- Is there a better way to describe this summation function?by /u/TheWiggleMonster on March 2, 2021 at 12:09 am
In python, the function I have is: for i in range(1,n+1): s+=s+(i%2) print(s) This just adds the consecutive sums together and 1 on odds. kind of like 2^n but how would you write it in a mathematical way? submitted by /u/TheWiggleMonster [link] [comments]

- If pi cannot be calculated with rational numbers, then what do they use to calculate it to trillions of digits with supercomputersby /u/concerned414 on March 1, 2021 at 10:12 pm
I want to write a program that will continue to calculate pi forever. Of course I won’t get nearly as close as supercomputers have, but still: I want to know what numbers (or formulas) that the creators of those supercomputer programs use. Maybe I somehow try to calculate the circumference (which is irrational) in my equation to create pi? submitted by /u/concerned414 [link] [comments]

- I did not get into any PhD programs for pure math. What do I do now?by /u/BigBlueMongoose on March 1, 2021 at 10:10 pm
Hi r/math, I am trying to keep this fairly private so I won’t have too many details. I can give more if needed, though. I am graduating this year with a bachelors in Math from a major US University. I love math and have dedicated my college experience to doing as much of it as I could. I have a lot of classes but regrettably little/no research experience. I thought I was fairly competitive going in but I suppose I wasn’t competitive enough for the programs I applied to. I’m not really ready to give up on pursuing a PhD in pure math but I don’t really know what that entails. As far as I know, my only option is to take a gap year and apply again. I don’t really see how my prospects would improve in that situation, though. I’ll get a chance to read up on a lot of material I’ve been too busy to because of school, and perhaps have some job experience, but that’s about it. Are there any better options than taking a gap year? The biggest regret I have in this whole process is not applying to masters programs abroad and if there was some way I could join one later, I would gladly take that. Ultimately, I feel sort of broken over this. Everything I’ve done in college was for math and I can’t help but feel like I’m just not good enough for it. I’m sure this isn’t a super uncommon experience. Do any of you have any advice on how to proceed? Thank you for your help. EDIT: My GPA was decent: >3.85 in math classes and about 3.85 in general. I was unable to take the GRE because of the pandemic. My biggest strength is that I have lots of graduate classes. My main interest is generally algebra. The schools I applied to were all top 40 PhD programs in the US. My letter writers were professors of mine; two taught numerous classes I was in and one was a ‘research’ mentor during an independent study program. submitted by /u/BigBlueMongoose [link] [comments]

- Has anyone else noticed this?by /u/adumbidiot_ on March 1, 2021 at 9:24 pm
EDIT: I discovered nothing new and just (accidentally) ripped off Fermat. My bad. I wasn’t sure what sub to post this in so forgive me if this isn’t the best one. Also I’m terrible at explaining so I’m sorry if this makes no sense. Last night I was messing around with a calculator when I realized a weird trick you can do with prime numbers (and only prime numbers). In other words, I ‘found’ (I’m using quotes cuz idk if anyone else has found this) a test you can do to test if a number is prime or not. Take a number N, and raise 2 to the power of N to get X. Add (N – 2) to X to get Y. If Y is divisible by N, then N is prime. You can also subtract (N + 2) from X to get Z. If Z is divisible by N, then N is prime too. This only works with prime numbers. (edit: never mind, Carmichael numbers pass it) For example: 2 ^ 3 = 8. 8 + (3 – 2) = 9. 8 – (3 + 2) = 3. Both are divisible by 3. 2 ^ 11 = 2,048. 2,048 + (11 – 2) = 2,057. 2,048 – (11 + 2) = 2,035. Both are divisible by 11. Let’s try a composite number. 2 ^ 4 = 16. 16 + (4 – 2) = 18. 16 – (4 + 2) = 10. Neither are divisible by 4. So my questions are: Has anybody else discovered this trick? Are there exceptions to this trick? (i.e. composites that pass the test, and primes that fail) Why does this trick only work for primes, and not composites? Gracias. submitted by /u/adumbidiot_ [link] [comments]

