- Where do you rank blackpenredpen?by /u/Tonlick on August 6, 2021 at 3:54 am
On list of greatest mathematicians of all time. Many in the math community are claiming he is among the best. submitted by /u/Tonlick [link] [comments]

- How many 6mm BB’s can fit in a square inch? (not sure if im right)by /u/JeronPlayz on August 6, 2021 at 2:38 am
I tried doing this. The radius is 0.118 millimeters from what I found. I attempted to use volume. 1^3 = 1 cube volume = 1 square inch sphere volume = (4/3)pi*r&3 equation = (4/3) * pi * 0.1181^3 = 0.00689829 1/ 0.00689829 = 144 Is my math right? I get 144.9311 BB’s per square inch. submitted by /u/JeronPlayz [link] [comments]

- Is the probability of 3 consecutive birthdays the same as 3 random birthdays?by /u/unholyverses on August 6, 2021 at 2:00 am
My siblings and I were all born one day after another (May 5th, 6th, and 7th), albeit years apart. This is usually my go-to “fun fact” whenever I’m forced to share one during icebreakers/first meetings. Today after I shared this during my summer orientation program, another guy interrupted to say that this isn’t that special, and that it’s basically the same odds of my siblings and I having any other random birthday. Would that be true? I’m still thinking that this would be rarer than non-consecutive birthdays, because each birthday would be conditional on the other birthday being a day prior, so the odds of it happening would be much smaller right? Or am I understanding probability completely wrong? submitted by /u/unholyverses [link] [comments]

- Combinatorics books suggestionby /u/account_number_95678 on August 6, 2021 at 1:57 am
I’ve read “A walk through combinatorics” by Miklos Bona and find the exercise problems very interesting. Looking for books which have problems of similar difficulty, if not more. Thanks. submitted by /u/account_number_95678 [link] [comments]

- Quick Appreciation Post to my Professorby /u/sauce4499 on August 6, 2021 at 1:53 am
Towards the end of the Spring semester this year, I mentioned to my Intro to Modern Algebra professor that I was interested in studying mathematics at the graduate level in the future. We talked about it for a bit, and I said that I was trying to read a bunch of new topics, explore what I can, etc. I told him I wanted to know a little about set theory, which made him perk his ears a little bit. He decided to give me some challenge problems regarding some sets and countability, and see if I could figure them out on my own. After a week, I emailed him with some of my solutions to the challenges. Not long after, he sends an email asking to meet through a zoom meeting to talk about them. He agreed with some of my answers, discredited some others, and gave me some more problems to try out. So, we have been doing this every week for three months now… and I can’t say how much fun I’ve had with this! We have touched on set theory, algebraic numbers, linear algebra, and we’re currently playing with straightedge and compass problems(as well as trying to prove that algebraic numbers form a field, but I haven’t shown closure under addition nor multiplication yet so I don’t want any spoilers). This has been a great summer for me because of the time I’ve been able to share with this Dr. math nerd, so thank you very much! submitted by /u/sauce4499 [link] [comments]

