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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[
"Budget"
] | [
"math"
] | [
"xelpkv"
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0
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""
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true
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false
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0.4
] | null | Your family income is 16+20 = 36 with you contributing 16/36=44% and him contributing 56%. If you want to split your expenses according to the same proportion it would be 0.44 * 880=$387.20 you and 0.56 * 880= $492.80 for him. | Yes, they make 25% more. If the bill total is 880, then their paying 660 means they’re paying 300% more than you. The way to solve this is: x + (1.25x) = 880 2.25x = 880 x = 880/2.25 x = 391.11 (what you pay) X plus 25%, or (1.25x) = 488.89 (what they pay) | Thank-you! | The rounding makes this not too accurate and has him pay more | Why is it 1.25 x? |
[
"Extreme math"
] | [
"math"
] | [
"xekj68"
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0
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""
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true
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false
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0.22
] | null | read the sidebar. | This looks like a homework problem. You need to think about cancelling some common factors. | Even after cancelling, you re gonna have the 150! To deal with (262 digits). Can't think of any practical reason to calculate it, but I'd suggest learning a basic programming language with a big int library if you need to do this kind of calculation frequently | 150! = 57133839564458545904789328652610540031895535786011264182548375833179829124845398393126574488675311145377107878746854204162666250198684504466355949195922066574942592095735778929325357290444962472405416790722118445437122269675520000000000000000000000000000000000000. But I suspect that this homework problem was tra... | Wolframalpha.com can do it |
[
"Is there a way to calculate expected value from probabilistic data?"
] | [
"math"
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"xed9lk"
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5
] | [
"Removed - ask in Quick Questions thread"
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true
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false
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0.78
] | null | The expectation value is best approximated by the average you are already taking. I think what is happening is that the plot doesn't adequately show the density of outcomes that are hitting the stop-loss level. If you impose the condition that wins - losses > -20 at all times, a lot of the runs are going to bottom out ... | You’re calculating expected value exactly right. Your problem is your geometric intuition here is leading you astray. From your first graph you should have a good understanding of this: once we have reached $980, the distribution of outcomes is going to look like a bell curve centered on $980 (i.e. the average ending b... | Look up martingales and the optional stopping or optional sampling theorem. It pretty much states that whatever stop-loss technique you can come up with (satisfying some conditions) will again give you a martingale. A martingale is a process with constant expected value (that's a property of a martingale, not the defin... | half of those would eventually climb above it again I did think of that possibility but decided that it shouldn't matter since the number of recoveries prevented by the stop-loss would be roughly the same as the number of downtrends prevented by it. The two would effectively cancel each other out, right? | Think of every run that hits the stop-loss level at some point as a subset. If you run them all from 980 until finished, it's still a binomial distribution, just centered around 980. The average of all of those runs will be 980. Replacing all of them with the value 980 changed nothing overall. |
[
"Jean-Pierre Serre is 96 years old today. Serre, at twenty-seven in 1954, was and still is the youngest person ever to have been awarded the Fields Medal. Happy birthday!"
] | [
"math"
] | [
"xeq1qy"
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899
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""
] | [
true
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false
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0.99
] | null | Serre is coming to my university to give a talk in one week. It just fascinates me how is he still able to lecture at his age | Met him in a conference as well. He mistook me for a waiter and asked me for a bottle of wine. | Met him in a conference once. Seemed genuinely curious in my research problem and told me to work hard. Happy birthday! | He came to my university to give a talk in 2006. He was already 80 years old, but he had the energy and the mental sharpness of a young man. I hope he's still doing well. Happy birthday! | A few years ago I went to see his talk. I lost the plot before the first minute was over. After the talk me and my friend just looked at each other and he went: "Well, that was undecidable." |
[
"Career and Education Questions: September 15, 2022"
] | [
"math"
] | [
"xf0gtf"
] | [
6
] | [
""
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true
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false
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0.8
] | This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered. Please consider including a brief introduction about your background and the context of your question. Helpful sub... | Hi everyone! I'm a PhD student interested in PDEs and free boundary problems (from the pure mathematician point of view) and I've almost finished a preprint I feel very proud about. My advisor has also said quite positive comments about my work. So now I'm thinking about where to send it, and I've been eyeing the journ... | If you really love math and enjoyed calculus, there's a chance you might like pure math. It's always worth it to give it a try by taking a intro to proofs course. Even if you don't like the pure math side of things, you can still appreciate the more applied side of math. You could lean into the more quantitative side o... | See if you can take a mathematical logic and proof or discrete math course. If you do well and enjoy the material that should give you an idea of what you are in for when taking linear algebra, abstract algebra, and real analysis and other proof based math. Math and Statistics are a great undergrad degree to obtain in... | hi! i'm not really sure if this is the right subreddit, but why can't i just get math? like i feel so usless and dumb, i'm in third year highscool and i still can't memorize the multiplication table. my mom locked me in a room with a multiplication table chart and forced me to learn it. i kept on crying and trying to m... | Anyone take the subject GRE today? I found it significantly more difficult than the practice exams. Also didn’t help that I had to get up at 5 AM to get to the test center. |
[
"Why are imaginary numbers even a thing?"
] | [
"math"
] | [
"xed8b1"
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0
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""
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true
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false
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0.44
] | null | Allowing us to take roots of negative numbers is only part of the story. We also can’t take a logarithm of 0, but we don’t simply invent a new number to serve as the log of 0 and go on with our day. The point is that you can prove that there is a set (the complex numbers) in which you can do almost everything you can d... | Because they simplify a lot of problems. Mathematics is a language and a tool to solve practical problems. Complex numbers are no different than any other part of maths. Just ask any electrical engineer if they would be able to model/analyze circuits without complex/imaginary numbers. | The name often does them a disservice but they are simply extending the real numbers such that we can take roots of negative numbers. Basically the process went as follows: Let's introduce this little guy here and define it such that ^2 = -1. Now expand this concept with the rules and regularities we already know about... | Yeah and why are “real” numbers a thing? Like where are they if they’re so real. Go out and find me a 2 somewhere. | Veritasium has a very nice video about that. |
[
"Any advice on making Abstract Algebra… less abstract?"
] | [
"math"
] | [
"xey7n1"
] | [
66
] | [
""
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true
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false
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0.87
] | So it’s pretty much the title. I have to take Abstract Algebra to complete my math minor. I am really struggling with it and we are only week 5. Our first exam is next week and I’m terrified. I think a reason I’m struggling with it is because I haven’t heard or been shown any real world applications and it feels like t... | My advice is that 'real world applications' is the opposite of what you need and won't help you. It will just obfuscate things and add extra detail that you don't need. What will probably be more helpful is some concrete examples of the objects you are working with. Go through your material and apply your theorems etc.... | Instead of real world applications, build up some go to groups you can use as examples to work with for the theorems. The dihedral and symmetric groups may be a good starting place since you have a very easy to understand group action in those cases | Try " Abstract Algerbra - A Geometric Approach" by T. Shifrin (Prentice Hall) | My advice is to lean into the abstractness, abandon all intuition, and regard abstract algebra as a subject about the formal manipulation of symbols. Edit: just to clarify, intuition can, and will, come later, but only after you understand, in your bones, what a quotient group is. | there's such a stark contrast in mathematical maturity between pre-understanding quotient groups and post-understanding quotient groups |
[
"How to develop a positive attitude when getting stuck while learning math on your own?"
] | [
"math"
] | [
"xezr6t"
] | [
53
] | [
""
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true
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false
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0.92
] | Self-studying undergraduate-level mathematics, I frequently find myself getting stuck when trying to understand a theorem, proofs or even while doing a problem. Now usually I am able to navigate my way out of being stuck, and gain some understanding in the process, but I feel like I do not have the right mentality at a... | you're an undergrad, so of course people are ahead of you in understanding the things you are looking up. be thankful they are. when you find yourself without any stack exchange to answer your questions that's when it gets real. | "If however, you want to learn group theory, it is not a good idea to open a book on page 1 and read it, working through all the problems in order, till you come to the last page. It's a bad idea. The material is arranged in the book so that its linear reading is logically defensible, to be sure, but we readers are hum... | I'm no where near your level of self discipline and intelligence but I have experienced similar issues. I find that math gives me a sense of peace. The grind of academic or corporate life can take that away. I suggest a meditation program. The meditation got me through it and improved my ability to concentrate and h... | Have you ever played any of the Dark Souls games? It's the same mentality. It may take hundreds of attempts and it may get frustrating and make you want to quit, but if you stick with it, you can have confidence in your ability to progress. Just because someone takes to it more naturally or has been doing it longer tha... | When reading a book, article, or even stackexchange answer, it's easy to see it as orderly and linearly progressing. On the contrary, mathematics is . I like to occasionally remind myself of the follow zoomed out timeline (all dates approximate): 300,000 years ago (ya) homo sapiens emerges 160,000ya modern homo sapiens... |
[
"Math Competitions for a 5 year old?"
] | [
"math"
] | [
"xelw2e"
] | [
7
] | [
""
] | [
true
] | [
false
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0.62
] | I know this sounds silly because he's so young, but my son LOVES numbers and math in general. He asks me to give him math problems in the car on the way to school. The problems are simple in the sense of "What's 22+13?" but he does the math in his head and figures it out. Did I mention he just turned five? He told me h... | You must be very proud of him, but I would think long and hard before teaching him that math is a competition. G. H. Hardy used to say that math competitions were bullshit and refused to participate in them. For one thing, they teach the wrong skills. They mostly reward speed and rote memorization of facts. They mostly... | Maybe. But you could also just give him problems from past Math Kangaroos to work on his own. | Friends of mine had a good experience with their kids in Math Kangaroo last year https://math kangaroo.org/mks/ I think it covers all grades | try some mock competition tests at home first. | "All students grades 1-12 qualify for participation in Math Kangaroo if they are able to work independently, read, and answer a multiple choice test." Per their website. My son can read just fine on his own, so I wonder if they would accept younger if asked? |
[
"Finished Euclid… Finished Archimedes… who should I read next?"
] | [
"math"
] | [
"xeoujb"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
0.71
] | In the past couple years I’ve started reading the original texts of my favorite mathematical idols. First was Euclid, my favorite man to ever live. Recently, I just finished Archimedes. I need recommendations of writings to read. I was thinking maybe Georg Cantor. Please leave a recommendation! | You could keep it in chronological order. E.g. do Newton’s Principia before Cantor. | Then Leibnitz, then Euler, then Gauss, then Riemann, then Pointcare, then Gauss, then Lyaponov, then Kolmogorov,...There are many mathematicians to read. | Done with triangles and planes? Good, next jump right to SGA | For good measure you must read Lebesgue. | Yeah maybe thrice for good measure. |
[
"Differential Geometry textbook"
] | [
"math"
] | [
"xeioz1"
] | [
88
] | [
""
] | [
true
] | [
false
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0.96
] | My dad (an applied mathematician) just shared with me (an undergraduate math student) that he regrets not taking a differential geometry geometry class in college. So I would like to do a self study with him on differential geometry. What would be the best way to do this? What textbook should we use as our guide? | do carmo if you want down to earth stuff, you can go with lee if you want to start getting into the modern stuff | For the differential geometry of curves and surfaces (undergrad level), Do Carmo for the classic approach, but I also recommend Barret O'Neills Elementary Differential Geometry. It uses differential forms which are valuable to learn in the modern day. For Grad level, I also recommend John Lee's 3 book series Introducti... | If you want something a bit more concrete, by Tapp is good. | Pressley's Elementary Differential Geometry is one of my favorites for an introductory text on curves and surfaces. | I would highly recommend the books "Introduction to Manifolds" and "Differential Geometry" by Loring Tu (in that order), the former of which is one of my favorite texts ever. They're not too demanding in terms of prerequisites (familiarity w/ undergrad topology, analysis, some algebra). I know others have cited Lee, wh... |
[
"History of Math: What is your favorite story of mathematical discovery?"
] | [
"math"
] | [
"xey75l"
] | [
205
] | [
""
] | [
true
] | [
false
] | [
0.96
] | My favorite professor (way back when) would always work history into the math lesson. It made learning easier when they told the stories of who made these math discoveries and why they were thinking about it. Like how Johann Karl Friedrich Gauss found a shortcut for serial summation or what Isaac Newton was thinking ... | It's not a big deal in the grand scheme of things but there's a legend that a mathematician tried for years to prove that you could tie a knot in four dimensions but couldn't, then tried the opposite and in a matter of minutes proved you tie a knot in four dimensions. | I've always been a fan of William Hamilton's discovery of quaternions, where he vandalized a bridge in order to write out the formula. | I loved the way one of my professors shared the story of René Descartes' inventing of the Cartesian coordinate system. Basically Descartes liked to stay in bed until late into the morning every day. (He may have even been confined to bed from being sick but I think that's apocryphal.) While watching a fly crawl around ... | Galois was amazing with the invention of Galois theory before 21 when he died an early death. It relates to solving polynomials of higher degree. We know the quadratic formula, then there are also formulas (involving radicals) for degree 3 and 4 polynomials but no general formula for degree 5 or higher. The true bea... | Much more recently, a team named Long and Narayanan proved a conjecture about chip firing games on graphs using a potential function which, when originally written, had terms in the summand corresponding to vertices and edges. After running an overnight code to see if there were any counter examples, they tried to prov... |
[
"How long does it takes to learn mathematical modelling from scratch? What books and lectures I should refer too?"