- Is e(π)^2 rational, irrational, or undetermined? Why?by /u/Jhonny_Rock on March 1, 2021 at 8:57 pm
I saw on Wiki that eπ has not been proven to be to be irrational. Is eπ2 irrational? Why? submitted by /u/Jhonny_Rock [link] [comments]

- What is the best way to actually enjoy learning math?by /u/ShayIsMissing on March 1, 2021 at 8:07 pm
I have never enjoyed learning math my whole life, I have always hated it and marked it as my least favourite subject because it was so boring to me. People who like learning math, how did you start liking it and how can others do too? submitted by /u/ShayIsMissing [link] [comments]

- What can we learn about the properties of particular infinite series?by /u/UsernameOrang on March 1, 2021 at 7:38 pm
I was wondering if there are ways of showing the type of number a convergent series is. For example, without calculating it, can one show that the sum of the inverses of the perfect squares is a transcendental number? The same stands for series that converge to a number like the square root of 2. Are there ways of showing that series converges to an irrational, but algebraic number, without actually calculating it? submitted by /u/UsernameOrang [link] [comments]

- Nonlinear Dynamicsby /u/OneOfTheSams on March 1, 2021 at 6:58 pm
I’m a senior Mechanical Engineering student with a minor in math, I think I want to do math postgrad. I’m in a course called Nonlinear Dynamics and Chaos right now – it’s freakin awesome I love it. Anyone in industry know where this stuff is heavily applied? Thanks! submitted by /u/OneOfTheSams [link] [comments]

- I’d like to create a visual representation of a percentage…by /u/jwalter007 on March 1, 2021 at 6:53 pm
Did you ever see the thing that shows the map of America and there’s a tiny dot on it somewhere. If I recall it right, the map was all of Earth’s existence and the tiny speck was the thousands of years that mankind existed…something like that. Id like to create something along those lines. It could even be a large colored circle with a tiny dot. The data will be the average number of day of our life (27500) the tiny dot will be 34 days. Anyone know of a calculator that can generate something like that. Or how I would create it accurately. It would be even cooler if it could represent something like my first example did. submitted by /u/jwalter007 [link] [comments]

- Looking for in-depth discussion about size comparison of large numbers/fast growing functionsby /u/FnordDesiato on March 1, 2021 at 6:26 pm
I’m a big fan of all things related to large numbers and fast growing functions. Unfortunately, this field seems to not really exist in serious mathematical debate. There’s the Googology community (including Bowers and others), there’s Harvey Friedman’s work, there’s Ramsey Theory (which is fascinating, but not really “big fish” with regards to the topic), and that’s about it – or is it? My problem with the googology community is that it often is lacking proofs of claims of fast growth rates, mixing up terminology, and a general absence of rigor. On the other hand, Friedman clearly is a professional mathematician, but his focus is on other things to which his large number work is merely a tool, and thus also not covering comparisons beyond basics. So, is there a place I’m missing that is actually dedicating math brain power to rigorous comparisons of large numbers and fast growing functions? Perhaps even literature that goes beyond pop-sci depth coverage? Or a community other than the googology folks (no offense to them!)? submitted by /u/FnordDesiato [link] [comments]

- How to motivate standard deviationby /u/hriely on March 1, 2021 at 6:22 pm
I am in charge of teaching a basic introductory statistics course and I’m reaching out for help with motivating the concept of standard deviation (appropriate for first year undergrads). In particular, motivating its utility as a descriptive statistic, if possible. Motivating the mean isn’t an issue since it’s a concept that most students encounter as far back as elementary school. Standard deviation, on the other hand, while simple to define, has given me trouble answering the inevitable “what’s the point of this” questions. Some explanations I’ve received in my own education, and why I hesitate to deploy them: If we substract all of the data points from the mean, we have an idea of how far from the mean they are. If we average them, we will get zero since the positive and negative contributions will cancel. Indeed, distance should be thought of as a positive quantity, so we square the differences to make them positive, and then take the square root to preserve units. This is probably my least favorite explanation. If our goal it to measure the average distance from the mean, it seems the more natural thing to do would be to compute the average distance from the mean, i.e., the mean absolute difference. And I suspect this is what most beginners would come up with if left to their own to devices to come up with a measure of spread. Mean square error is superior to mean absolute error since it penalizes outliers more. My main objection to this explanation is that there are infinitely many functions that penalize outliers more than the absolute value, e.g. cubic, but also, it requires me to explain what I mean by “penalty,” and why we would want to penalize outliers. I suppose the latter could be used to preview the idea of statistical models, but when explaining descriptive statistics to first years, I wonder if that would take us too far afield and be needlessly complicated. Mean square error is differentiable, and thus amenable to gradient descent. My issues with this point are the same as (2): many other differentiable cost functions, and would require me to get ahead of myself. Standard deviation is “algebraically preferable” to average distance to the mean in the sense that it is easier to state and prove theorems about it. I suspect this is probably close to the best answer, but without some good examples, is vague and hand-wavy. If this is the best answer, what is the most compelling way I could convey this to a beginner? submitted by /u/hriely [link] [comments]