- A Strangely Deep Problem about Sequencesby /u/AcademicOverAnalysis on August 6, 2021 at 1:08 am
Hello everyone! If you keep up with the YouTube side of mathematics and education, there are a bunch of contests being conducted right now. I think this is really great for the community, where 3Blue1Brown is asking for anyone to produce “explainers” of one kind or another. This could be a blog post, a video, or any internet creation. The hope is that we see a diversity of new arguments, mathematical discussions, and other content that wouldn’t have been posted if not for this contest. Linked below is a video that goes over a fun little problem from A Hilbert Space Problem Book by Paul Halmos. It’s a simple problem to understand, and the solution to it is surprisingly deep. It allows us to introduce the idea of a Reproducing Kernel Hilbert Space through what are called Generating Functions. The prerequisite for this is primarily a knowledge of power series and some linear algebra. I try to build up what I can in the first few minutes, which lets us get to some more advanced ideas. Ultimately we are talking about a connection between sequences, Hilbert Spaces, generating functions, complex analysis, and the Hardy space. You can find the video here: https://youtu.be/ZT8FrJlhqsY Since 3blue1brown is running his Summer of Mathematical Exposition (SoME1) contest, I thought I’d go with a bit more of an accessible topic this time. That’s also the plan for the future, where I will mix in research, graduate, and undergraduate work into my channel content. As I said before, this one is aimed at someone who has had Calculus 2 and some Linear Algebra. Experience with complex analysis will help, but all we need from there are power series (analytic functions). This is roughly where I got my start studying Reproducing Kernel Hilbert spaces, and functional analysis itself. Where my PhD adviser handed me and my fellow students the book “Banach Spaces of Analytic Functions,” which was all about Hardy spaces. I picked up the book where this came from, “A Hilbert Space Problems Book” shortly thereafter. Both are excellent resources, if you haven’t found them already. Please give it a watch, and let me know what you think! Do you think it’s too far above my target audience? submitted by /u/AcademicOverAnalysis [link] [comments]

- AMC Scores/College Applicationsby /u/ExactDependent8 on August 6, 2021 at 12:42 am
I did well on amc + aime (barely missed USAMO). However, I’ve got very conflicting advice on how helpful this will be for college admissions (people telling me its roughly equivalent to USAMO, others saying its the same as any other AIME qual). What are your opinions on this? My top schools are Yale and Columbia (weird choices for math ik), does anyone know how they consider amc/aime scores? Before anyone mentions it, I know this isn’t completely mathematics based, but I asked a2c and other places and they had no idea (i.e comparing AIME to the math portion of the SAT is pretty inaccurate). submitted by /u/ExactDependent8 [link] [comments]

- If you prove a theorem is true under finite field arithmetic with n elements for all values of n, did you prove it holds true for regular arithmetic? What about modular arithmetic?by /u/Threight on August 5, 2021 at 9:35 pm
This question came to me randomly and I can’t find anything on it from a quick google search. Intuitively I would say yes because if n can be arbitrarily large and the theorem stays true, then it should also be true if “n is infinite” (abuse of terminology) But also I’m sure I’m missing something that has to do with an obscure property of FFA or the repetitive nature of modular arithmetic that doesn’t exist in regular arithmetic. submitted by /u/Threight [link] [comments]

- Is there a direct way of calculating the divisors of n+1 having the divisors of n?by /u/TECHNICALMCPLAYER on August 5, 2021 at 9:16 pm
I post this question here to discuss about methods of computing or approximating the divisors of n+1 knowing the divisors of n. Also, comments about properties of that divisors are welcomed. Please don’t post the well-known method of factorization, as my question isn’t about brute force and that method needs to take a large number of prime number for large numbers. If you have a proof of why is imposible to know these divisors or (if you dare) a proof of why is imposible to determine some properties of them, you are also welcome. submitted by /u/TECHNICALMCPLAYER [link] [comments]

- I could use some advice about ‘jumping back into math’ for collegeby /u/Nintendo64Cartridges on August 5, 2021 at 8:41 pm
I haven’t studied mathematics actively in about 8 years since high school where I studied up to precalculus. I’m considering learning computer science in college, and I’ll need to learn calculus. I’ve found a few ‘Precalc Full Course for Beginner’ videos on YouTube, some being 5-7 hours long. Are these valuable or should I take the Khan Academy route, back up to algebra, and work my way up? I’m rusty but determined. Is there any way to refresh my algebra and precalculus efficiently to be prepared to learn calculus in about 1-3 months? Thank you for reading. All advice is greatly appreciated. Edit: I just wanted to say thank you to everyone for the advice. I’ll be reading all of your comments, and compiling a list to get started on right away. submitted by /u/Nintendo64Cartridges [link] [comments]

- Was majoring in mathematics worthwhile for you?by /u/AidePast on August 5, 2021 at 7:37 pm
As an example: so many mathematics majors end up as programmers & so few people end up in a TT position, why are you not better off majoring in computer science & allocating mathematics to free time? submitted by /u/AidePast [link] [comments]