] | [
"math"
] | [
"khjyad"
] | [
1
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.55
] | null | In that case, learning how to solve the Navier-Stokes equations should suffice. | I think you should focus on that. Fluid mechanics is incredibly complicated stuff, and without calculus it is difficult to even understand the basic language of physics. Learn calculus 1, and learn it well. Learn calculus 2, and learn it well. Then do linear algebra, and linear that very well. Then learn calculus 3. Th... | Mathematical modelling is just using mathematics to model things. It can take a lifetime to be an expert. It can take much less time to gain basic competence. Nobody can recommend you anything without saying what your background is and what you want to model, though. You will need to know basic mathematics--calculus, l... | Do you already know calculus? | Start with `Practical Applied Mathematics’ by Howison once you’ve learned differential equations, linear algebra etc |
[
"Outside of official submissions, do you use Latex for personal note-taking?"
] | [
"math"
] | [
"khby37"
] | [
130
] | [
""
] | [
true
] | [
false
] | [
0.97
] | [deleted] | Yes, speed-texing has a huge learning curve but once you endure the pain to set everything up you will find it so worth it especially for your OCD. Here is the tutorial: https://castel.dev/post/lecture-notes-1/ It took me a weekend to set up and I was not knowledgeable of any software mentioned nor am I a computer wiza... | Maybe this is overkill, but for a while now I have used LaTeX for literally everything. Homework, notes (when I have to make them nice), letters, random documents, presentations, you name it. It’s the perfect solution. The writing is neater than anything I could write by hand, and I have an electronic pdf of everything... | I freely admit that I shamelessly stole not only this guy's LaTeX workflow, but his color palette (Nord) and terminal/font (termite/iosevka) too. These articles are so good. Since I don't like taking notes in class, I use this for my homework assignments, which just required a couple changes to his rofi scripts. I woul... | I write notes down normally in class, then before midterms or exams I TeX condensed notes with only important results and proof sketches. | Yes!! My first couple drafts were rough but after a semester or too my notes look better than they ever have beforehand and they’re permanently stored on my computer If you’ve got a fast wpm and get down the basic latex math commands and formatting convections you can get some really, really good notes! And whenever so... |
[
"What is the difference between vector fields and vector valued functions?"
] | [
"math"
] | [
"khvguv"
] | [
11
] | [
""
] | [
true
] | [
false
] | [
0.93
] | [deleted] | Vector-valued just means the output is a vector (just like real-valued functions are those whose outputs are real numbers). All vector fields are vector-valued functions, but not all vector-valued functions are vector fields | They are the same on , but are different when you study other topological spaces (manifolds). Namely, there is no reason why the value of a vector field at different points must land in the same vector space: maybe you have a different vector space for each point in your topological space. In the physicists language a ... | Pick any function from to . There's a vector-valued function. You could even get ridiculous with it and make something like f(x)=[W(x), W(W(x))] where W is the Weierstrass function. A vector field is a specific function whose input is a point in your space (whatever "space" means here), and whose output is in the tange... | A vector field is a coordinate-free idea. For example, you have the earth, and at each point above the earth you have wind. You can describe the wind by a vector field: at each latitude, longitude and altitude, the wind blows at some speed in some direction. So at each point, we have a vector. That's what a vector fiel... | So a vector valued function could be many different shapes as there are vector spaces of different dimensions so you could have a vector valued function, c(t) from R to R^3, which would be curve, or c(t) from R^2 if you are mapping into a 2 dimensional vector space. A vector field is a function from a point on a manifo... |
[
"What are your favorite non-math math books?"
] | [
"math"
] | [
"khzecm"
] | [
19
] | [
""
] | [
true
] | [
false
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0.95
] | Im talking about books that arent textbook like. More like casual reading. I just spent a whole lot of time reading the funny quotes on . Mathematicians are the most aloof and esoteric people on the face of this earth and I would love to read a book that brings forth that fun aspect of being someone who does math for f... | Not a math book but definitely a comp-sci book that I recommend anyone to read. It is very accessible and manages to explain how we got to modern day computers from simple systems like morse code. The book builds intuition for how a computer works from the ground up with explanations for a general audience so don't thi... | In addition to the books others have mentioned, I'll add by Siobhan Roberts, a compelling portrait of John Conway, who had a larger-than-life personality. | This is exactly what I’m looking for. Thanks! | Edward finkle, love and math, glimpse of a hidden reality, I listened to this on audio book during a long road trip and loved it. | The Music of the Primes by Marcus du Sautoy. It's about the Riemann Hypothesis, the history behind it, and some more current developments. |
[
"Is all of professional (pure) maths so abstract and sophisticated?"
] | [
"math"
] | [
"khw6v8"
] | [
23
] | [
""
] | [
true
] | [
false
] | [
0.93
] | Hello everyone, I'm a first year masters student in an Algebra program in the Netherlands. I've loved maths since I was about 6 and up to until recently my favourite branch of maths has been Number Theory. That changed this year as I tried to learn Algebraic Geometry. Aside from being hard as cold steel, I get absolute... | You certainly don't need to be an expert in algebraic geometry, but you can't totally hide from the basics of the subject as a number theorist these days.That said, algebraic geometry is scary at first, almost always because of the confusing, dry top-down way it is taught. The use of algebraic geometry is fun in that y... | Ah, classic Quora, the second answer is some random engineer who gives an incorrect answer to a wrong question. | I kind of have this idea that there is active research in combinatorics but you need to be a top of the top level mathematician to get into that world. Combinatorics is a field like any other, with plenty of researchers who are not "top of the top." There are plenty of other areas with a lower level of abstraction than... | Modern algebraic geometry is one of the most abstract fields in pure maths, and is often taught without the adequate motivation of classical algebraic geometry (i.e. what someone who isn't already a trained pure mathematician would recognise as geometry). There is plenty of modern pure maths that isn't this abstract, a... | My possibly unpopular opinion is that most mathematicians are notoriously bad at teaching math. The motivations and concrete examples are frequently (nearly always) skipped or rushed over in favor of unending towers of abstraction. In your case for instance I bet you'd benefit immensely from studying well the theory of... |
[
"Mathematopia: The Adventure Map of Mathematics - a map of the 1st year Maths course at the University of Oxford showing the connections between the topics. Created by one of my students Zhaorui. Have fun exploring!"
] | [
"math"
] | [
"khh6hw"
] | [
611
] | [
""
] | [
true
] | [
false
] | [
0.97
] | null | First year maths students study catagory theory? | Reminds me of this one ! | No, this goes a bit beyond first year | I think there is a really good lesson here, in that the map is limited to the maths, and the connections, that this student has covered. I've seen other attempts at "maps of mathematics" and it just doesn't work if you don't make it clear what the limitations are. Mathematics is not a planar graph, to put it mildly. | You had the perfect chance to call this mapthematica |
[
"I made an online \"hyperbolic paint\"! It uses the Poincaré disk model. Code included!"
] | [
"math"
] | [
"khiu0c"
] | [
2904
] | [
""
] | [
true
] | [
false
] | [
0.99
] | null | Bug report: you can draw outside the white circle. What happens to those points when you move is quite interesting. | I figured it was cool enough to leave it as it is. | That’s not a bug, that’s a feature! | Before learning hyperbolics: :) After learning hyperbolics: :( | Link: https://editor.p5js.org/zokalyx/full/ESz3r4_Tu . You can see the code if you click on the right top corner. For those who want to learn some more, the basic idea of hyperbolic space is that it is curved, meaning that it does not behave like a regular sheet of paper. The most fundamental difference that appears in... |
[
"Is it possible for an efficient algorithm to (provably) exist, yet finding one to be undecidable?"
] | [
"math"
] | [
"khrkqj"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
1
] | (For TL;DR, read the second and last paragraphs of this post.) This is a thought that came to me when I was thinking about possible resolutions of the P vs. NP problem. Most people believe that P≠NP, or that if P=NP then polynomial time algorithms to NP-complete problems have huge constants or exponents. However, I ha... | If there is a polynomial time algorithm A for 3-Sat, then there is also some algorithm B outputting a formal description (say a Gödel number of a Turing machine) of A in constant time since algorithms are finite objects. So "finding" a polynomial time algorithm is not only decidable, but in fact can be done in constant... | In second paragraph I specified that by "find" I mean find the algorithm prove efficiency and correctness of it. I know the terminology I use is not very strict, but I couldn't think of a better word. | This is possibly cheating, but if it is possible to verify that a solution to a problem is correct, then there is a known algorithm that will find the solution and whose run time is a large constant multiplied by the run time of the most efficient algorithm to solve the problem. So if we can verify a proposed solution ... | "Given an integet k, is k bigger than BusyBeaver(Graham's number)?" is both decidable (as is any constant threshold problem) but no algorithm can be proven correct unless something bad happens to your axiomatic system (consequence of Chaitin's theorem). Is this what you're after? | More simply, 'output 1 if the continuum hypothesis is true, and 0 if it is false'. |
[
"Can a non-trivial continuous dynamic system be expressed without differential equations?"
] | [
"math"
] | [
"khtb9f"
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19
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""
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true
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false
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0.96
] | I'm really interested in continuous dynamic systems that produce complex behavior: reaction-diffusion systems, Kuramoto–Sivashinsky equation, etc. So far, all of the continuous nonlinear systems I stumbled upon online have been described in terms of nonlinear PDEs. I'm an amateur mathematician with little training and ... | Dynamical systems theory is a subset of the study of differential equations. That depends on who you ask! To me and many other mathematicians a dynamical system is just a continuous action G×X→X of some topological group G on a space X (occasionally even a semitopological semigroup is enough) | Im not and expert, but I guess one example of a way how one could create a continuous dynamical system without derivatives is by means of fractional function composition, which can be obtained be solving Schröder's equation . Effectively, the state of the system would be given by f (x), where ^(t) indicates (continuou... | Sensitive dependence on initial conditions is part of being an initial value problem, aka a differential equation. Dynamical systems is all about studying the behavior of differential equations (both pdes and odes). Most of the analysis tools we have for dynamical systems are based upon the differential equations invol... | And I don't agree that dependence on initial conditions is enough to claim that a system must only be described by a differential equation My specialty is dynamical systems. I know quite a bit about the subject Dependence on initial conditions is a definition from dynamical systems theory. It means that an initial valu... | Sure, but the action is still described by an ODE, SDE, DDE or PDE |
[
"What Are You Working On?"
] | [
"math"
] | [
"khl9za"
] | [
8
] | [
""
] | [
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 . | Navigating the Lovecraftian/Escher-like university bureacracy in order to register for classes next semester. Why do I have to fill out — and ask my advisor to print, sign, and scan — a paper version of the "request for registration action" that I've already filled out online and which my advisor approved online!!?!? ... | Modern algebra, right now I’m on groups. | Lovecraftian/Escher-like Making me realize how sad it is that we can never have a collab graphic novel from these two. | Blitzstein's Probability Theory, Chapter 9 (Conditional Expectation). Hoping to eventually turn this into a good foundation for some graduate level Machine Learning knowledge. | Adam and Eve’s laws are pretty fun, I’m hoping to review this chapter in the next few days. |
[
"Turning Rectangular Wave into Sine (Fourier series question)"
] | [
"math"
] | [
"khierj"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.81
] | I learned about the Fourier Series in class and was wondering if it is possible to take a rectangular wave and filter it into one of its harmonics (i.e. a sine wave)? I'm coming from an electrical engineering background, so I was wondering if this was possible to implement in hardware too, with some kind of low pass fi... | It is indeed possible. One (practical) approach would be to design a lowpass filter that cuts out (most) high-frequency contributions. That is the principle behind subtractive synthesis , which is one of the oldest synthesis methods. Mathematically, though, you can express sine as a infinite sum of square waves, produc... | Thanks for your response. I do want to implement this and I have the frequencies of the harmonics. I designed a low pass filter and then tried a band pass filter for a higher harmonic, but to no avail (I simulated them in multisim - a circuit software). | theoretically, if you know the frequencies you can just use a filter that filters the frequencies you dont want and that would get you an specific harmonic do you want to implement this? | im not sure if this is the best way to achieve that but you would probably need a higher order filter. you are using an analog filter right? maybe an active filter is a batter idea but i dont know much about them | Well, you can use a bandpass filter tuned to select the fundamental or one of the harmonics contained in the square wave. However, keep in mind that in the real world: One project I have worked on had such a "shaping" filter to turn a 10kHz square wave into a 10kHz sinusoid and just a 1st-order op-amp HPF followed by a... |
[
"If you have a 1/8 chance to get something, how big is the chance to get it if you do it 8 times?"
