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Questions asking for advice on various mathematical matters. Be careful that your question is answerable, and also that it is not a polling question (e.g. "What is the best / your favorite way to...").

97 questions with no upvoted or accepted answers
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666 views

Balancing Coursework with original research

I am a first-year graduate student in a US university pursuing a PhD in mathematics. I am a bit frustrated in trying to balance coursework with original research. I saw students who spend most of ...
122 views

Strategy for self-studying after M.S.

For someone who has finished their M.S. degree in pure mathematics, what is a good way to keep learning mathematics within your specialization? Would you suggest reading research articles from ...
232 views

A discontinuous function $f: X \rightarrow Y$ satisfying: for each closed ball $B$ of $Y, f^{-1}(B)$ is closed in $X$

Find a function $f: X \rightarrow Y$ between metric spaces $X$ and $Y$ that is not continuous but has the property that for each closed ball $B$ of $Y, f^{-1}(B)$ is closed in $X$ Solution Attempt: ...
823 views

Classical geometry vs. p-adic geometry

I am interested in learning more about $p$-adic analysis and some of the geometric theories that are commonly used. However, it seems that many of the tools there are developed from analogous "...
642 views

How important is the “prestige” of your university for undergraduate mathematics?

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and didn'...
1k views

Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
549 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-module and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, and A Primer of Algebraic D-Modules ...
93 views

Elementary Differential Geometry before Manifolds?

Many courses called Differential Geometry (at least in Germany; at least as far as I know!) solely deal with manifolds and not classical/elementary Differential Geometry (curves, curvature, ...
2k views

How to Read Michael Artin's Algebra

I am currently reading Algebra by Michael Artin (for self study). I'm finding the book pretty interesting, but I'm still not sure how I should study the book. For example, should I try to prove every ...
644 views

Isolation and self-study

A little background: I am currently a sophomore (studying mathematics) at an unknown university in the Middle East. My mother is European so it does not make sense to study mathematics in the Middle ...
122 views

Is there a proper etiquette for asking an author for their (mathematical) software?

This may not be the correct place to ask such a question. I have read a mathematical paper on multiclass total variation clustering. I wish to use the algorithm in the contents to compare with another ...
1k views

which branch of maths studies Standard Logical Matrices

In classical logic you have truthtables like: & | T | F ---|---|--- T | T | F F | F | F In many valued logic you have tables like: (this one is ...
132 views

A partial ordering on textbooks

After college, it has been very difficult to continue learning math as a hobby, I have the time for it, but I get incredibly frustrated when I run into something that it feels like I will never ever ...
1k views

Topic appropriate for undergraduate research program

This may be not appropriate to ask this kind of question here. But please feel freely helping me. In our Maths faculty, there is not a program like Undergraduate Research Program(URP), however, the ...
73 views

I am in my last year math undergrad. I am taking theoretical statistics and a dynamic modeling course, and I need 2 more courses after these. While I received As in everything I did at a community ...
94 views

How do you stay focused in advanced (pure) mathematics lectures?

Throughout my entire university career, I've found it incredibly difficult to focus during lectures, so much so that I at one point stopped going because I found it easier to just learn it on my own. ...
71 views

Good source of measure / integration computation problems to build intuition?

I have taken course in measure theory based from Royden's "Real Analysis" last year and now am reviewing the subject using Folland. However, neither book seems to have many "computational" problems. ...
271 views

Can random function of a random variable provide unbounded probability ratio function?

I have an interesting problem which arises from hypothesis testing. Basically, we have a random variable $X$, which follows a continuous distribution $P_0$ under the hypothesis $H_0$ and follows ...
294 views

Concrete Mathematics: Not taught how to solve problems.

I've read and studied the first 3 paragraphs from Concrete Mathematics and now I've made the first couple of problems. When I got to the actual homework problems I was lost because I tried to solve ...
644 views

Literature on Chern-Weil Theory and the Chern-Gauß-Bonnet Theorem

At my university there are plans for a graduate seminar on Chern-Weil Theory and Chern's generalisation of the Gauß-Bonnet Theorem. Unfortunately I am having a though time in finding adequate and ...
491 views

start studying advanced topics in number theory

I am a first year undergrad and have had elementary course in Number Theory which includes only basic introductory topics like: divisibility,gcd-lcm,primes,congruences, number theoretic functions etc. ...
144 views

What is the most relavant math for statistics students?

As they say "the more math you learn the better". Unfortunately, I did not have a lot of mathematical training in my undergraduate. Now I am doing a master in mathematics, mainly to make up some ...
178 views

(Soft question) How to study for a proof-based math class?

I'm an undergrad at a top US university and I'm currently taking an Introduction to Analysis class. I really really enjoy this class and it's actually getting me more interested in math in general. I ...
157 views

Algebraic Number Theory and Euler's constant

After studying Herstein's books for Algebra (undergraduate and graduate) alongside some books in Analytic Number Theory, I decided to study Algebraic Number Theory as well. I read a recommendation on ...
94 views

Is there active research on topological groups?

