- AoPS book recommendationsby /u/SchrodingersCat1234 on December 4, 2021 at 7:20 pm
Hi, this is my first post here. I’m currently in the 11th grade and want to take part in some of the Canadian Maths competitions held by the university of Waterloo, namely the Euclid, Fermat and hypatia. I’ve never been exposed to Olympiad maths before and have heard that the AoPS books are a great place to start. The competitions are in Feb, March and April next year. For anyone who has done these, which books/volumes would you recommend in order to do the best that I possibly can? In general anyways, what are the first few books one should start with? Thank you. submitted by /u/SchrodingersCat1234 [link] [comments]

- What does the term Euclidian geometry refer to?by /u/Slickyiaz on December 4, 2021 at 5:53 pm
I know it’s obviously a variant of geometry discovered by Euclid but what exactly is different about it? submitted by /u/Slickyiaz [link] [comments]

- Smallest number of areas to see all combinationsby /u/Aurelius_boi on December 4, 2021 at 10:56 am
I have a selection of n colours and want to judge which colours work together. I only have limited paint so I want to paint as few shapes as possible and still want to be able to examine all possible combinations. The practical constraint is that each area should have a similar size & shape as otherwise one colour impression might overweight. My current approach is much alike to scribble where I add a square at a time and try to get the biggest decrease of missing combinations. But is there a better way? Is there a structural approach? Are squares the best option? Where can I find info on work which tackles this problem? In my case, n \in [5,14] submitted by /u/Aurelius_boi [link] [comments]

- Was looking through my university’s library for math books and found this interesting book on lattice theory by Lieber. Ive never seen a textbook formatted like this and with cool illustrations. Thought some people here may be intrigued.by /u/RylieTran42069 on December 4, 2021 at 5:48 am
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- Physics book for a Mathematician?by /u/Son_Brohan on December 4, 2021 at 1:23 am
In particular I’d like a book that uses an axiomatic system to retrieve the theory of Newtonian mechanics onward. I have no physical intuition so I’d prefer something that starts from first principles. After some googling I can’t seem to find any such reference and generally it seems like physicists have an aversion to axiomatic systems. Would appreciate any recommendations! submitted by /u/Son_Brohan [link] [comments]

- Is there a concept dual to that of universal cover?by /u/samtenka on December 4, 2021 at 12:12 am
Given a based topological space X, we can construct a based universal cover X’ whose points are pairs (x, p) where p is a homotopy class of paths from the base point to x. We have f : X’ –> X, the projection to the first coordinate. When X is path connected and sufficiently nice, X’ is path connected and f is a based covering map. Moreover, f is initial among based covering maps of X by path connected spaces. Is there a concept dual to this one in the sense that homotopy groups (whose elements are homotopy classes of based maps from spheres) are dual to cohomology groups (whose elements are homotopy classes of based maps to eilenberg maclane spaces)? For example, just as we have a good fibration X’–>X that kills first homotopy and preserves higher homotopy, do we also have a good cofibration X–>X” that kills first cohomology and preserves higher cohomology? By “good” I mean any of several things: defined canonically / characterized by a universal property / related manifestly to the universal cover / useful for computation / visually interesting / etc submitted by /u/samtenka [link] [comments]

- How do you professional mathematicians work 8 hours in a day? My brain is often spent after 4 hours, if not less.by /u/sam1oq on December 3, 2021 at 11:19 pm
When I’m working on math problems, be it reading or doing exercises, my brain power tends to evaporate after 4 or so hours. So I always wonder, do you professional mathematicians spend 8 hours a day doing focused thinking about extremely difficult problems? And if not, what do you do in the remaining time? I’ve been doing math for a couple of years now but I’ve never been able to go at it for the entire day and so this always bugged me. It seems too intense to do for an entire day but maybe I’m missing something? submitted by /u/sam1oq [link] [comments]

- Philosopher Wins Over €1 Million Grant for Project on Mathematical Knowledgeby /u/ninguem on December 3, 2021 at 10:11 pm
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- Minimal amount of abstract algebra required for category theory?by /u/RaygekFox on December 3, 2021 at 9:57 pm
I dived into category theory recently(reading Basic Category Theory by Leisner), although I don’t have a strong background in abstract algebra. I learned some basic group theory on my own and I only know the definitions of the rest of important structures. I understand some of the examples from the book on categories, mostly about groups/monoids, but I think I don’t really understand the ones involving more complicated structures well enough. My question is whether my approach is fine considering that I learn CT just out of interest, or I will miss really a lot without further knowledge in algebra? If I need algebra, is there any “crash course”, containing just enough information for understanding examples from CT, missing some details which are usually covered in standard algebra courses? submitted by /u/RaygekFox [link] [comments]