- Anyone cares to suggest the best books about mathematical proofs.by /u/–fk– on March 1, 2021 at 5:58 pm
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- At what level of math can you start to apply math to your own questions/problemsby /u/Hisroyalfreshness62 on March 1, 2021 at 5:44 pm
Hi everyone, I’m an sophomore undergraduate and I’ve taken a Lin alg, Diff eqs, Calc IV but I was wondering at what point can you take what you learn in class and start trying to apply it to questions that you come up with yourself. The analog to this in CS is that you can learn data structures and graph theory in class but you can always go home and write a program that easily incorporates these things and allows you to apply them to your own work. I guess I was wondering if/when this starts to become possible for math. Is there any way to start exploring math on your own without just doing text book problems for example? Thanks! submitted by /u/Hisroyalfreshness62 [link] [comments]

- Book suggestions on dynamical systemsby /u/e—i–MA on March 1, 2021 at 5:18 pm
Hello. I want a book that is written in a most generalized way: I mean its definitions be general and it covers different topics. For example, it should cover different types of stability for continuous and discrete dynamical systems, in particular the discrete ones. Of course, the book shouldn’t be too advanced but it should be general, especially in definitions. Do you know any such book? I have downloaded several books but none of them is exactly what I want. Thanks. submitted by /u/e—i–MA [link] [comments]

- Matching rules for original penrose tilingby /u/Piscesdan on March 1, 2021 at 5:00 pm
Does anyone here have the matching rules for the original penrose tiling(i belive it’s sometimes called p1)? It’s the one with, pentagons, rhombuses, stars and “boats”. The only thing I foound out is that there are three “versions” of the pentagon, depending on the context. I could not find them myself. submitted by /u/Piscesdan [link] [comments]

- What Are You Working On?by /u/inherentlyawesome on March 1, 2021 at 5:00 pm
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: math-related arts and crafts, what you’ve been learning in class, books/papers you’re reading, preparing for a conference, giving a talk. 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 Career & Education Questions thread. submitted by /u/inherentlyawesome [link] [comments]

- CodeParade – Sounds of the Mandelbrot Setby /u/bionicjoey on March 1, 2021 at 3:51 pm
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- Bezout’s identity and continued fraction connectionby /u/benpaulthurston on March 1, 2021 at 2:46 pm
I noticed something playing around with a Bezout’s identity calculator. If we have two numbers such as 333 and 106 and we want to find 333*x + 106*y = gcd(333, 106)=1, there is a standard method using the extended Euclidean algorithm. But I noticed if we write the continued fraction version of 333/106, or 3+1/(7+1/15) or [3; 7, 15]. We can then just remove the deepest layer of the continued fraction so we have 3+1/7 and that is 22/7. And 333*(-7) + 106*22 = 1 is the result of the Bezout’s identity calculation. The pattern seems to be this process will give y/(-x) if there is an odd depth to the truncated continued fraction and (-y)/x for an even depth. I don’t know if this is already well known, I just learned about Bezout’s identity more in depth today from Michael Penn’s video. Or really whether it shouldn’t be surprising at all for some reason, let me know what you think. submitted by /u/benpaulthurston [link] [comments]