So I came across something called "Topological Groups". I have just taken a course on topology/and some basic algebraic topology which i really liked. My mind was blown. I said topological groups are ...
109 views

Standard and/or advanced curriculum preparing for a grad school in Applied Math

I was wondering what would be a list of Applied Math courses (sort of like a road-map for an Applied Math student interested in a Applied Math PhD) which preferably contains absolutely essential ...
62 views

Study guide on calculus

I have studied calculus until line integrals and double integrals,and I think i quite understand the ideas and concepts, but im afraid i haven't done as much excercises as i desired , and it has ...
633 views

Applications of Probability Theory to Coding/Cryptography Theory

I'm looking to do a PhD in probability, with my project(s) having applications to for example the following (non-exhaustive). Coding theory: eg algorithms for sending data quickly which can be ...
130 views

Efficient way to rigorously learn AI prerequisites

Question: My formal goal is to be able to rigorously understand the mathematical basis for modern statistical learning methods (ML, deep learning). I am told by math people that this involves: linear ...
420 views

GRE Math Resources

I am planning to give the MATH GRE. I intend to go to physics graduate schools but I may have to given the MATH GRE according to my college's requirement. I very much like maths, but I'm overloaded ...
38 views

Looking for references for learning the words and sentences used in proofs

I'm familiar with textbooks on logic, proof techniques, and sets. But I have yet to encounter a textbook that dives into the language used w/ definitions and sentence structure used in proofs, for ...
74 views

Information requested regarding variant square brackets

This is a usage question that may or may not be relevant to mathematics. However, as the representative to the Unicode Technical Committee for the STIX project [*], which involved adding mathematical ...
127 views

Book Suggestion, Analysis (Multivariable Calculus)

I am doing my 4th Analysis course. Now we are doing functions from $\mathbb{R}^{n}$ to $\mathbb{R}^{m}$ And we are talking about differentiabiity . I have a lot of problems understanding the course ...
823 views

Quality of Videos Lectures and Lectures vs Textbooks

I am a student trying to learn different subjects by watching video lectures and reading on my own time. I was wondering if the lectures from ICTP and nptelhrd are a great use of my time. I tried ICTP ...
855 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis -...
60 views

What should one do if one works on a problem and submits a paper only to find that it is already in some book?

What should one do if one works on a problem and submits a paper only to find from the editor, that the work is already in some book? The work is is not really easy to find on the internet and was ...
169 views

My first simple direct proof (very simple theorem on real numbers). Please mark/grade.

What do you think about my first simple direct proof? What mark/grade would you give me? Besides, I am curious about whether you like the style. Theorem Let $I = [a,b]$ be a non-empty closed ...
1k views

Bachelor Thesis - Galois Theory Research Topics?

I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was ...
659 views

Can I research in complex analysis, PDE and differential geometry without exposure to mathematical physics?

I love mathematics, but physics is far away from my interest. I see that recent mathematics research is strongly connected to mathematical physics which is something doesn't interest me! I love ...
68 views

Is it worth it to understand why math works, even in college? Or because of the pace should I just stick to memorizing steps and formulas.

I will be taking a college pre-calc math class soon and I was wondering if it is worth to try to understand math or just memorize formulas. You know, all the "Why does this work?" questions and math ...
47 views

Research topic- Evolutionary Graph Theory

I read Evolutionary Dynamics by Martin A. Nowak and became fascinated with evolutionary graph theory. I'm mentoring an undergraduate student in the subject and would like to give him a research ...
58 views

Career Advice: Where to apply Analysis in Industry?

$\textbf{Background:}$ I am a fourth-year undergraduate at a major university in the US, and I will be staying for a fifth year before proceeding to pursue a masters degree. I have taken courses in ...
69 views

Bachelor thesis in mathematical physics.

After 3 years of study of mathematics and physics, I wish to write my bachelor thesis, starting in September, on a mathematical physics subject. I have prior mathematical knowledge of differential ...
426 views

Suggestions for a reading list in Statistics and intro to machine learning

I have built a reading list based on recommendations and suggestions found on several posts from this community. My intention is to use this reading list to acquire a good understanding about ...
42 views

Confusing regarding final year modules

My university has released the modules that I am available to take next year in my final year of undergrad. A PDF was also provided grouping the modules into their respective mathematical topics. I'...
390 views

Study order of Fourier Analysis, Functional Analysis and Operator Theory?

I hope my question is in the scope of MSE. I want to study 1- Fourier Analysis, 2- Functional Analysis and 3- Operator Theory, all from scratch. Which one I need to study first? second? and third? ...
162 views

ENS Paris preparation

Good morning everyone, I'm a french student who wants to pass the contest of ENS Ulm I need specific problems and exercises, I hope someone would help me here... I know there are many french student ...
101 views

Need for a Analysis Book with the following requisites

I am a maths graduate .I have to appear for an entrance exam which has in its syllabus the following. Background: I have Read Analysis from Bartle Sherbert and Understanding Analysis:Abbott. ...
I got stuck on this syllabus about abstract algebra: Let $J$ be a set and $\{ \pi_J \ : \ j \in J\}$ be a collection of profinite groups. Show that $\prod_{j \in J} \pi_j$ is again profinite. ...