- Rudin vs Pughby /u/MathematicianWannabe on December 3, 2021 at 8:15 pm
I would like to venture into functional analysis. It’s been a while since I’ve done any actual analysis and the highest I got was taking a graduate course in measure theory which I found quite difficult but very interesting. I thought it would be best to start by going through an introductory analysis text to strengthen any weak links (which admittedly I never had a good grasp on in the first place) and do more problem. From there I will probably revisit measure theory and then finally move onto functional analysis. I want to do all this properly to really understand what is going on. Given my background I would like a book that’s not written as a first pass in analysis. I’ve done some searching and I’ve narrowed my search down to two texts: Baby Rudin and Pugh. The former needs no introduction, though I always find it too terse for self teaching. I’ve heard great things about Pugh but there is not much information out there on it. Can anyone stack these two books up against each other in the context of self teaching, or maybe even recommend another text? Is there anything in one that is not in the other? Glancing through Pugh’s table of contents he seems to spend a less time on sequences and continuity than Rudin. Thanks! submitted by /u/MathematicianWannabe [link] [comments]

- Suggestions for a good/easy to understand introductory book on Functional/Delay Differential Equations?by /u/the_silverwastes on December 3, 2021 at 6:54 pm
Hello! I’m currently an undergrad and have taken intro courses in ODE’s and PDE’s, and am currently working on a project where I’m going to be using DDE’s. However, I’ve honestly never studied them before in any class. I’ve been looking for YouTube lectures/tutorials, but I couldn’t find much that was useful, and I’ve seen suggestions for books, but I want to look for something that’s easy to initially understand, and explains stuff well. Particularly, I want to look into finding solutions for linear and non-linear DDE’s. I’ve seen An Introduction to Delay Differential Equations with Applications to the Life Sciences mentioned in a lot of places, along with Delay Differential Equations: With Applications in Population Dynamics, so I’ve downloaded them, but I’m not sure which one to start with. Could someone let me know which one of these, or any other books are good intro textbooks that could be understood by an undergrad student? Also, as a side question, is there any other particular area/field of math that I should study well in order to understand the theory behind DDE’s better? (Or generally for PDE’s as well)? I’d really appreciate if anyone could let me know! Thanks! submitted by /u/the_silverwastes [link] [comments]

- This Week I Learned: December 03, 2021by /u/inherentlyawesome on December 3, 2021 at 5:00 pm
This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn! submitted by /u/inherentlyawesome [link] [comments]

- Is it ok, to be bad at some parts of Mathematics?by /u/tonystark36 on December 3, 2021 at 4:15 pm
I am really interested in Mathematics recently, but only in Number theory and not in other parts like Geometry. I love number theory but am terrible at Geometry, is it ok to be like that, or should I do something about it? submitted by /u/tonystark36 [link] [comments]

- Statistical modeling vs Mathematical modelingby /u/Normal_Flan_1269 on December 3, 2021 at 3:23 pm
As a statistics major, a lot of the classes I take revolve around “statistical modeling” ie. Linear models, statistical learning, time series, etc. how to fit models to data. Aside from statistics classes a lot of my mathematical classes have been great for building up the rigorous foundation to see the mechanics behind statistics. In a lot of my math classes, such as differential equations for example, I hear a lot about “mathematical modeling”. A lot of use statistical modeling/math modeling as interchangeable, but I feel there has to be some kind of difference between them. Is there really any difference between the goal of statistical models, and mathematical models? In terms of how they look to solve a problem, and what conclusions they come up with? What would you say is the differentiation between statistical modeling methods and mathematical modeling methods? submitted by /u/Normal_Flan_1269 [link] [comments]

- math interested teens hmu!by /u/legendarytacoblast on December 3, 2021 at 8:23 am
hey everyone! i’m a 15 year old girl in high school, and passionate about math. i love 3blue1brown, richard borcherds, zach star, and flammablemaths. i do a lot of self study (currently learning the ropes of abstract algebra) but don’t really know anyone irl who pursues the same interests! if any of y’all high school kids do, pm me. i’d love to chat, share experiences/ideas. that’s all 🙂 btw if this post should be redirected elsewhere, pls lmk submitted by /u/legendarytacoblast [link] [comments]

- The Structure Theorem for Modules over PIDs is one of the coolest things ever.by /u/kapoorkhanna on December 3, 2021 at 4:57 am
When you read the theorem in an Abstract Algebra class on its own, it doesn’t really sink in very well. But when you apply it into Linear Algebra for the Canonical Forms, that’s when it hits perfectly. I love Linear Algebra a lot and even took a summer break after my second year of undergrad just to read Linear Algebra at home. There are multiple ways of arriving at the Jordan and Rational Canonical Forms, as several textbooks would highlight. But the Structure Theorem technique is like one of the slickest and neatest ways of getting to the forms. What I like most about it is how it relates the Minimal and Characteristic Polynomials of the matrix. The Structure Theorem is probably the easiest way to prove that the two are equal if and only if the matrix is cyclic. submitted by /u/kapoorkhanna [link] [comments]