- Is expected value broken?by /u/EverySingleDay on March 1, 2021 at 2:44 pm
Say you wake up from a month-long coma. You find $100 in your pocket, and to your left, a stranger is sitting with a coin in his hand. He says that, if you’d like, he’ll flip the coin, and if it’s head, he’ll give you half of what you have, i.e. $50. If it’s tails, you have to give him 40% of what you have, i.e. $40. He correctly asserts that the wager is in your favor, as the expected value is +$10 for you. Would you like to play? You say sure. Then, you hear a good friend sitting to your right cry out “Wait, no! Before you fell into the coma, you played this game twice before! It’s a bad wager!” Who’s right? Is this a good game to play, or a bad one? You’ll notice that, if you play this game multiple times, you are likely to lose money over the long run. Indeed, before the coma, when you played twice, you actually started with $111.11. You then won once and lost once, in no particular order, and ended up with the $100 you are holding now. In fact, for every pair of win and loss, regardless of the order it happens in or whether they happen consecutively or not, your wealth will decrease by 10%. It’s clear that this game is not in your favor to play. Why is the fact that you played prior to the coma relevant to whether the current bet at hand is in your favor or not? If it’s not relevant, then why is it a bad idea to play this game every time you wake up from the coma? submitted by /u/EverySingleDay [link] [comments]

- Mathematicians in industry, do you still learn mathematics for fun at your own free time?by /u/advanced-DnD on March 1, 2021 at 12:11 pm
We all know leaving academia is common. I wonder if one would still get the time to enjoy learning mathematics while working privately for a firm. submitted by /u/advanced-DnD [link] [comments]

- [MathOverflow] Mathematicians using physical experiments for mathematical endsby /u/flexibeast on March 1, 2021 at 10:29 am
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- “Fargues and Scholze have uploaded […] one direction of the local Langlands correspondence” to the arXiv.by /u/PeteOK on March 1, 2021 at 6:42 am
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- Escapism via mathby /u/PaboBormot on March 1, 2021 at 6:36 am
Hope this is appropriate for this sub. So I’ve been having a hard go with my mental health recently. I’m seeing a therapist and doing all the necessary (but maybe not sufficient!) stuff to get better – exercise, self care, sleeping right, etc. But sometimes the pain is too intense and I feel like I just want to not exist for awhile. That said, I have two questions: 1) Can anyone relate to using math as an escape valve? How well does it work for you compared to other escapism tools? 2) What are some good books/topics I could use for this purpose? I’m pretty mentally exhausted so I can’t handle very difficult things at the moment. So ideally it should be relatively easy going but engaging. Just to provide a bit of background, I’m a first year masters student who has taken standard intro graduate courses in analysis, algebra and geometry/topology. I also know a little bit of combinatorics from undergrad. submitted by /u/PaboBormot [link] [comments]

- Math Writer: Rich Text Web Based Math Editor with Markdown, AsciiMath and LaTeXby /u/RentGreat8009 on February 28, 2021 at 9:28 pm
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- What are the two fields of mathematical research which seem unrelated but are deeply connected to each other?by /u/kaecilius_strange on February 28, 2021 at 8:37 pm
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- Where Can I Learn About Cohen’s Forcing Technique?by /u/real_humen on February 28, 2021 at 6:31 pm
Hello All, I am very interested in independence results in math. I know that Cohen used a technique called forcing to prove the continuum hypothesis is independent of ZF, and my understanding is that forcing and some more modern versions including iterative(?) forcing are among the only techniques mathematicians currently know of to prove independence of a given theorem from ZFC. My question is, does anyone know online resources where I can learn about forcing and how Cohen used it to prove the independence of ZF? I have looked on YouTube everywhere and the best I can find are some lectures that give very vague and general idea but don’t walk through any details. I have the original pdf paper of the Cohen proof, but it’s a bit hard to get through completely on my own. Thanks! submitted by /u/real_humen [link] [comments]

- Simple Questionsby /u/inherentlyawesome on February 24, 2021 at 5:00 pm
This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than “what is the answer to this problem?”. For example, here are some kinds of questions that we’d like to see in this thread: Can someone explain the concept of maпifolds to me? What are the applications of Represeпtation Theory? What’s a good starter book for Numerical Aпalysis? What can I do to prepare for college/grad school/getting a job? Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried. submitted by /u/inherentlyawesome [link] [comments]