] | [
"math"
] | [
"kegqrk"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.25
] | null | Only once or at least once? | at least once | The chance to get it (at least once) in 8 attempts is equivalent to the (inverse) chance to not get it 8 times. So 1/8 =a chance, 8=n times, do 1/((1/a)^n). But this looks like homework, and there is a subreddit rule about that. | I was just genuinely curious and wanted to learn how to use it on other equations | One in eight. Assuming you meant 1:8 not 1/8. One in eight, not one eighth. |
[
"Self-study book on doing proofs"
] | [
"math"
] | [
"khinir"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
0.93
] | null | As an electrical engineer transitioning to mathematics I have to recommend . He takes his time explaining the different strategies that go into proofs and gives step by step examples with commentary. There is also lots of exercises that will help you get better so do them all! He has a structured approach to how he bre... | i am an electrical engineering student too and i wouldnt suggest a book focused on proofs. i would suggest to learn them with one of the 'basic' courses with proofs. you can learn proof based linear algebra, discrete mathematics or if youre more greedy real analysis | Polya's is the usual text referred to, but I also like Kevin Houston's . | How to Prove It and Book of Proof are pretty common recommendations. Book of Proof is free online and pretty cheap in print. | those courses and maybe abstract algebra or topology (they dont strictly need anything but you should have seen linear algebra and analysis respectively before taking them imo) this is from an engineering student, probably math students have basic courses on geometry or logic and set theory too |
[
"Telling supervisors you don't want to take the course they recommend"
] | [
"math"
] | [
"kh5ctu"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
0.84
] | So I'm currently in grad school doing my Msc at the moment. At my school acceptance requires supervision upon entry. So the courses I take, my supervisors have to agree to. The problem is, my supervisors want me to take PDE and I don't think it's for me... I've tried to find enjoyment from it, but I feel like alot of t... | Maybe your PDE 2 class focuses more on stuff like distribution theory, sobolev spaces, and functional analytic methods for PDE? I found that my first grad PDE class was very vector calc heavy and that my second course was a lot more topological / functional analytic. | You just tell them, and if your supervisors are normal and well-adjusted people, they will accept your ability to make your own choices, and life will go on. | Or at least talk to them and explain your thinking and see what they come back with. | I've done research on the area of PDEs. When I took my first PDE course I hated it (Evans is a known killer of enthusiasm). I felt that it was a total mess, and not the same "flavour" as the other analysis courses. However, as others have pointed out, a second course in PDE could be much more related to functional anal... | Yes, chapter 2 and 3 of evans are absolutely nothing like chapters 5, 6, 7. Chapters 2 and 3 are very computational and IMO quite uninteresting. |
[
"applications of measure theory"
] | [
"math"
] | [
"kecw3i"
] | [
0
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.4
] | null | Probability theory is literally measure theory, but specifically concerned with spaces of measure 1. | Measure theory → probability → stochastic calculus → mathematical finance Measure theory → Hilbert spaces (L -spaces) → functional analysis → mathematical language of quantum mechanics | Probability theory | the definition of what probability is | Banach Tarski involves non-measurable sets. Measure theory avoids this paradox by being more careful |
[
"What is the nth root of x for n is irrational?"
] | [
"math"
] | [
"ke6p2f"
] | [
4
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.75
] | null | Would probably just be x =exp(1/n*log(x)) | The more general question is how we define irrational exponents. x is defined as the supremum of x for rationals p/q < r. Alternatively, the limit of x where a_n is a sequence of rational numbers approaching r. Once we have this definition we can define the r-th root of x as x . And then again, use either the supremum ... | 1/n makes sense whenever n is a real number not equal to zero. It's a real number, not a rational number (if n is irrational), but one can take exp(y) for any real number and it makes sense. | How about taking the limit over rationals? | Since reals are just the closure of rationals (which means, taking all possibile limits), it doesn't look like cheating to me 🤔 |
[
"How to add chances?"
] | [
"math"
] | [
"kdwoox"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
1
] | null | C( , ), or " choose ", is !/[ !( – )!]. | Look up binomial distributions. This is a 1/6 chance of success over 10 attempts so you'd calculate the probability of either exactly o e success or the probability of at least one event (depending on what you're looking for). If I remember the formula right, it is: BiNom(n, s, p) = n = tries, s= success, p= prob of su... | Thanks will look it up, it seems way complicated then I thought it would be | Once you become familiar with probability distributions, it's actually very very easy. Binomials are the simplest discrete distributions and are used to model any series of events such as this from probability of 5 heads out of 20 coin flips to the probability of 1 1 in 10 dice rolls. | Oof binomial distribution I'm in the same problem buddy, I'm still struggling with that and normal distribution. The coin and dice cases seem easy but then you look close can be confusing |
[
"Is it possible to recover from this? Have you experienced something similar?"
] | [
"math"
] | [
"keirwm"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.46
] | [deleted] | The people who are successful at mathematics are those that don't give up when things get challenging. | I entered my undergraduate institution expecting to study medicine. My first semester I took calculus II and received a mark of D+ (one of the lowest possible). That is, I must have been in the bottom 10% of the 600+ people that took the class. This was a very big psychological blow to me at the time, because I had don... | No! Do not give up! There are so many versions of math, and applications of it in real life! Find what you are most passionate about, get through the tough classes, and ENJOY the other classes!! You can do it! Don’t let “gate keeper” classes stop you! You got this! | These moments are foundational for education and learning, this IS the work. One tough class or tough exam doesn't define you. You are someone who was willing to take the challenge of being a Math major. Many people do not make it as far as you've gotten! Do not discount your efforts! These challenges will be there, th... | What would you prefer to be doing instead? |
[
"I'm shit tired"
] | [
"math"
] | [
"kdzj94"
] | [
35
] | [
""
] | [
true
] | [
false
] | [
0.69
] | [deleted] | I hear that, it is not satisfying when teachers skip over the good stuff to get in a lot of theorems all at once. Especially when it feels more like memorization because there was not enough time to consider the setup. But congrats on your last class! Such a tiring semester but now we get a break | Haha no break. Gotta prepare for the final. | There is no end of learning ;) Thanks tho! | Of course, I like that attitude | You got this, rest up and read through again tomorrow. The end is in sight! |
[
"What are your favorite math, or math themed songs? Post below!"
] | [
"math"
] | [
"kefje5"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.75
] | null | https://www.youtube.com/watch?v=BipvGD-LCjU | Lobachevsky by Tom Lehrer | New Math (Tom Lehrer) | “Lateralus” by TOOL. They embedded Fibonacci in the lyrics and melody. source | I could pick any more or less rhythmically complex song but I'm gonna go for Mudvayne's "Pharmaecopia", just because I remembered that the chorus is in 11/8, which is a pretty weird choice of time signature, but not foreign enough that you can't headbang to it. If you want me to pick something that actually might melt ... |
[
"Great short explanation of de Rham’s theorem"
] | [
"math"
] | [
"kdween"
] | [
43
] | [
"Image Post"
] | [
true
] | [
false
] | [
1
] | null | Very well done video! Great introduction to the subject. The basic ideas of De Rham's theorem should be put into more undergraduate calculus courses, IMHO. I think it's understandable enough and might inspire students to continue pursuing math (and conversely scare some people away who realize math is much more than ta... | I remember as an undergraduate going through details of de Rham cohomology. I would’ve appreciated seeing this short video as a great overview of the work I’d be going through! | Its always bothered me that the exterior derivative really doesn't encompass the concept "derivative" writ large. After all, d = 0 so how is one supposed to interpret any coordinate expression involving any higher-order derivatives? You can always alternate using the exterior derivative and the hodge dual, I suppose,... | it's a mess because these are simply different concepts. they sort of collapse into one thing in one dimension (calc 1), but God isn't nice enough to let us enjoy that forever. the exterior derivative certainly doesn't encompass the notion of derivative as a whole. it's only the "correct gadget to generalize the FTC, g... | I was not able to see how chains form vector space, and how \del is a linear operator. Tried to look up chain definition in the Wikipedia, and it seems that it is something more complex than a smooth map from [0,1]^n to M |
[
"Is there a reason why trinary operations are absent? Is there some theorem that shows any trinary operation has equivalence in binary operation(s)?"
] | [
"math"
] | [
"kdytj6"
] | [
37
] | [
""
] | [
true
] | [
false
] | [
0.94
] | The second question is my suspicion as to why this is true. Thanks | Often we don't really care about binary operations or ternary operations, but instead n-ary operations that take any finite sequence of values as an input. For example, we might have an operation f such that f(), f(x), f(x_1,x_2), f(x_1,x_2,x_3), and so on are all well-defined. The nicest, most interesting, and most na... | I don't have a good answer to your overall question, but here are my thoughts. I agree that a lot of the naturally occurring operations are either binary, or can be broken down into binary operations, as you suggested. Adding 3 numbers, multiplying 3 numbers, etc. all break down nicely. These binary operations don't ev... | I had a slight suspicion that this "abundance" of binary operations might have something to do with the ability to "associate" the arguments of the operation in some way, apart from the fact that most of the operations that arise naturally are binary (or unary). | If so, they’re definitely used! I understand they are used but I don't think this is answering what OP is wanting to understand. It is really blatant that so many algebraic structures used and studied utilize binary operations. I understand there are exceptions of course but the vast majority, the popular ones, are all... | If so, they’re definitely used! I understand they are used but I don't think this is answering what OP is wanting to understand. It is really blatant that so many algebraic structures used and studied utilize binary operations. I understand there are exceptions of course but the vast majority, the popular ones, are all... |
[
"Plotting implicit curves"
] | [
"math"
] | [
"kduhrm"
] | [
27
] | [
""
] | [
true
] | [
false
] | [
0.97
] | Hello, Short Question: What is an efficient algorithm to plot implicit 2D curves with good results? Background: I recently started learning python. As a training project I wanted to write a program that does some 2D fluid dynamics computation and visualization, because thats a topic I have to learn for my university cl... | There are a lot of different ways that people try to plot implicit curves, but it depends on the context. On modern computers if you just want to make a picture on screen I would recommend plotting them by rasterizing on the GPU. https://observablehq.com/@rreusser/locally-scaled-domain-coloring-part-1-contour-plots If... | Some good suggestions in the other comments. My two cents: the simplest solution is to probably just write a pixel-shader on a GPU. The single-instruction-multiple-data computation needed for computing function values over a grid is exactly what GPUs are good for. Simply compute f for every pixel (x,y) and color the pi... | Thank you very much, the first link looks pretty much like what I want to archieve | Thank you, this was the first thing I tried, but not on the GPU. But I think I will rather focus on my main project an maybe learn GPU programming later :) | Here are a few papers that will lead you down the way: ideas/scope, keywords to search, references, etc. (all freely available pdfs): Reliable Two-Dimensional Graphing Methods for Mathematical Formulae with Two Free Variables Robust Adaptive Polygonal Approximation of Implicit Curves Quadtree Algorithms for Contouring ... |
[
"What are some good books to get into Optimal Transport and Optimization in general?"