- The Poincare conjecture is a corollary of row reduction (Yes, really)by /u/DamnShadowbans on August 5, 2021 at 7:13 pm
The topological Poincare conjecture is well known to most topologists. It says that if a compact n-dimensional manifold is homotopy equivalent to the sphere, then it is in fact homeomorphic to the sphere. What many may not know is that the proof is remarkably straight forward. We start with the notion of a handle. Fixing a dimension n, an i-handle is a copy of the space D^i x D^{n-i} and to attach an i-handle to a manifold W with boundary is to find an embedded copy of S^{i-1} x D^{n-i} in the boundary and glue in the i-handle along this (recall, the boundary of D^i x D^{n-i} is S^{i-1} x D^{n-i} union D^i x S^{n-i-1}). For example, if I take a solid 3 ball, I may attach a 1-handle to it to obtain a kettlebell looking object which has boundary the torus. Somewhat difficult theory (work of Milnor together with Kirby-Siebenmann) tells us that any manifold W (with or without boundary) has a handle decomposition, in the sense that we start with a component of the boundary, N, and we may attach handles to N x [0,1] until we end up with something homeomorphic to W. Given such a handle decomposition, it leads to a handlebody chain complex (with a generator for each handle) that computes the homology of W/N. Now let us prove the Poincare conjecture (and I will liberally sprinkle in necessary facts about manipulating handles). Suppose M is a manifold homotopy equivalent to S^n . Then I may remove two disks and by analyzing homology (or some more geometric method if you wish), I conclude that the inclusion of one of the boundary spheres S^{n-1} into M – (D^n union D^n) is a homotopy equivalence. This implies that M – D^n / S^{n-1} has trivial homology. Now take a handle decomposition of M-(D^n union D^n) , its associated handle complex is acyclic and it turns out by applying something called “handle cancellation”, we are able to find a handle decomposition with handles only in dimensions k and k+1 for some k. The acyclicity property of M-D^n=M-(D^n union D^n)/S^n than implies that the map from the k+1 chains to the k chains is an isomorphism. Now here is where it gets cool. By picking some ordering of the handles, we can represent this map as a matrix. There is some standard stuff we can do here. There is a notion of orientation of a handle, and if we change the orientation we will negate a row (or column). We can also permute our ordering of the handles and permute our rows (or columns). A more interesting fact is if our matrix has a 1 in (i,j) and otherwise 0 in the ith row and jth column, then the same handle cancellation implies we have a handle decomposition whose associated matrix just deletes the ith row and jth column (this is a reflection and a generalization of the fact that the 3 ball is a union of two solid tori (i.e. a 3-ball is a 3-ball with a 1-handle attached and then a 2-handle attached). There is another handle trick called handle sliding which takes as input two (oriented) handles of the same dimension, and the effect on the matrix is to add the row corresponding to the first handle to the row corresponding to the second handle. So we have handle operations that allow us to 1) swap rows, 2) negate rows), and 3) add a row to a different row. If you recall from linear algebra class, this is exactly enough to perform row reduction on an invertible integer matrix. So in fact, we can assume our handle decomposition gives rise to a handle complex with only index k and k+1 handles, and the matrix representing the differential is the identity matrix. But of course, the identity matrix is very easy to apply handle cancellation to. In fact, if we apply it enough times we are left with the empty matrix. Hence, there is a handle decomposition of M-(D^n union D^n) (our original manifold minus two disks) which has no handles, i.e. it is S^{n-1} x [0,1] with nothing attached. But this means M-(D^n union D^n) is homeomorphic S^{n-1} x [0,1], so M is homeomorphic to S^{n-1} x[0,1] with a disk glued to either boundary component. However, the latter is more commonly known as S^n , so we conclude that M is homeomorphic to S^n , otherwise known as the topological Poincare conjecture. submitted by /u/DamnShadowbans [link] [comments]