- Did any famous mathematicians write books on apportionment?by /u/iamablackbeltman on December 3, 2021 at 3:35 am
After seeing Matt Parker’s recent video on apportionment (https://youtu.be/GVhFBujPlVo), I’ve become fascinated with the subject and would like to read more. Though, I can’t find any books delving deeply into the mathematics of the subject. Have I missed something? Is there a well-respected book I can buy to read more on the subject? submitted by /u/iamablackbeltman [link] [comments]

- What do you do when you can’t solve a problem?by /u/BetterThanYou8 on December 2, 2021 at 11:28 pm
I spent about 6 hours today looking at a problem I wanted to solve. I couldn’t solve it. I read many textbooks and looked at their examples and problems with solutions but none seemed applicable to the question I had been set. What do you do when faced with a similar scenario? submitted by /u/BetterThanYou8 [link] [comments]

- There’s an ongoing effort to rewrite Principia Mathematica using Coqby /u/a_critical_inspector on December 2, 2021 at 11:07 pm
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- How much Algebra does Algebraic Topology usually employ?by /u/VaultBaby on December 2, 2021 at 9:37 pm
Hi! I am currently having my second course on Algebraic Topology and it seems that the further we delve into the topic, the more algebraic it gets. I actually quite enjoy Algebra, so I have no problem with it, but I’ve been wondering, what would you say is the actual algebra/topology ratio that the branch has? submitted by /u/VaultBaby [link] [comments]

- UPenn completely scammed everyone in math last yearby /u/RageA333 on December 2, 2021 at 7:07 pm
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- Has the phrase “we see that…” ever made you feel dumb?by /u/juniorchemist on December 2, 2021 at 6:24 pm
I seem to find variations of this in every math/STEM text: “we see that…” “it’s trivial to prove that…” (often followed by the author skipping steps for “brevity”) and sometimes I want to shout that no, I don’t really “see,” and it isn’t “trivial” to me. I feel so stupid when that happens. Has that ever happened to you? submitted by /u/juniorchemist [link] [comments]

- Is this just me?by /u/Atlasman123 on December 2, 2021 at 6:16 pm
Is this just me? I realized that when I was in school I started to like math only when it got harder? To explain, when I was in school and they made us memorize our multiplication facts or simple formulas I hated math with a passion. Only when I started algebra and calculus did I start to love math. I think I changed my mind because it became a puzzle-game rather than a list I had to memorize. I have so much fun trying to solve difficult problems because solving them was so satisfying. I also believe that my ADHD may have had an influence on the way I perceive doing math, so that may be a possible explanation. Thoughts? submitted by /u/Atlasman123 [link] [comments]

- Career and Education Questions: December 02, 2021by /u/inherentlyawesome on December 2, 2021 at 5:00 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]

- What qualities would make one cut out to actually continue working on being a mathematician?by /u/megahypochondriac on December 2, 2021 at 2:27 pm
I kind of want to know this generally, but also because I’m starting to feel like I’m probably just not smart enough for it anymore. I’m so far into my math degree that while I do well in, and understand my higher level classes, I literally can not remember anything from my calculus classes. Especially when it’s needed for other stuff. At this point, I have to Google integrals and derivatives, and I can’t remember any major theorems either. And honestly it’s just starting to make me feel really really dumb. I guess my biggest issue is how I can’t remember most important things on spot, which is also why I always mess up exams but do really well on assignments and stuff. I’m honestly just thinking of not even trying for grad school because I doubt I’ll be able to pass the qualifying exams for anything either. But yeah, that’s that. Back to the main question. (And I’m really really sorry if it’s kind of stupid but :/). What qualities should a good mathematician have? And also, just how important is having an amazing memory 😩 submitted by /u/megahypochondriac [link] [comments]

- Do you think Computer Science a branch of Mathematics?by /u/Captainsnake04 on December 2, 2021 at 2:15 am
This is a question that, at least to me, always seemed to generate an unexpectedly large amount of disagreement. Personally, I always saw the “science” in the name as a misnomer, and I see it as mathematics. But whenever the topic is brought up, a lot of people disagree with it. I think it’s a field of math because, unlike in the sciences, we don’t put much emphasis on experiments in computer science. Furthermore, the birth of computer science came from the field of formal logic, which is definitely math. At first, the topic came up at the dinner table, and our family was split 50-50. My brother and I both arguing that it was mathematics, and our parents arguing that it was science. This led me to think it was just an issue with familiarity, since my brother and I are both moderately experienced coders and both know more math than our parents. However, when the topic was brought up during a meet of my school’s math team, there was still a lot of disagreement, so I don’t think someone’s viewpoint just comes down to familiarity. Do you think computer science is a science, or a branch of mathematics, or something else entirely? submitted by /u/Captainsnake04 [link] [comments]

- Quick Questions: December 01, 2021by /u/inherentlyawesome on December 1, 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]