] | [
"math"
] | [
"kdrib2"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
1
] | I'm about 3/4 done with my undergrad in applied math and I am starting to look at optimization in general so I can decide on a subject for my thesis and possibly for a graduate degree. I want to spend what little time I have for winter vacation learning a bit more about Optimal Transport. As I said, I'm an undergraduat... | https://optimaltransport.github.io/book/ | I am reading Optimal Transport by Cedric Villani right now but admittedly it is aimed at graduate level minimally. But it's also very thorough. | “Optimal transport for applied mathematicians” is very accessible. Certainly easier than Villani’s books. | Ah sorry I should have included that. It's by a Filippo Santambrogio. Despite the name it's perfectly rigorous and has full proofs of most of the theorems. | Thanks! I will take a look at it |
[
"Lemma on random affine equations"
] | [
"math"
] | [
"kduvk9"
] | [
45
] | [
""
] | [
true
] | [
false
] | [
0.97
] | Hi all, I have a simple lemma on affine equations that I need for a paper, but it seems like the kind of thing that would be proved already and I'd rather just cite it. Have you seen this before, and where can I cite it? Lemma: Let Fq be a finite field with q elements. Let M : Fq -> Fq be a uniformly random matrix, a... | lemma should be the plural of lemon | If you don’t have an answer here might be worth asking on MathOverflow | Your proof sketch is short enough. I'd just upgrade it to a proof and put it in the paper. You don't elaborate on all the details, but a proof like this should be perfectly fine for a research paper. | Funny story: I did that last time I used it, a few years ago, which was only for F_2. And yesterday I was like... what was that lemma again? And I tried to find it on the internet, and couldn't, and I grepped my own files and found the lemma but not the proof, and I wanted the F_q version this time so I needed to re-... | Sounds very similar to something we proved and used in coding theory class. |
[
"Concrete, well understood but non trivial applications of modern mathematics"
] | [
"math"
] | [
"kehl4m"
] | [
398
] | [
""
] | [
true
] | [
false
] | [
0.97
] | First of all, Ive been here long enough to anticipate some answer so Ill start by saying what this post is not about: This is not a thread about general applications of mathematics neither to "the real world" nor to vague broad areas of knowledge. I know about crypto. Now with that out of the way: Earlier today I was r... | Just to continue on the representation theory train, this is extremely useful in quantum field theory. Particles at their most fundamental constituents correspond to irreducible representations of some relevant symmetry group to your physical system, and invariant tensors of these irreps (eg quadratic Casimirs) can be ... | Perhaps too basic, but this was the example that made me love math. What is the closed form for the Fibonacci numbers? Everyone knows 0, 1, 1, 2, 3, 5, 8, ..., given by F(n+1) = F(n) + F(n-1) are given most easily by a recurrence. But there's a complicated formula called Binet's formula. Once you have it, you can easil... | Fourier transforms are used for multiplying large integers. The multiplication algorithm taught to elementary school students takes O( ) bit-operations to multiply two n-digit numbers. When gets large, this takes quite a long time. The first algorithm to do better than this is the Karatsuba method , which breaks each ... | I think that Multi-grid method for solving Finite Element Analysis (FEA) problems fits your criteria. Proving rates of convergence for this method required a lot of approximation theory in Sobolev spaces and understanding how the method is really von Neumann's Alternating projection algorithm. Proving convergence for... | I believe Arnold, Falk, and Winther's finite element exterior calculus uses nontrivial differential topology (e.g. de Rham cohomology and consequently ideas from homological algebra) to inform designing good finite element schemes for solving PDEs numerically, with obvious applications. |
[
"About “burnout” and “failure” type posts in this subreddit."
] | [
"math"
] | [
"ke2fzr"
] | [
613
] | [
""
] | [
true
] | [
false
] | [
0.9
] | I’ve followed this sub for years now so this is nothing new, but recently (likely due to finals) there has been a huge influx of repetitive posts talking about personal struggles with math. I was wondering how the community feels about these as a whole? Some of the posts are more general discussion topics like how do y... | Maybe we could have some kind of burnout thread when finals season rolls around? | It’s up to all of us to decide what this subreddit is about. Is it a community of mathematicians and maths fans to discuss everything maths related, or a community specifically for the discussion of mathematics? Personally I think it’s a great people have a place for burnout/failure posts. I’m sure a lot of people who ... | This sub needs flair like... teacher, student (pregrad, postgrad, phd..), professionals, amateurs (lovers and haters alike!) | Weird, no one's bringing up the fact that it's 2020. If I cared enough, it'd be interesting to scrape this sub and see the volume of burnout posts in past final seasons. Something tells me it's not been this high before. My two cents... It's a small enough thing to leave a space for struggling people to look for a litt... | I think there are already not a ton of places to talk about burnout (especially in a venting type fashion) to others who understand academia or the subject. I think these posts are fine and the benefit for the poster outweighs whatever annoyance they may cause me. Especially during finals and a pandemic and all. |
[
"Simple Questions"
] | [
"math"
] | [
"keczee"
] | [
19
] | [
""
] | [
true
] | [
false
] | [
0.9
] | This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread: Including a brief descri... | A vector field is actually defined as a section of the tangent bundle. The intuition behind this is that a section by definition is a choice of a tangent vector above p for every p on the manifold. | There's no real consensus on this except in specific cases - variables representing constants/scalars should go before indeterminates, vectors, matrices, and functions. In general, just stay consistent with your ordering and figure out which one is visually the most natural for your given situation (e.g. if you're goin... | nah the quaternionic units i,j,k are still square roots of –1 | The first thing to do is to check if it has any nice roots. For example, in the cubic equation you give, 1-4+5-2=0, so 1 is a root. This means that (x-1) is a factor of the equation. Now you can use long division to compute (x - 4x + 5x - 2)/(x-1) which is the rest of the equation. This will be a quadratic, so you can ... | If you multiply an eigenvector by any scalar you still get an eigenvector of the same eigenvalue. So unless c+di=0 you can multiply by 1/(c+di). Giving you something of the form [a+bi, 1]. So an eigenvector can always be written on the form either [a+bi, 1] or [1, 0]. |
[
"Is there a conventional name for 1/sqrt(2pi)?"
] | [
"math"
] | [
"zsmed5"
] | [
2
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.6
] | null | Its name Jeff | Alright, I'll name it Jeff in my code, that'll help. | It's also the normalizing constant for the density of a standard normal distribution, but that's a semi-related idea. It's actually a pretty important constant that comes up frequently when dealing with integrals of exponential functions. I'm not aware of any special names or symbols given to 1/sqrt(2π) though. | If you have to ask, the answer is no. Even if there is a name, it's clearly not widely known enough to be used without explanation. As always, you can call it alpha or k or something as long as you explain that's what you're doing. | Gaussian Normalization Factor ? Since integral(exp(-x for x for all real Axis are equal to sqrt(2*pi) |
[
"To square a circle, don’t you just divide the circle circumference by 4?"
] | [
"math"
] | [
"zsefil"
] | [
0
] | [
"Removed - incorrect information/too vague/known open question"
] | [
true
] | [
false
] | [
0.15
] | null | But then how would you take that arc and make a straight line with the same length, using only a compass and straight edge? | sunlight is not mathematics. | Well, you figured it out. Your PhD is in the mail. | No, it isn’t. | an abstract, theoretical mathematical construction is not literally the same thing as a physical beam of photons coming out of the sun. |
[
"Born On This Day in 1887 was Indian mathematician Srinivasa Ramanujan"
] | [
"math"
] | [
"zsgmwj"
] | [
1094
] | [
""
] | [
true
] | [
false
] | [
0.98
] | null | Though he had very little formal training, his work was substantial and innovative, often using methods that were completely novel. In 1918 he became one of the youngest Fellows of the Royal Society. | This man is a genius. Shame he had such a rough life and it ended that early for him | Hope he can bless me on this day cuz I have an oral exam in calculus in less than an hour | Was an oral exam, had luck with the topic and got an excellent Seems like I indeed got blessed | His life might seem rough from our perspective. From his perspective, all he was doing was following his heart so closely, which most of us people are not able to do. |
[
"Career and Education Questions: December 22, 2022"
] | [
"math"
] | [
"zsqxuh"
] | [
6
] | [
""
] | [
true
] | [
false
] | [
0.81
] | This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered. Please consider including a brief introduction about your background and the context of your question. Helpful sub... | Giving some advice as a recent PhD grad. For anyone thinking of a mathematical research career, don’t discount national labs / government contractors / FFRDCs / UARCs. They have plenty of interesting problems to work on, and recruit from more fields than you might think :) Sure if you want to work specifically on this ... | I think that this depends on the person. In my experience, at any given college, the strongest math majors are almost universally people who would be among the strongest CS majors if they were CS majors, and visa versa (not as in they could immediately do the other subject, but that if they had done the subject since t... | When'd you decide not to go with the academia route, and how was applying and interviewing for these jobs? I'm only a first year grad student student but already know I'm not interested in the coding/finance route if academia doesn't work out. | I assume you have to be a citizen of that country to be eligible? Because I’m coming in as an international.. | Hi everyone! I just completed my first semester of a PhD program with the intent of pursuing analysis and... well, I got what's considered a 'bad grade' in my program for the first semester course in real analysis ("AB"). Allegedly getting a "B" is equivalent to failing the course. I got pretty terrible scores on the e... |
[
"How to further my knowledge of numerical analysis?"
] | [
"math"
] | [
"zspxwb"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.67
] | So I have been interested in quite a qhile in numerical analysis, particularly the solving of differential equations. I have looked at a lot of books on the subject but of all the textbooks I've looked at, they don't go further tahn Runge-Kutta methods. What material can I read on to go beyond those methods? | Almost every field of mathematics is proof-based. Courses in Numerical Analysis may focus on proofs/theory, computation/implementation, or a mix of both. It depends on the classes, and sometimes the preferences of the professors teaching them. When I was in grad school, we had a base Numerical Analysis class that was e... | I would look up course outlines for courses on Numerical Analysis from big universities, and see what they use. This is always my approach when learning a new subject, I want to know what the common texts are that are used across Universities. I did a bit of browsing and this looks pretty comprehensive. | Have the books that you read not given an overview of what Numerical Analysis is all about? The opening chapters should be able to give you a more eloquent and succinct writeup than I can give in a paragraph on Reddit. | I have not taken such a course. I’ll just look at the book or google | Questions like does it work as advertised ? Under what conditions does it work ? How much error should we expect ? How fast is it ? Are all questions to be answered by proofs. |
[
"A list of my favorite math websites"
] | [
"math"
] | [
"zsq3k0"
] | [
119
] | [
""
] | [
true
] | [
false
] | [
0.92
] | I know that there is a ton of quality math content out there so please place any recommendations in the comments below. | Don't forget the best math website - your department's website that was written in html by one guy in an afternoon back in the mid '90s and is kind of a mess and should be updated at some point but fuck it it works (unless you're on a mobile device in which case it only kind of works) and just nobody's gotten around to... | dont forget https://oeis.org/ | Our department pages look quite nice. Some pages of some professors or courses leave a lot to be desired, but that's part of the charm | Some of my favorites: Detailed info on finite groups of order up to 500 or so: https://people.maths.bris.ac.uk/~matyd/GroupNames/ Keith Conrad’s expository notes: https://kconrad.math.uconn.edu/blurbs/ A collection of exercises in abstract algebra: https://yutsumura.com And of course if you want practice problems, lots... | Holy shit, we really live in a simulation |
[
"Examples of proving finiteness via compact + discrete"
] | [
"math"
] | [
"zspop5"
] | [
17
] | [
""
] | [
true
] | [
false
] | [
0.95
] | Sometimes you can show a set X is finite by giving it a topology, and then separately showing this topology makes X both compact and discrete. I'm pretty sure I've seen many examples of this strategy, but I was trying to think of some earlier, and kept drawing a blank (except for vague, "non-canonical" examples like I'... | Let f: X -> Y be a smooth map between manifolds of the same dimension, X compact, and c a regular value of f. Then f (c) is finite by this argument. The finiteness of this set can then be used to define the degree of f. | In model theory the Ryll-Nardzewski theorem is a great example. One of the things the theorem says is that when you have a /aleph_0-categorical theory the space of types is finite using that is compact (consequence of compactness theorem of logic) and that the countable model is atomic and saturated so every type is an... | If you take a lattice (Z-submodule of R^n) and generate sublattices (for example taking the Z-span of successive minima), you can show that these sublattices have finite index as subgroups in your original lattices with this argument. | except for vague, "non-canonical" examples like I'm pretty sure you can show class groups are finite like this by realizing them as quotients of some open in the ideles, but iirc it takes some work to show compactness this way Why is that a vague non-canonical example? It's a very interesting way of proving class grou... | The introduction of http://virtualmath1.stanford.edu/~conrad/248APage/handouts/compactidele.pdf says about the use of topology and idele groups that "if one strips away the adelic language in the case of number fields (especially when S is precisely the set of archimedean places) then one essentially recovers the class... |
[
"What are some practices you do to get better at math?"
] | [
"math"
] | [
"zsgpgs"
] | [
10
] | [
""
] | [
true
] | [
false
] | [
0.78
] | Would like to know if you're using certain apps, books, etc. Your practice schedules and such. Been struggling to do maths and I'm going to college soon, where I know I can't just calculator my way out of. | I do math. | You need to practice the specific problems that you'll be needing in college. Find a text book or go through your past exercises and redo them | Always do the problems to check your understanding of the topic. Don't be afraid to ask others for help when you need it (clarifications, guidance or hints, not simply receiving the answer from someone else, because you learn when you struggle), you don't have to tackle math alone. I used to struggle with math and hate... | IMHO, having solid bases about previous topics before facing new topics is one of the most important things. Math builds upon itself. If, for example, you have troubles or doubts when adding two fractions, you will have troubles or doubts when solving a simple linear equation. So you can go to the free website of Khan ... | Practice. Nothing beats practice. |
[
"Proofs that don't provide a satisfying explanation for why a result must be true?"
