippee me. I’ve been making a lot of math art on Desmos. It’s mostly just me manipulating parametric equations, but I’ve also gotten good enough to manipulate Bezier curves with that software. Here’s an example. . I made th... | Sch*mes I'm reading Geometry of Sch*mes. I just finished chapter one. I hope global specs don't come up next. (They probably will.) | Thinking about meshes, as usual. I've been even more split in my focus than normal. There's been essentially three things attracting my attention. The first is that I have been thinking about these maps I call , yet again. The short story, which I've given before, is that they form a class of maps between discrete pose... | Triple integrals in spherical coordinates, taking a test on Thursday. | Erdos-Lovasz Tihany conjecture |
[
"Axler's Measure, Integration & Real Analysis study group"
] | [
"math"
] | [
"m0gar4"
] | [
59
] | [
""
] | [
true
] | [
false
] | [
0.94
] | Hello everyone! I'm a 1st year MSc Data Science student and I saw that Axler released a new book on Measure Theory. It's free and it's very well written after skimming a bit through it. Now, I'd love to go through it. But I'm very swamped by my own classes to have the motivation to self-study it on my own. But if we ma... | What a coincidence! We're learning measure theory from that book itself and I'm sitting in that same class right now lol | That's awesome! Do you have recordings of your lectures or some exercises? Also are you interested in joining? It would be great to have you! | Yes, they are | How can you be so sure of yourself? Measure theory is the mainstream of mathematical analysis and probability theory. These fields can get very applied. | Actually I work in the more theoretical side of machine learning and the people in the field I talked to are experts in that area. It's true that some people phrase their maths in the language of measure theory but it's entirely unnecessary. I use stochastic differential equations regularly and never use measure theory... |
[
"Why/not Pure Maths?"
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"math"
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"m08ff8"
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5
] | [
""
] | [
true
] | [
false
] | [
0.65
] | Recently got asked in an interview why I chose Pure Maths over Applied Maths. On the spot I could really only come up with something like 'The patterns in Pure Maths surprise me more than the ones in Applied' but I'm pretty sure they could tell I was making it up Just curious then, what are your reasons for going the p... | I'm allergic to paychecks. | Depends on the field, but focus on what they care about, not you. If you're particularly young, you could say something like "I plan to stay on the cutting edge of this field, and having a solid foundation in Math uniquely positions me to understand the current, state-of-the-art applications on a foundational level. Th... | I think things like number theory used to be considered "pure math" but lo and behold | Applied math tends to live more towards things like computational linear algebra and numerical methods for solving PDEs and other analytic problems. Pure math has a more abstract focus and have many areas which aren’t studied as commonly in applied settings but are still very important in developing those tools down th... | Pure math is more "for fun" than applied math is. |
[
"Now that we're at ~31 trillion digits of pi..."
] | [
"math"
] | [
"m0fpoh"
] | [
553
] | [
""
] | [
true
] | [
false
] | [
0.96
] | [deleted] | We do have an algorithm that gives us the n-th digit of pi, and as such you don't NEED to store the previous digits to compute the next ones. On the other hand, it's kinda pointless computing other digits of Pi if you don't have the physical space to store the previous ones. As such, theoretically speaking, since the u... | > it's kinda pointless computing other digits of Pi if you don't have the physical space to store the previous ones it's kinda pointless computing digits of pi at all after like the fifth one or something | It's closer to 15 digits for some precise applications (GPS), but fair point otherwise. | GPS is so 'precise' that they ended up defining their own value of pi. That is: If you use a more (or less) accurate value of pi than published in the standard, your navigation results will be subtly off. The GPS definition of pi only has 14 digits. http://www2.unb.ca/gge/Resources/gpsworld.april10.pdf | I assume it’s because they already set the satellites to use the 14 digit version. Meaning anything that tries to be “more accurate” will have errors with respect to the signals it receives from the satellites. In other words the issue is software compatibility, not physics. |
[
"I have recently learned that if the determinant of the coefficient matrix of a homogeneous system equals 0 then the system has a non trivial solution. Why is that?"
] | [
"math"
] | [
"xextp6"
] | [
1
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.54
] | null | You really need some basic understanding of linear algebra to be able to understand this (see links below!). But the gist of it is this: If the determinant is zero, then you can't calculate the inverse matrix because that would involve division by zero. If no inverse exists, then the linear transformation defined by th... | If the determinant isn’t zero, then the linear transformation it represents isn’t a bijection The opposite is true. A bijective linear transformation have nonzero determinant. | What do you remember about the meaning of the determinant from your linear algebra class? | You should read a book on linear algebra! It doesn't sound like you understand it, which is bad since linear algebra is by far the most important subject in all of math. A square matrix is invertible if and only if its determinant is nonzero. Hence if a square matrix has determinant 0, it is not invertible. This means ... | If the determinant isn’t zero, then the linear transformation it represents isn’t a bijection, with the rank nullity theorem you show that it isn’t injective, so its kernel isn’t trivial, so there’s a non trivial solution (in fact a whole infinity of them). There might be a quicker (and more elegant) proof, but that’s ... |
[
"What color are algebra and analysis?"
] | [
"math"
] | [
"xer58d"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.35
] | null | I think algebra is (light) green and analysis is either dark blue or black (and I like it). | Both are yellow, because that's the colour of the textbooks. Thanks, Springer. | I would either go with blue or violet / pink for analysis. Or yellow? | Red-violet with green-yellow polka dots. | Both are green but I think it's just because they both start with A Set theroy: Yellow Algebraic Geometry: Red Graph Theory: Brown PDEs: Blue Calculus: Beige Statistics: White Probability: Light Blue Topology: dark blue (I think just because my copy of munkres is dark blue) Complex Analysis: Orange/light brown Linear A... |
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