- How important are university grades for a career in academia?by /u/ataket1 on August 5, 2021 at 5:24 pm
I’m studying Bachelor Mathematics at the TU of Munich. I recently got a below average note in an Abstract Algebra course that I loved. I’m pretty bummed out about it. I thought I had understood the concepts quite well, and after reviewing the exam my mistakes were quite obvious to me. So I’d like to ask: How important are grades in contrast to actually understanding the material? I’d appreciate it if you could also provide your own university/grad school experiences regarding this topic 🙂 submitted by /u/ataket1 [link] [comments]

- What’s your favorite integer and why?by /u/5minusone on August 5, 2021 at 5:05 pm
I see the “favorite number” question passed around every now and then, but I’m gonna ask with integers, cause there are a lot of neat little quirks that some have that go unnoticed. Personally, 0 is my all time favorite. There’s just something that’s so satisfying about “n-n=0.” 0, being the numerical manifestation of nothing, is completely neutral, and is the additive identity, being invisible in a sense. Its rules are simple, but is one of mankind’s greatest inventions. I also like 36. It’s triangular, antiprime, and square; what’s not to love? submitted by /u/5minusone [link] [comments]

- Does poor spatial ability impair learning math? How do I improve it?by /u/dudeydudee on August 5, 2021 at 5:03 pm
As I’m studying math and coding, the syntax of equations and logical statements are more or less okay. But when it comes to graphing, visualization, and representations of concepts I get lost. I think I underestimated the importance of these things for learning math. I also have a terrible sense of direction and other poor spatial awareness so it might be my brain lol. What are some tactics for overcoming this deficiency? submitted by /u/dudeydudee [link] [comments]

- Career and Education Questions: August 05, 2021by /u/inherentlyawesome on August 5, 2021 at 4:00 pm
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 subreddits include /r/GradSchool, /r/AskAcademia, /r/Jobs, and /r/CareerGuidance. If you wish to discuss the math you’ve been thinking about, you should post in the most recent What Are You Working On? thread. submitted by /u/inherentlyawesome [link] [comments]

- Is the hexagonal tiling the most efficient tiling if we allow for non-regular tilings?by /u/Rare-Technology-4773 on August 5, 2021 at 3:41 pm
The honeycomb conjecture from this wikipedia article has as a condition that the shapes which make up the tiling are “all of unit area”. If we require them instead to be “on average of unit area” does the optimal tiling change? submitted by /u/Rare-Technology-4773 [link] [comments]

- PhD in numerical analysisby /u/EthanCLEMENT on August 5, 2021 at 1:34 pm
Hi everyone, I am in my last year to complete my master’s degree in machine learning. However, I took a class in numerical analysis last semester and I truly enjoyed it. I am good at math and I can code decently but my math background didn’t go farther than calculus 3 and linear algebra ( I took differential equations too ) and numerical analysis seems to be very math heavy at least to enter the PhD programs. I was curious if it was realistic/ possible to do a PhD in numerical analysis despite my obvious lack of skills in analysis and math at the graduate level in general. submitted by /u/EthanCLEMENT [link] [comments]

- Probability of Coin Flip Subsequencesby /u/rain5 on August 5, 2021 at 11:16 am
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- problem-solving oriented group on Automata, Languages, and Complexityby /u/xTouny on August 5, 2021 at 7:12 am
Hello, This post is an announcement of forming a collaborative group for solving problems related to Automata, Languages, and Complexity, which are usually at an introductory theory of computation undergrad course. The focus is on solving problems not reading for the first time. We hope members share their insights, approaches, and strategies together. Sharing even partial progress is welcomed as others might contribute upon it. As we believe everyone’s time is limited, The group will take a week-based iterative approach for communication, So that you don’t need to check new messages every 5 minutes. This is an excellent chance for members interested in theoretical computer science to form new connections and friendships, Especially that we will be challenging everyone’s skills by tackling non-trivial problems. A seemingly good candidate for the problem set is Du & Ko’s book Problem Solving in Automata, Languages, and Complexity, who authored Theory of Computational Complexity as well. The only requirement is basic mathematical maturity and a familiarity with Sipser’s introduction. Members coming from pure math background are welcomed, but they will be asked to self-study the materials on their own. If you are interested send me a direct message here on reddit. All feedbacks are welcomed. submitted by /u/xTouny [link] [comments]