] | [
"math"
] | [
"zsqagl"
] | [
45
] | [
""
] | [
true
] | [
false
] | [
0.84
] | Sometimes, I find that while you can give a proof for a result, the proof seems extremely unsatisfying in that it gives you little intuition as to the result should be true. For instance, it's a well-known result that the Gaussian integral (the integral of exp(- ) from -∞ to ∞) is equal to the square root of π. There a... | It's not clear to me why you feel that the answer in the link is more intuitive; the only difference is changing the vocabulary from "function of the form f(x)g(y)" to "pair of independent random variables", and at the end of the day you still have to go through the usual calculation using polar coordinates. But I digr... | Vocabulary can have a big effect on what feels intuitive and what doesn’t. Maybe a little more nontrivial, but “the axiom of choice is obviously true, well ordering is obviously false, and who can tell about Zorn’s Lemma?” | The quadratic reciprocity theorem can be proved with little elementary number theory but its nature isn't really understood unless you go a bit into algebraic number theory | This might be cheating, but I’d have to say the finite sum of squares or cubes. Very easy to prove with induction, but those induction proofs don’t really tell you how someone came up with the formulas in the first place, just that they work | The first time I learned the proof of Fourier inversion, I was pretty confused--it seemed very technical and bizarre. When I learned the language of tempered distributions, I saw someone rewrite the proof of Fourier inversion in that language--despite the two proofs being essentially identical, it was only once I saw i... |
[
"How to take notes when reading math books?"
] | [
"math"
] | [
"zsfo0r"
] | [
26
] | [
""
] | [
true
] | [
false
] | [
0.93
] | Hi, I recently finished school and I have a lot of free time until I start university. My teacher told me that I already know most of what they teach in the first year (the first year is shared by multiple majors). So I decided to self-study some math books in the meantime. Currently, I am reading Linear Algebra by Ser... | note taking is just something that takes practice, paraphrasing is a perfectly fine way to do it. Some people like to take copious notes and then write on the margins a short note describing what a particular section is about. You can include drawings, equations or anything you feel needs to be written down. There isn'... | In my case, notes are for writing, not for reading. I write to help me think step-by-step and precisely, and the stuff I write may be examples, the words in the book paraphrased in a different setting, more familiar notation, or even verbatim, or they could be questions that come to mind, random insights I have about r... | Personally, I approach note taking like I'm writing my own reference for later, I would buy a nice hard cover note book, and rewrite things (theorems, definitions, proofs, notes) out nicely and formally. It gives you practice writing formal math, and you'll have a nice collection of notes later on your bookshelf. | I only note down my alternate way of a proof, steps in proof that would make it clearer, and deviations in lectures from book. My books become my reference book. | I’m going to add to this but will say if you can afford it, an iPad is paramount for note taking. |
[
"[2212.09835] A non-constructive proof of the Four Colour Theorem"
] | [
"math"
] | [
"zruc58"
] | [
411
] | [
""
] | [
true
] | [
false
] | [
0.98
] | null | 7 pages of generating functions, impressive. | Are mathematicians that don't use generating functions called degenerates? | Any sufficiently advanced use of generating functions is indistinguishable from magic - Arthur C. Clarke probably | tl;dr: (a) if there is a counter-example to the 4-color theorem, then only an exponentially-small proportion of large maps can be 4-colored (b) but a good proportion of maps can be 4-colored explicitly This requires counts for graphs with different properties. Some of these counts were given in the 1960's by Tutte. As ... | OK, section 4.2 makes no sense to me. So they have this set Q, right? Which is the set of plane graphs that can be written G=A*B*C*D, where * denotes joining at a cut vertex. Their goal is to show that every G∈Q can be 4-colored, and then use that to argue (as is described elsewhere in the thread) that a nonzero fra... |
[
"Constructing functions with different local extrema having a given planar curve as a level set"
] | [
"math"
] | [
"zs95cb"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
1
] | I have an open, bounded, and simply connected region in the plane with boundary (Holder continuous, ). My understanding of this is that we can express as , where is Holder continuous, and the boundary would be . Any such function would necessarily have its gradient vanish somewhere inside . However, it seems reasonabl... | Can't we just add or subtract an arbitrary bump function? | Surely something like “the distance from the boundary in question” works? | Yeah, that's what I was thinking for making a second different one, thanks -- any ideas on how to construct the first one? | Makes me think of ray marching and signed distance functions. But would that be regular enough? Probably take the square of the distance or something? | Whenever I'm feeling too irregular I just convolve myself with a gaussian. |
[
"Book on multi-variable analysis/Calc?"
] | [
"math"
] | [
"zs3t47"
] | [
11
] | [
""
] | [
true
] | [
false
] | [
0.82
] | Hi. Looking to strengthen my multi-variable calc before this semester. Any suggestions? I'm reading Loomis' Advanced Calculus right now, but I'm finding it a bit too advanced. for background: took analysis course last semester and felt that it really elucidated some statistics concepts. I’d like to find the rigorizat... | I would recommend 2 books, assuming you've already had introductory analysis: 1. Multivariable Mathematics by Theodore Shifrin 2. Calculus on Manifolds by Michael Spivak The second is pretty advanced in terms of the way results are presented, but it actually a very narrow amount of content, just multidimensional differ... | Try Hubbard and Hubbard: https://matrixeditions.com/5thUnifiedApproach.html | Analysis II by Terence Tao or Principles of Mathematical Analysis by Walter Rudin. | To add to this comment, Shifrin's book is accompanied by a battery of fantastic lectures on Youtube under titles: MATH3500 & MATH3510: Math3500-3510 | I really dislike Spivak's calculus on manifolds, and usually I like Spivak -- I am not sure who the target audience is, since it's not a good enough treatment for a first course and not advanced enough for a second. |
[
"Are Math Competitions Indicative of Your Skill in Math?"
] | [
"math"
] | [
"zse5mh"
] | [
43
] | [
""
] | [
true
] | [
false
] | [
0.78
] | Currently in Calculus BC, been enjoying the class and I'm pretty confident about my skills in math but my teacher sometimes has us do math competition problems and I fucking suck at them, am I secretly bad at math or something | You’ll be ok. Life is a continuous pursuit of what’s at the intersection of worthwhile and interesting and just beyond your reach. | I did a lot of competitions in high school for math. My performances ranged from below average to top ten. In reality math competitions were for fun and didn't really say much about my ability. | I mean... such a statement can only come from ignorance of math competition problems. They do require a lot of creativity, ingenuitiy, intuition and raw math ability. Go check IMO or national-level problems and you will see. There is no "standard bag of tricks", that's simply wrong. To be at the very top as a competito... | It's less that there's no creativity, and more that there's only scope for much creativity once you can use all of the standard tricks (because it's much harder to come up with one of the standard tricks on the spot than it is to already have learned it). I agree with your overall point that there are plenty of success... | This sounds a little reductive. No, you don't just learn a couple of tricks and then become a master. Olympiad mathematics is no different from ordinary mathematics in the sense that you gain intuition by reading theory and doing exercises and then using that intuition you can solve problems better. The concrete differ... |
[
"Is there a way to explain topics like Algebraic Topology or Differential Geometry in a strictly formal manner, not requiring any kind of imagination?"
] | [
"math"
] | [
"zrw23u"
] | [
18
] | [
""
] | [
true
] | [
false
] | [
0.74
] | As someone who has lots of trouble imagining things, it would be awesome to find a way to get into these topics using only "formal language" and no imagination Any ideas? | Well these are all rigorous developed subjects, if that's what you mean. So almost any introductory textbook on the subject. See Topological Manifolds by Lee for example. | Maybe a better way of phrasing what you want is "no visual intuition," since imagination is absolutely required for any kind of mathematics. That said, https://math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf is a good formal approach to algebraic topology. But you should still try to practice your visualization skill... | Clearly not, considering you've felt limited enough to come here and ask how to do better... | Read a book like Hatcher, and try and make sense of all the geometric arguments in it. | Some people are literally incapable of visualisation. They can no more improve it than someone in a wheelchair can learn to walk. |
[
"The parking fee for the first hour is 5$, then 3$ for the all the other hours. How do I make an equation that works even if there's 0 hours?"
] | [
"math"
] | [
"unywsu"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.3
] | null | (2+3h) (1 - 0^h) | Since "if" and "for" statements are fine in math, I can only assume you want this equation to be in some form you have not yet specified. That being said, 4h - |h-1| + 1 seems to fit the bill (Where |x| is absolute value). Of course, the notation |x| carries with it an implicit if statement, but no such equation exist... | Fourier begs to differ as long as infinitely close approximations are okay | That's a cunning way to work around "no if statements". | I sorta suspect OP would think it would not be ok (And neither fourier series nor taylor series looking things would give a polynomial) |
[
"If asked to round to a certain digit should I round to the digit in my working as well and if not what digit should I round to in my working"
] | [
"math"
] | [
"unwh8r"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.14
] | null | You never, ever round something before the final result. Also: wrong sub, try either simple questions thread or r/learnmath | No work with exact values until your final value, if you round all your values then your final value may be significantly difficult. | What if I’m dealing with irrational numbers | Also exact form can be much easier to work with | Also would this change depending on if you are meant to show your working or not |
[
"Dropdown Numbers?"
] | [
"math"
] | [
"unwh16"
] | [
0
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.38
] | null | https://www.reddit.com/r/maths/comments/u6qdgz/all_digits_in_a_dropdown_number_are_different_and/ | Then just write out all the possible collections of 3 digits (which have to be either 2 evens and an odd or all odd), average them to see what works, and permute as appropriate. | What is a "dropdown number"? | It’s essentially a concept where one digit in a number equals the average of the whole number. For instance, 1025 is a dropdown number since the average is 2 and the 2 is a digit within the number. | For the search for consecutive numbers, consider that the digit sum needs to be divisible by 3. Do you know how to check whether a number is divisible by 3 or not? To find all numbers, just look at a given average and think what the other two digits can be. |
[
"Is it technically incorrect to say a function is more convex than another function?"
] | [
"math"
] | [
"unnjt2"
] | [
18
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.95
] | null | You are talking about curvature, not convexity. | Probably that (g(x)-f(x))''=6x-2>0. But of course this is only true for x>1/3. So maybe g ISN'T more convex than f on the whole interval. (I am unsure if this is really a definition though.) | This is similar to the concept of curvature which you can define by finding the osculating circle at a point. | In mathematical economics, the notion "f is more convex than g" is expressed as There exist a convex function h such that f(x)=h(g(x)) | You can say a function is strongly convex. Then you can ask how strong is it? So, in this sense, you can say that one function is more convex than another. |
[
"What part of mathematics is worth learning for a high schooler?"
] | [
"math"
] | [
"uniik0"
] | [
4
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.67
] | null | Calculus is interesting, but I don't think I should learn it yet, seems like a really big subject) Calculus isn't even a branch of math. It's the name for a sequence of courses taken in school or university. Nobody in math does research on "calculus". They work in analysis (real analysis, complex analysis, harmonic a... | Maybe learn proofs or discrete mathematics | Counting (no I'm not kidding), it's easy enough to get started early and can develop a foundation for a lot of things. | In that case I would recommend you study diffEQ, calculus and linear algebra. All of those tend to be very necessary for your intended route | This. Also elementary number theory. Edit: As a concrete suggestion for a book, you could try checking out Eccles' "An Introduction to Mathematical Reasoning: Numbers, Sets and Functions" . |
[
"calculating volume."
] | [
"math"
] | [
"uni6tr"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.67
] | null | You’re not doing anything wrong. Multiplying 280 by 0.33 gives you the volume in cubic feet. ~92.4 cubic feet isn’t smaller than 280 square feet. They’re two different measurements, it doesn’t make sense to compare the two. It’s like saying that 2 miles is smaller than 20 miles per hour. If you have a rectangle that’s ... | Figures I was thinking of it wrong. Thanks! | Of course, 280square foot area filled to 1ft height is 280 cubic feet. You sure you got area, not iorcumference? 280*0,33 is 93,35 cubic feet of volume. or 2,6m3 in metric. Regardless of the shape. | Nothing, 280 be less than 280 ft Note, however, that you’d need to convert this volume to cubic yards anyway. 1 yard = 3 ft, so 1 yd = (3 ft) = 27 ft 280/3 ft = (280/3)/27 = 280/81 yd | How silly of me. Thank you! |
[
"curious"
] | [
"math"
] | [
"unei6u"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.13
] | null | OP thinks you didn't attempt to figure this out on your own before asking. | What they’re saying is you didn’t think hard enough about the solution to your question, it’s quite literally as simple as division | How long would it take for you to get 82 million? What about 123 million? The answer is as obvious as it seems. | It just seems like an odd question to ask, because it's literally just taking the big number and dividing it by the less big number. In the context of a math subreddit, it doesn't seem like a worthwhile question. (To explain this commenter's point of view) | 8 trillion / 41 million = 195,121.95 seconds = 3252.03 minutes = 54.2 hours |
[
"Has anyone taken mat1033c in college?"
] | [
"math"
] | [
"unfe0l"
] | [
0
] | [
"Removed - incorrect information/too vague"
] | [
true
] | [
false
] | [
0.25
] | null | What is mat1033c? Different colleges have different names for classes. | Intermediate math college class | That doesn't clear anything up | I assume it's a math class? | Yes math class |
[
"Is there a clear way for me to reverse Modulo calculated number?"
] | [
"math"
] | [
"un82no"
] | [
0
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.43
] | null | All numbers of the form 23 + 99k equal 23 modulo 99. That means that just knowing b and c there is no way to get a. | a = 5, b = 2. a % b = 1 a = 7, b = 2. a % b = 1 The value of a % b is the same value for two different values of a. Thus, you can't reverse the operation to find what a originally was. | Think about an analogue clock. By just looking at the minute hand you cannot tell what the hour is. By looking at the hour and the minute hand, you can't tell if it is AM or PM. | Always happy to help, but just as a side note, questions about simple topics belong to the quick questions mega thread or r/learnmath . | Always happy to help, but just as a side note, questions about simple topics belong to the quick questions mega thread or r/learnmath . |
[
"Is there any differnce between these two answers?"
] | [
"math"
] | [
"unea0r"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
1
] | null | Apologies, not f(0), but f(1) = 0 and 1<2 but f(1) = 0, not less than. | Yes, the first answer specifically did not include 1 (it was the interval <-inf,1> and <1, 2> not inclusive). Also, post it on r/learnmath next time. | My answer is the 2nd picture | First, I think you should look at rule 3 of the subreddit. Second, your answer implies that f(x)<0 at all values of x<2 which is not true since f(0) = 0, which is not less than 0. | No, f(0) cannot = 0 because f(0)=-2 (f(0)=x -4x +5x-2), and sorry didn't read the rules, I planned on posting this on r/mathematics but they don't allow photos :/ it was the difference or differential I had to solve |
[
"Examples of mathematical development as a result of findings from other fields"
] | [
"math"
] | [
"undvh0"
] | [
39
] | [
""
] | [
true
] | [
false
] | [
0.92
] | null | Work in physics and engineering has inspired a huge amount of research in mathematics, so your question feels a bit like shooting fish in a barrel. Important parts of calculus, ordinary and partial differential equations, Fourier analysis, functional analysis (esp. work on unbounded operators), wavelets, and coding the... | here’s an interesting example of how Hegel inspired some discoveries https://philosophy.stackexchange.com/questions/9768/have-professional-philosophers-contributed-to-other-fields-in-the-last-20-years/9814#9814 | won the Fields medal a few years ago That was quite a lot more than just a few years ago. | You're completely right, I'm just here to add on to this the large highway between math and the rest of the world that is numerical methods. Results and ideas bounce back and forth along this all the time. | The only example I can immediately think of is covered in William Gasarch's excellent article, . |
[
"Is this normal for a conference?"
] | [
"math"
] | [
"un7riw"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
1
] | null | Carpooling is weird but plausible. However bringing $200 in cash is really weird. Cooking together sounds super fun but the setup sounds sketchy. Do you know anyone else going? Are there any plenary speakers that are well-known and easily searchable (with photos)? Can you ask your advisor these questions and show him t... | No, it's not. The food cash is particularly strange. They are saying that they have been told they won't be able to reimburse it bit are still asking for cash, this is a red flag. Organizing transport together is not strange, although it's not the norm. | This is pretty weird but within the realm of imagination for what can happen at a conference. Math conferences aren’t the most well organized affairs, but usually they would be able to grant assurances of reimbursement beforehand. | This sounds like the organisers are a bit cash strapped and try to do a fun low budget conference. Where does this one take place? | I'm too young to know if it's normal, but I wish it was. Sounds pretty cool |
[
"We broke math. (I think)"
] | [
"math"
] | [
"uo02rb"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.4
] | null | Indeed that's a hole in the fundamentals of mathematics. Have already contacted Harvard for a meeting with you. | read the sidebar. | Not to be rude, but did you try reading it? There are rules to posting in various subreddits. Your post violates the rules. | I think you’re just bad at math. | Please enlighten me with your method to get 36 |
[
"Today, May 12th was chosen as a day to globally celebrate women in mathematics #WomenInMaths. It was the birthday of Maryam Mirzakhani (1977-2017), the first and only woman to win the Fields medal"
] | [
"math"
] | [
"unrqep"
] | [
749
] | [
""
] | [
true
] | [
false
] | [
0.93
] | null | The only woman to win the Fields medal | RIP, Maryam Fuck cancer | Only woman so far* | I hope my title will age like milk in July | #WomenInMaths on Twitter: https://twitter.com/hashtag/womeninmaths About Maryam Mirzakhani: Biographie: https://mathshistory.st-andrews.ac.uk/Biographies/Mirzakhani/ Profile: https://www.quantamagazine.org/maryam-mirzakhani-is-first-woman-fields-medalist-20140812/ |
[
"How accurate is this list of greatest mathematicians?"
] | [
"math"
] | [
"unj4rl"
] | [
5
] | [
"Removed - incorrect information/too vague"
] | [
true
] | [
false
] | [
0.69
] | null | That question is unanswerable because "greatest" is subjective. | John von Neumann > Fermat IMO But {mathematicians} is a partially ordered set at best. | How do you define greatest? I don’t see a natural ordering on the set | Them's fightin' words, bucko | Euler should be the first 4~5 spots, followed by the rest. |
[
"The Lost 4-Dimensional Rotation"
] | [
"math"
] | [
"unbeue"
] | [
179
] | [
""
] | [
true
] | [
false
] | [
0.97
] | null | “Orthogonal” is the most technically correct term, which is just a precise way to capture the intuitive idea of what “perpendicular” means. Two vectors are orthogonal if their dot product is zero. Two subspaces of a vector space are orthogonal if every vector in the first space is orthogonal to every vector in the seco... | Yes you're right, I should have said something like "you can't have two planes intersect at only a single point in 3D." What do you think? | Since you can’t have two perpendicular planes in 3D. Am I missing something, is the perpendicularity of planes defined different than what I'm thinking of (perpendicularity of their normal vectors)? | It's a good and succinct explanation of what's going on, but I have to nitpick your use of "axes", especially in the 4D case. You can't rotate about an "axis" in 4D; the intution in rotating about an axis in 3D only arises since each plane has a single orthogonal line, and each line has a single orthogonal plane (throu... | This is also how unit quaternion multiplication q q works: it's a double rotation of q , one in the plane containing the real line and q , and one in the "fully orthogonal" plane normal to the first plane. I have a half-written blog post about this which I was planning to edit eventually but I'll take this opportunity ... |
[
"What is research in set theory like?"
] | [
"math"
] | [
"unszqa"
] | [
29
] | [
""
] | [
true
] | [
false
] | [
0.92
] | What do set theorists do? How do research-level set theorists prove things? Are there certain tools that are used in set theory? I know of consistency/independence results, but is that all set theorists do? Or are there other things that set theorists spend their time on? If it matters, I'm mainly curious about large c... | I know of consistency/independence results, but is that all set theorists do? No, but it is what I do, so I'll talk about it. My research is aimed roughly at the following theme. There are some interesting combinatorial properties that large cardinals have; is it consistent for those properties to hold at small cardina... | I know of consistency/independence results, but is that all set theorists do? There's been additional work in understanding ordinals and ordinal arithmetic the last few years, generally just in ZF, or ZFC. /u/sniffnoy is one of the people involved in that so he can probably do a better job outlining some of what's happ... | Confusing. There are a ton of different things involved in set theory these days, but in general set theorists are concerned with independence results. You mention LCAs. What you should know is that these are not the only directions that new axioms move towards. There are also small cardinals. There are topological axi... | I mean I'm not exactly a set theorist... I have been working on computing types of WPOs, but I don't think there's that many other people working on this; mostly just myself, Andreas Weiermann, and some collaborators of his? I mean I can say more about this but it is very much not what most set theorists do... | Yeah, I agree it isn't what all set theorists do, but Andreas seems to be a set theorist, or maybe he's more of a logician? And you seem hard to classify at this point. But yeah, I agree this isn't a big area. It was an example of something in set theory that is different than consistency or independence. |
[
"Is there some piece of math that was initially regarded as crackpot but later gained acceptance?"
] | [
"math"
] | [
"untyn3"
] | [
256
] | [
""
] | [
true
] | [
false
] | [
0.96
] | null | Difference in infinities (cantor and transfinite cardinal numbers), non-euclidean geometry. | Lewis Carroll wrote to attack Hamilton's notion of quaternions, which Carroll thought was absurd. https://www.npr.org/2010/03/13/124632317/the-mad-hatters-secret-ingredient-math | The concept of 0, imaginary numbers, higher dimensions, irrational numbers, literally 80% of math as we know it today. | Early group theory. When Galois submitted his paper to the mathematicians of his day, they thought it was trash. Euler's solution of the Basel problem was not fully accepted at first. Bernhard Riemann encouraged the study of hyperdimensions in math at a time it was not really appreciated. Category theory Irrational num... | Cantor was really mistreated due to his work on transfinite numbers. |
[
"Is there a name for..."
] | [
"math"
] | [
"uo0vkq"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.32
] | ... a conjecture that seems plausible but falls apart when subjected to the inaccuracies of the real world? I'm coming from a music theory background , not maths, so bear with me. One of the tropes of harmonic theory is that simple ratios between 2 notes are consonant and complex ratios are dissonant. So, take an A at ... | Do you mean a conjecture about math or about behavior of something in the real world? Many mathematical models of the real world are going to be reasonably accurate under small measurement errors since the models themselves involve ignoring something (friction, etc) or idealizing something (treating population as a con... | Consider that a conscious being who could differentiate frequencies with a sufficiently high resolution perceive the nudged octave as dissonant. So it comes down to what motivates your definition. One very important lesson from mathematics is how often seemingly conflicting ideas are not in fact conflicting, but playin... | (i.e. like most math classes), then this question doesn't really make sense and here is my response: This is kind of a weird question, that relies on a misunderstanding about what "truth" means in the context of mathematics. Is there a name for... ... a conjecture that seems plausible but falls apart when subjected to ... | Are you sure that's what theory predicts? If notes of equal amplitude have frequency f1 and f2 respectively (peaks occur every 1/f seconds for each note), then they create a sound of amplitude x = cos(2 pi f1 t) + cos(2 pi f2 t) If f1 = 880 and f2 = 1760, then the peaks in x occur regularly every 1/880 of a second, ie ... | I got many conjectures about math that fall apart quickly. Let me go grab them out of the trash bin |
[
"What is the \"Hartshorne of X?\""
] | [
"math"
] | [
"unr65h"
] | [
45
] | [
""
] | [
true
] | [
false
] | [
0.89
] | In your opinion, what is the quintessential text in your subfield? | Richard Stanley for Combinatorics | Kobayashi & Nomizu "Foundations of Differential Geometry" Federer "Geometric Measure Theory" Morrey "Multiple Integrals in the Calculus of Variations" Hörmander "Analysis of Linear Partial Differential Operators" Dunford & Schwartz "Linear Operators" | Vakil is the Hartshorne of algebraic geometry 🙃 | Ahlfors complex analysis | Hartshorne(algebraic number theory) = Neukirch |
[
"Help Finding a Scrabble-Legal Grid of Size 6"
] | [
"math"
] | [
"unkg1c"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
0.85
] | I'm a big fan of crossword puzzles/Scrabble and I had a thought: what's the largest size NxN that you can populate with letters such that the grid is legal for Scrabble (meaning the rows left to right, and the columns top to bottom, form words found on the NWL2020 word list) To answer this question, I performed a numer... | Nice question. You might like to look at https://en.wikipedia.org/wiki/Word_square#Modern_English_squares which shows symmetric squares up to 9x9. One issue with your probability analysis is that the various events (that individual rows and columns form valid words) are not independent. If those events tend to be posit... | I think your estimate is very pessimistic: English letters aren't evenly distributed, and there's a structure to English that helps you out (consonant-vowel alternation). I think it should be reasonably possible to brute force using words instead of letters and using an optimized data structure: I'll take a look and se... | Small nitpick on "Interestingly, the expected value for grids of size 6 is approximately 0.5, meaning that numerically, it’s about a 50/50 chance that there exists a legal grid of size 6." I'd argue that's not really true (depending on what you mean by about 50/50) Imagine a smaller case, with say 4 boards. For E to be... | Use of a crossword puzzle generator software reveals that indeed there are plenty of order-6 grids. I'm searching for an order-7 now. | I assume you mean forbare, not forebare? I was v. confused for a minute looking at this |
[
"Sources for Understanding the Qualitative Difference between Elliptic, Parabolic, and Hyperbolic PDEs"
] | [
"math"
] | [
"une5me"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
0.9
] | Hi, I'm trying to understand how PDEs (and systems of them) of different forms behave qualitatively (and perhaps quantitatively) based on being classified as parabolic/elliptic/hyperbolic. It seems like the sources I've looked at do a decent job of mathematically defining them (i.e. for an equation [;a\cdot\frac{\part... | For understanding the difference between elliptic, parabolic, and hyperbolic pdes, you really want to keep in mind the primary examples of each: respectively, the Laplace, heat, and wave equations. For elliptic equations, you get properties such as solutions being harmonic, mean value theorems, maximum principles, and ... | There is a very physical discussion of this in Sommerfeld's 'PDE's in Physics' book (with a few pictures), it properly shows why we even care about characteristics in the first place, and contains many other topics such as this . | I would recommend for anyone beginning in PDEs my favorite undergraduate textbook for the subject: Partial Differential Equations by Evans. It goes well into the mathematical properties and contrasting one with another. It also has a good taste of more advanced topics for beginning graduate students | Thanks for the response! I'm not sure if I'll have time for a PDEs math course while I pursue a physics degree. Evans' book seems like a good resource from what I've been able to see online. Thanks for the feedback! | Building on this, I think the best way to think about it is in terms of blow-up. Elliptic PDE are ridiculously nice and are like complex analysis in PDEs ( deeper reasons for this of course and not totally correct as many other things are complex analysis in PDEs but ya know). Treasure them. Parabolic PDEs can blow up,... |
[
"Argument with my friends"
] | [
"math"
] | [
"vum1jb"
] | [
0
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.4
] | null | Do your friends know that? Because the way the OP is written the answer isn't 40%, it's 36%. | 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! | Can there be two tokens in one envelope? If no, then yes I believe you are correct. | One token, thanks | You said elsewhere there is only one token in the envelope... So if there is only a 20% chance of red and only a 20% chance of blue... what the hell else is in the envelope? You're not saying the probability of the envelope being empty and so this is not a well formed question. If you have just the two possibilities an... |
[
"Quick Questions: May 11, 2022"
] | [
"math"
] | [
"und5im"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
0.86
] | This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread: Including a brief descri... | You can apply f(x) = x to these numbers and compare the results. As it is a monotone function for x > 0, the order is preserved. | If xy=yx=0 then 1=1 =x +y . So we deduce y=0 since there is no odd part of x +y . Which means that 1=x which is by assumption even. | One way to argue could be that the x>0 part is connected because sin(1/x) is continuous, and that the closure of the graph is the whole space, which you can see by constructing a sequence that converges to each point. | I think it’s even easier than that: |x| is bounded by (a constant multiple of) |x| for x in any compact region containing the origin. Replacing x with x - y should give the result. | A useful paradigm in math is that if I want to decide if two objects are equal, we should start by showing some of their invariants are equal. Now a lot of invariants are naturally graded, and very often two invariants are isomorphic, but not in a graded way. So keeping track of the grading allows us to show that our o... |
[
"I am tired of people going crazy after a number because they show up in their life."