- Is it too late for me to move to quantum cryptography?by /u/edwardshirohige on August 5, 2021 at 6:24 am
I’m a final year masters student and I’ve started appying for PhDs. I took a crypto course last sem and I really liked it. I’ve been attending a school on quantum crypto and I’m loving it. Is it too late for me now? Most of my summer projects have fortunately been on the mathematical side of Quantum Information Theory. To be specific, I wanted to ask if profs and institutes will take my applications quant crypto PhDs seriously. The issues I see are that I don’t have a strong physics background, only a few basic courses(including one on quantum mechanics.) My CS background is decent at best and my masters thesis is on operator algebras, which is very much unrelated to quantum cryptography as far as I know. (There’s Non Local games that have some applications to QKD and non local games require a fair bit of operator algebras and I fortunately have done a reading project on that. ) My recommendations are also going to be from people working on operator algebras and related fields. What do I do from this point? Any advice? submitted by /u/edwardshirohige [link] [comments]

- Motivation for Topologyby /u/acantholysized on August 5, 2021 at 1:11 am
Perhaps this is the wrong subreddit, so forgive me if it is (and please point me to where I should post this). I am working through Munkres’ Topology (with Mendelson’s Introduction to Topology for reference for point-set topology), with the goal to become familiar with algebraic topology. I’m struggling to move forward, in a somewhat existential manner: what is the motivation for learning algebraic topology? My original interest came from a desire to reason about things visually (geometrically), but using the power of algebraic structures to do so. I came to algebraic topology and was interested in its relation to algebraic geometry (and here I could be completely misunderstanding how the two fields relate). Put another way, my motivation to learn is stemming from wanting to study things “visually” and algebraically, and I fear I may be putting my effort in the wrong direction. I apologize if this is a rambling comment, I will reply to comments that request clarification of my situation. Thank you :). submitted by /u/acantholysized [link] [comments]

- Lecture 1: Gauge Theory for Nonexperts (Timothy Nguyen)by /u/IamTimNguyen on August 4, 2021 at 4:46 pm
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- Quick Questions: August 04, 2021by /u/inherentlyawesome on August 4, 2021 at 4:00 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]

- Australian mathematician discovers applied geometry engraved on 3,700-year-old tablet | Archaeologyby /u/Nunki08 on August 4, 2021 at 3:34 pm
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- I can’t help but be in awe of the level of talent and depth of discussion I see hereby /u/Bruh-I-Cant-Even on August 4, 2021 at 1:41 pm
I did my undergrad in math and, to cut it short, I sucked. I never took an analysis course because I knew I’d fail and the last class I took, (engineering math) I barely scraped by with a passing grade. Still, every time I come to this sub I can’t help but be amazed by the depth of discussion and love for the field so many of y’all have, as well as the sheer talent. Almost everything here goes over my head, but it’s just wonderful to see how enamored by math most mathematicians are–hell, it’s what made me pick the subject in the first place. Y’all really are amazing! submitted by /u/Bruh-I-Cant-Even [link] [comments]

- I’m a chemist. Yesterday in r/chemistry we debated the greatest ever chemist. I put forward Gauss for math. Thoughts? Greatest ever mathematician and reason why.by /u/damolux on August 4, 2021 at 9:48 am
I’ve another slow day so if you want to join in, you’ll be keeping me entertained. Obviously a bit of fun. Yesterday’s debate if you’re interested https://www.reddit.com/r/chemistry/comments/ox5yh7/einsteinnewton_for_physics_darwin_for_bio_gauss/ EDIT: As with yesterday, there are too many posts to keep up with. Great chatting with many of you today. I love these types of debates. If anyone is interested I’ve set up a subreddit to have a few more over the next few days (and other stuff) r/atomstoastronauts submitted by /u/damolux [link] [comments]