] | [
"math"
] | [
"vucy99"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.78
] | null | Since the real numbers form a field, not just a ring like the integers, they are closed under division as well as multiplication, meaning that every real number is divisible by every other real nonzero number, meaning that every nonzero real number is a unit because every nonzero real number divides 1. Defining divisib... | Imagine when he will discover that half of existing numbers are divisible by 2 | True, I meant integers | Define divisibility for numbers other than integers. | existing numbers Most real numbers are not divisible by 2 or by any other natural number |
[
"What is the difference between ~ and ± when approximating?"
] | [
"math"
] | [
"vu7fiu"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.4
] | null | ~3 meass "about 3" so the real value will be somewhere around 3 (but without saying how close). In contrast 3 ± 0.5 tells you that the real value will be somewhere between 2.5 and 3.5. | ± gives a upper/lower bound, ~ does not | Thank you! | Cool! Thank you! So, it basically boils down to the accuracy of it? | Yes |
[
"Switching to pure math from an applied math background."
] | [
"math"
] | [
"vu5e8l"
] | [
14
] | [
""
] | [
true
] | [
false
] | [
0.82
] | null | You have to understand where he/she coming from. I’m a statistics major, which I’d consider to be applied math. It has a few pure math classes, like real analysis and upper division linear algebra, but is still far removed from pure math as a whole. Even I’m wondering how I’d be able to switch over to a pure math backg... | No its not possible. Once you contaminate yourself with the inpurity of applied math, you are forever banned from the pure math sacred documents and books. /s Seriously though. Talk to teachers, take a broad view on the pure math topics available at your knowledge stage. Pure math can you give you formalism that is neg... | I feel that. A lot of "applied" courses in the STEM field are more like "here's how to use these formulas and theorems, now plug it all in IRL and the output is your answer." You wind up not understanding what you're doing, nor the tools that you're using. I went through the same in my undergrad years, so I'm currently... | Of course you can. | What sort of low effort question is this |
[
"like seriously, how to derive the gamma function?"
] | [
"math"
] | [
"vu3ack"
] | [
0
] | [
"Removed - ask in Quick Questions thread"
] | [
true
] | [
false
] | [
0.38
] | null | There’s no derivation, it’s a definition. If you’d like motivation for the definition though, look at laplace transforms and in particular see the laplace transform of t If we’d like an analytic continuation of the resulting formula with n factorial to complex n with real part greater than 0, we can just take the integ... | The shift over is i think mostly historical coincidence but note the gamma function is unique if you require the extension of the factorials to have some intuitive properties as described here https://en.m.wikipedia.org/wiki/Bohr%E2%80%93Mollerup_theorem . | The reason I think it is very natural to have it shifted over is because the Gamma function integrates over (0, infinity), and the Haar measure for the multiplicative group of positive reals is dt/t and not dt. So really people should write Gamma(s) = integral t^s e^(-t) * dt/t To me, writing the Gamma function in this... | I guess so, I genuinely tried to help though but not exactly spoon feeding. Sometimes I feel Stackoverflow does it right by mandating OP to provide his/her own effort. This build OP's confidence and they get to know their mistakes. We are not replacement of Wolfram. | I guess you're being downvoted for inferring what OP meant to ask?? |
[
"My wife has the same cvv on 2 different cards"
] | [
"math"
] | [
"vu0vn6"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | null | Since both of the events are independent. P(A/B) = (1/(10** 3)). | Python gang | Men of culture | Higher. Depending on the number of cards she has. | 0.1% assuming each digit is independently selected (they may excluded cvvs such as 000 or 111) |
[
"any good mathematical podcasts?"
] | [
"math"
] | [
"vugt8p"
] | [
101
] | [
""
] | [
true
] | [
false
] | [
0.95
] | null | Exclusively math: My Favorite Theorem, Mathematical Objects, The Joy of X, Breaking Math Not exclusively math: A Podcast of Unnecessary Detail, A Problem Squared, The Joy of Y, Complexity, The Math and Physics Podcast Edit: added punctuation because Reddit ruined my list format. May edit again in future if I think of m... | There's a series of podcast episodes conducted by 3blue1brown. You can find it on YouTube by searching for Grant Sanderson. | The Joy of Y Is where Strogatz has been? I've been relistening to Joy of X episodes because they haven't released new ones in a long time. Hooray, I have more to binge! I will note that Joy of X isn't all math either, and it's better for it. You will get lots of math, but the occasional neuroscientist guest will mix th... | It's more about talking about math exposition than math itself | The Numberphile podcasts! |
[
"Thinking of other mathematical concepts as graphs!"
] | [
"math"
] | [
"vuecx7"
] | [
20
] | [
""
] | [
true
] | [
false
] | [
0.87
] | I saw a a few days ago, where the commentator said, "It made intuitive sense to me to think of every mathematical concept as a graph" I'm just starting graph theory and I don't understand how one would think of other mathematical concepts as graphs. If someone has an idea what this means/in what way this is possible, p... | Groups are commonly represented as graphs via a Cayley graph. | I’m not sure what that poster was trying to say. It’s clear that you cannot think of mathematical concept as a graph. Even if you could shoehorn a concept into the structure of a graph, it probably would not lend itself well to study of that concept. A more reasonable statement is that there are many existing mathemati... | Many ideas in Algebraic Topology such as homology and homotopy can be understood by extending graphs to higher dimensions. For example a node or vertex (point) is zero dimensional, an edge is one dimensional, you could think of the planar regions enclosed by edges as two dimensional surfaces. Going up one more dimensio... | Category theory intersects a lot of different disciplines of math, and category theory is all about understanding the relationships between objects while abstracting away most of the properties of those objects. In other words, the structure of a category "sort of looks like a directed graph." This means that the categ... | If you're familiar with trees (a form of graph) you can, for example, put algebraic operators into a tree. take 2 + 2, if '+' is a parent node/vertice to two '2' child node/vertices then reading that tree a particular way can allow us to evaluate that algebraic expression. |
[
"Novel Solutions to Simple Problems"
] | [
"math"
] | [
"vu6ide"
] | [
11
] | [
""
] | [
true
] | [
false
] | [
0.93
] | I'd like to discuss this topic because I recently remembered a curious case that happened a couple of years ago here in Italy. Here's the story: you may have heard of parabolic segments, it's that shape you get when a line intersects a parabola in two points: the finite area between the line and the concavity of the pa... | What do you think of this whole situation? Why did it gain so much traction and press coverage? Two things are infinite: the universe and public ignorance of mathematics, and I'm not sure about the universe. | I think the most notorious example of this phenomenon is "Tai's rule": https://www.reddit.com/r/math/comments/98sbdt/in_1994_a_medical_researcher_published_a_paper/ https://academia.stackexchange.com/questions/9602/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper | This is literally perfect. I had never heard of this """paper""" before, but it's beyond absurd. Thank you, you made my day. | I love that this story is about Italians and unfounded hype about a geometry result :P | I make heavy use of the trapezoid rule in my thesis, I’m definitely going to cite this paper :D |
[
"Book recommendations like Chaos by James Gleick?"
] | [
"math"
] | [
"vu4er0"
] | [
16
] | [
""
] | [
true
] | [
false
] | [
0.92
] | Hey folks, looking for some new reading material. Recently I've devoured Chaos and The Information, both by Gleick, Godel's Proof by Nagel and Newman, and GEB. I'm really interested in the funky edges of math, the math that kicks you in the what-does-this-say-about-nature part of the brain. I'm also looking explicitly ... | I enjoyed the books by Marcus du Sautoy about group theory and prime numbers: Finding Moonshine, and Music of the Primes. Written for a lay audience. Also, how about Four Colours Suffice, by Robin Wilson, about the map-colouring problem? | Thank you, I'll check them out! Four Colors Suffice is especially tantalizing. A whole book for one problem. I love it when math reveals surprising depths. (If only someone could solve the Collatz Conjecture so I could read THAT book.) | You might like Prime Obsession (about the Riemann Hypothesis) or Weapons of Math Destruction (about algorithms and their societal consequences). Also, Jordan Ellenberg has two math-for-everyone books I’ve not yet read that people seem to like. There are also some good (auto)biographies of mathematicians with some math ... | Take a look at meta magical themas by hofstader | Thanks! The Riemann Hypothesis is fun, I'll check that out. Counter recommendation for you, since you mentioned biographies: A Mind At Play by Soni and Goodman is an EXCELLENT biography of Claude Shannon, my favorite mathematician. |
[
"How to keep my brain sharp and develop problem solving/logical thinking?"
] | [
"math"
] | [
"vtz18f"
] | [
50
] | [
""
] | [
true
] | [
false
] | [
0.91
] | I’m 18, should I be doing competitive math, competitive programming, discrete math, etc? What would be most helpful? | Do whatever interests you, and it doesn’t have to be competitive unless you enjoy that. | I find it relaxing just working on problems from “the Putnam and Beyond”. It’s a cool book that has a couple of pages of math and then pages and pages of cool (and sometimes quite difficult) problems with solutions. So if you want to practice your problem solving, flip to a page and try some of the exercises. If you ge... | Read read read and read some more Textbooks, novels, biographies, anything to keep you reading And make sure you about what you’re reading, don’t just look at words on the page | Further along this line, I recommend Project Euler. If you know any basic programming, it's perfect. 800+ math problems that you are asked to solve using code. For me, it really hammered in some good mathematical thinking and problem solving skills. | I'm 16 and love competing and doing discrete math but I have friends who hate doing those, so just do whatever interests you. If you really want suggestions I would recommend reading philosophy, learning a new language(I enjoyed learning Greek) or you could watch MIT ocw lectures to continue learning. |
[
"How to keep math as a hobby?"
] | [
"math"
] | [
"vtyafp"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
0.79
] | null | Get books on topics you're interested in and work through them. Find YouTube channels you like and engage with them (3B1B, Michael Penn, etc). Talk on reddit. | I'm curious; where are you from that psychology of all things is hyper-competitive? | Germany. I think the only degrees that are consistently more competitive than psychology are human medicine, veterinary medicine and dentistry. | To preface: I don't have a lot of recommendations other than what has already been stated. Although there are some interesting books (not textbooks) on math that could be worth reading through - need to find them. I was drawn to your post because I also am in a similar position. I wanted to study medicine or psychology... | I think the difference is that psychology is just a normal bachelor in the UK that doesn't directly lead anywhere. Here in Sweden (and probably in Germany) if you study psychology you're studying a longer programme and becoming a clinical psychologist directly after. For example, at Stockholm university the psychologis... |
[
"What is your favourite expository paper?"
] | [
"math"
] | [
"vtvxo7"
] | [
46
] | [
""
] | [
true
] | [
false
] | [
0.99
] | Inspired by I encountered highlighting four expository papers about the 2022 Field Medalists written by Andrei Okounkov, I wanted to read expository papers. So, I ask all of you to share your favourites! Edit: Thank you all for the suggestions! | There are plenty of great expositions in the AMS notice/bulletins. My favourite is the exposition to the proof of Fermat Last theorem(modularity for semi stable elliptic curves proof by Wiles) written by H. Darmon AMS notice | Donaldson, in addition to being a great mathematician, is an extremely lucid expositor. Many of his expository papers can be found on the arXiv . Recently he's posted several nice articles on Atiyah's and Uhlenbeck's work. | A lot of what motivated me to learn Fourier analysis was on Guido Weiss paper on harmonic analysis. Its very well written. Heres the link to it: Harmonic Analysis . | I have been reading these annual series of books of expository papers - https://press.princeton.edu/series/the-best-writing-on-mathematics#:~:text=Mircea%20Pitici%2C%20Series%20Editor,available%20to%20a%20wide%20audience . | Cumulatively I've learned more from his blurbs than I have from any given book. I wish he'd write more, I don't think I've seen a change in the catalogue in the last ~6+ years. Actually, I wish he'd write an actual textbook on an algebraic topic, something more specific than "a course in abstract algebra", but not too ... |
[
"Am I the only one who gets annoyed when the only exercises in a book are of the form \"show that...\"?"
] | [
"math"
] | [
"vu3j7m"
] | [
284
] | [
""
] | [
true
] | [
false
] | [
0.84
] | I miss exercises such as "calculate these 50 derivatives/integrals" and calculation exercises in general. When I studied calculus those specific exercises were the reason why I have such a good understanding of it currently. I'm not saying that I hate proofs, I really liked calculus, set theory or group theory proofs, ... | As is written in Baez's book, deep mathematics is "painfully abstract" and you at some point need to deal with it. On the other hand, I totally get your point in that physicists rather does Differential Geometry better than mathematicians because they calculate with the real world. Definitely DG is the most painfully ... | On the contrary, I like doing “show that…” problems because they already gave you a destination that you have to reach. You just have to find your way there. They are hard but I find it more rewarding when I managed to solve them. Computational problems on the other hand I tend to doubt my works without seeing the solu... | Definitely DG is the most painfully abstract subjects among mathematics Algebraic geometers: Them's fightin' words | That is definitely a completely unreasonable response to your question. Doing an AG class without working out basic examples is kind of ridiculous. | You’re not alone in believing that computations are important. They are vital to one’s understanding of a subject. But so is the ability to prove statements. Computations usually lead to conjectures which then need to be proven. Also I get that computing derivatives and integrals might feel fun(to some), just doing tho... |
[
"Stupid theoretical question"
] | [
"math"
] | [
"kleoc2"
] | [
3
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.71
] | null | If youre gonna count backwards from infinity,you have to start somewhere,lets say n.this means n+1 wont be counted so you cant really do it | Ah ok that makes sense. Sorry I know it was kind of a stupid question. | Count from 1/x x going from 0 to 1/60. Obviously though infinity is not a number. 1/0 dne | One interpretation of "infinity" that sort of gets what you want is hyperintegers. You can construct a sequence a_1 = H, a_2 = H-1, a_3 = H-2 ... a_H = 1, where H is an infinite (i.e. nonstandard) natural number. This (hypernatural) "sequence" counts backwards and contains every standard natural number. For example, a_... | Actually I think hyperintergers are EXACTLY what I was thinking thanks! I had forgotten what they were called. I think I'll do more research into them. I know infinity isn't really a number per se, I just remember the vsauce video where they talked what the ending to a problem that goes on forever would be. |
[
"I don’t get the concept of math"
] | [
"math"
] | [
"kle61e"
] | [
14
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.89
] | null | When you go to university you will see that math is so much more then formulas. I would recommend finding a book that introduces logic and maybe basic proof, like Proofs and Fundamentals by Blach. There may be some material that wouldn't make sense because you don't have the background, but most intro proof books are u... | When it comes to stuff like general relativity then mathematics isn't really a tool for 'proving' the theory, but rather a language that allows you to state the theory. To think that mathematics can prove some deep properties of our universe is slightly wrong, it can theories about how our universe works and using this... | I started with the intent of becoming an electrical engineer, but switched to math in college. Formulas, like the quadratic formula, are complex when you look at them. Hopefully you recognize the phrase "completing the square"? Completing the square for arbitrary b, c and a != 0 is where the quadratic formula comes fro... | Math is like a puzzle that we collectively figure out. It is not just numbers. Check out graph theory or knot theory, both of which can be intuitively shown visually. https://www.alternativeslibrary.org/2016/01/what-do-puzzles-have-to-do-with-math-education/ | Math is more about WHY those formulas are true than how to use them. In university, courses begin to focus more and more on teaching you to prove the truth of what you're using or discussing. |
[
"Permutation Problem?"
] | [
"math"
] | [
"kla9x2"
] | [
1
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
1
] | null | If the two scores are independent of each other and we assume a uniform distribution (which you don't, but I don't see another specified) then each score has an average of 5.5. Hence, the average of the two scores must be 5.5. Formally, we want sum_i,j p( s_i, r_j ) * ( s_i + r_j ) / 2 = sum_i,j p( s_i ) p( r_j ) * ( s... | If the person ranks the base object for attribute#1 as 1, and its reciprocal object as 10, then the final average for that attribute is 1, not 5.5. You might have misunderstood. I don't get your formal breakdown at all. You can think of the 10 objects as labeled B1, R1, B2, R2, B3, R3, B4, R4, B5, & R5. B&R are base ve... | Regarding my notation: s is the base score, r is the reciprocal s_i is a specific score, r_j same for reciprocal p( s_i, r_j ) is the probability of s = s_i, r = r_j and you can probably guess the other p function meanings In general, avg = sum p(x_i) * x_i I’m using notation that I have seen in many basic probability ... | I don't know what you mean by independent. I mean... reading an entire book on probability would probably be really enlightening and I'll make use of the information in future, but to read one just to answer this one question is a bit overkill. I don't know the jargon, I really don't know if I'm giving you the details ... | Ah, ok. Forget the last division by two for a moment. So, now R1 = 1, B1 = 10 gives a score of 2. You can divide by 2 at the end. Let's just think about R1 and B1. In total, there are 10 choices you can make for R1 and 9 for B1 (they can't have the same rank, so once you choose R1 there are 9 options left). So, 90 opti... |
[
"(Theory of Groups) Can someone explain to me \"left coset, right coset\"?"
] | [
"math"
] | [
"kl5df0"
] | [
2
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
1
] | null | Left and right costed just indicate what direction you are multiplying. They are otherwise the same. The coset equivalence relation is just equivalence as sets. For example, as a set of the symmetric group S_4, for coset H={e,(1,2)}, H and (1,2)H={(1,2),e} are the same. | A left coset ie a ℤ = {az| n \in ℤ } is the set of multiples of a. Then, if we were to map ℤ to ℤ /n we would get a set of left cosets. a is a member of a ℤ but so is 2a. Hence, their representation in ℤ /n would be the same. Concrete example. ℤ /4 ={0,1,2,3} as there are three possibilities. Either a integer is... | Shorthand like " ℤ/4 = {0,1,2,3,4} " can be tricky when you are learning the nuts and bolts of quotients for the first time. I would expand that out to: ℤ/4ℤ = {0+4ℤ, 1+4ℤ, 2+4ℤ, 3+4ℤ}. Those elements really are the cosets (basically the subring translated by an element). You can start to feel what cosets look like wit... | Let G be a group and H a subgroup. Then for an x in G, xH = {xh for h in H} is a left coset of H in G. For clarity, I will only speak about left cosets since there isn't much difference. Each coset of H in G cuts out a portion of G. You can see this by considering if y is in a coset xH, then for any h in H, yh is also ... | I recommend taking a small group that you can work with easily and doing some calculating. Sym(3) has 6 elements. You could take a subgroup of order 2 like H={e, (12)} and work out what the left (or right) cosets are. There have to be three since each coset will have 2 elements and they partition the group. The dihedr... |
[
"Is the idea behind Vect(M) the same as <M>? (M a subset)"
] | [
"math"
] | [
"kl4f2d"
] | [
11
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.84
] | null | More generally, Vect( ) (which I believe is usually referred to as Span( ) in English-language texts) is the smallest subspace containing . We call this the subspace by . Similarly, < > is the smallest subgroup generated by , or the subgroup by . The same idea appears with other objects such as ideals, algebras, module... | (EDIT: I reply this under the idea that you're talking about a random set; if M is actually a subset of a structure, the same idea below still apply, you just have to consider just the substructure only) More generally, you might want to look into free construction. Starting with a set M, you can construct an object <M... | These are very interesting and useful views. Is there a source for this meta-math notations? Who is chartered with math notation curation? | One of the uses of category theory is that its very good at noticing broad relationships. So that’s a good source for finding the connections in the first place. No one person makes notation. It’s built up over time, and often changes | What is <M> ? |
[
"What is your favorite theorem in mathematics?"
] | [
"math"
] | [
"vue45b"
] | [
327
] | [
""
] | [
true
] | [
false
] | [
0.95
] | I searched 'favorite theorem' on google and found out this post: This post is 10 years old, and it was not able to add a new comment. So, I am asking this question again: What is your favorite theorem and why? Mine is the fundamental theorem of calculus, because I think it is the most important fact in calculus, which ... | The theorem that says that an integer can be written in the form a²+b² if and only if every prime of the form 4k+3 appears in its prime factorization an number of times. How random is that? | I'm torn between Cauchy's residue theorem and Riemann's rearrangement theorem. They're both just so mind-blowing and fun to apply. Mine is the fundamental theorem of calculus, because I think it is the most important fact in calculus, which is the biggest innovation in the history of math. Oh man you've probably angere... | Riemann rearrangement theorem is the quickest I’ve ever gone from “that can’t possibly be true” to “well I mean I suppose that’s obvious” upon hearing a theorem. | A finite automaton equipped with two counters and a one-way read-only input has the same decisive power as a Turing machine. (I can add some references later if people are interested, a bit pressed for time now. You can find this in any good automata theory introduction book, e.g. Hopcroft.) | Let X be a metric space with the metric d, and define another metric on X by d'(x,y) = min(d(x,y), 1). Then the topology induced by d is the same as the topology induced by d'. I just really love the theorem because it really encapsulates that all that really matters in point-set topology is what happens 'near' points. |
[
"Book recommendation"
] | [
"math"
] | [
"kkycea"
] | [
35
] | [
"Removed - post in the Simple Questions thread"
] | [
true
] | [
false
] | [
0.81
] | null | Introduction to Proofs and Mathematical Vernacular Book of Proof - Richard Hammack Both are open source (free) and I always seem to forget the authors. But they'll be easy to find. Edit: u/abolishvalue provided a correct title/author | I believe /u/YungJohn_Nash is referring to Richard Hammack's Book of Proof . It is good. | This might be a somewhat controversial opinion, but I don’t think “intro to proofs” books are worth one’s time. That’s not to say there aren’t good books in this genre, but rather that a better use of one’s time is to find an introductory book on some topic, and to go through it carefully by reading every proof and doi... | I went with Mathematical Reasoning by Ted Sundstrom when I started with proofs. It was a really great first introduction to proofs and I enjoyed it a lot. It’s open source and provides a lot of solutions to exercises. | Yup that's it! If I could give you more than one upvote I would. Instead, I'll edit my own comment. |
[
"Ridiculous Grading Curve?"
] | [
"math"
] | [
"kkvdkf"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.5
] | null | I’m a CS major at Caltech, so I had to take an introductory discrete math course last year. Virtually everyone got really low scores on the final (but not for lack of effort on our part)—we’re talking sub-50%—and the final was worth 40% of our overall grade.[1] The curve was quite significant, to say the least, so I en... | Lol I took a course in college where my average was a 27% and it was the top of the class. The prof just made up the tests on the way to class and didn’t worry if the questions were reasonable or even solvable at all, just let the curve take care of it I don’t know how much or how little I learned in that class but... | Discrete math was the first class I experienced this in too! I understand the stress, I don't feel like I'm doing well and the professor just sticking an A on mediocre work makes it hard to gauge where I'm actually at academically. | More common than I ever would have expected. But ultimately there is quite a bit of variance in instruction quality and exam difficulty. In fact, I remember our topology course had an "easy" semester and a "hard" semester because of the different instructors. | I was a math major at Columbia and this was definitely the norm. |
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