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...").

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42
votes
2answers
826 views

Effective Research Notes

Note-taking for research is vital to your success as a mathematician. As I look back at some of my handwritten notes, I realized how poor they were. I had thought to myself, "What happened?" I was ...
8
votes
1answer
573 views

So bad at maths sometimes I feel depressed about it [closed]

I taught myself how to count before I even learnt how to talk or read. Playing with numbers was all I did when I was young. I didn't have anyone to foster that type of passion that I believe I still ...
2
votes
1answer
95 views

Book recommendations for topics leading upto Algebraic geometry

I'm interesting in studying algebraic geometry (specifically either from Shafarevich or Hartshorne). Assuming a high school and basic college math education, what should be the topics and the order ...
3
votes
1answer
48 views

Texts on Coxeter groups

I'm looking for an introductory text on Coxeter groups. It can assume undegraduate knowledge of Algebra (Groups up to and including the Sylow theorems in Fraleigh, elementary knowledge of rings, ...
1
vote
3answers
72 views

Should I start with complex variables before fourier series?

My math professor has said that it would be useful to start with complex analysis before learning fourier series in the signals and systems course(I'm an undergrad EE). Do you agree with that and why ...
6
votes
2answers
76 views

How to improve concentration when beginning to work on a math problem that seems boring?

I am a college student and my current situation is that I have an extremely hard time getting myself to start doing math. I feel like math is 'boring,' but ONLY until I start actually doing it. Once I ...
5
votes
1answer
76 views

Is a thorough study of algorithms useful for a mathematician?

In my university, there is a core course called "basics computer science for mathematicians". The topics covered range from algorithms, to the bases of programming, to theory of computability. The ...
0
votes
1answer
89 views

Dollar weighted return. Formula or definition?

I was learning dollar-weighted return and I was a bit puzzled by the following and I would like to have some advice. I understand that it's basically the internal rate return, but using simple ...
9
votes
3answers
505 views

Instructive examples of elegant, clear, rigorous, terse, but “non-dull” mathematical prose

On the "About" page of the Mathgen project one can read: "More seriously, I think this project says something about the very small and stylized subset of English used in mathematical writing. ...
78
votes
5answers
4k views

“Advice to young mathematicians”

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the ...
43
votes
14answers
3k views

Nobody told me that self teaching could be so damaging…

Even though I've been teaching myself math for a couple of years now I only just started (a month ago) at the university. My experience is rather mixed. For starters, I'd like to mention that I'm 21 ...
3
votes
1answer
305 views

Advice for Math Majors -What to do if you come into college with a lot of college credit? [closed]

In high school I was a good maths student and took AP Calculus BC my freshman year and got a 5 and then took Multivariable Calculus, Linear Algebra, Differential Equations, Introduction to ...
3
votes
2answers
68 views

Simple everyday math

I am looking for a book that contains (instead of crossword puzzles) math problems beginning with simple addition, subtraction, multiplication and division and progresses to more difficult area ...
0
votes
1answer
40 views

How to argu on the interval of real line?

We have the two real intervals [a,b] and [c,d] as shown below, From figure it is very clear that $c\leq a$ and $b \leq d$. I wanted to know what one can give argument on it why is $c \leq a$ and ...
20
votes
2answers
378 views

How can a beginner researcher or Ph.D. student efficiently and effectively learn new concepts while staying motivated?

I hope this question is appropriate for MSE. The situation is that someone is reading a book (e.g. a monograph), possibly helpful in his/her research, and the content is sufficiently extensive or ...
3
votes
1answer
193 views

How to submit a conjecture for review?

I was recently attempting to solve one of the more known, already proved, problems in mathematics when I stumbled across an observation I thought might be worth digging into further. Unfortunately I ...
9
votes
1answer
431 views

Research in algebra.

First of all, I don't know if this is the right place to ask about this. If not, please direct me somewhere I can get more help. I like algebra a lot as a mathematics undergraduate student on his 3rd ...
4
votes
1answer
103 views

I love maths, but my school is limited in its teachings. [closed]

I'm not sure how well this question will be received but, I feel there is no harm in asking. I'm 17 soon to be 18. I was in my applied maths course, but not anymore, not due to difficulty, but I can ...
1
vote
1answer
3k views

James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've ...
6
votes
5answers
395 views

Book recommend for topics of Integrals in multivariable calculus.

I am an average student and have to study following topics on my own for the exam : The measure of a bounded interval in $\mathbb R^n$ , the Riemann integral of a bounded function defined on a ...
1
vote
1answer
133 views

In need of some advice! [closed]

I am doing Mechanical Engineering (2nd year) and it's already becoming clear that I am no more interested in this course.I am very much motivated to study Theoretical Physics and Pure Mathematics(I ...
2
votes
0answers
317 views

Group Theory Research Topics [advice] [closed]

I'm currently a Senior Mathematics student in the US. I'm interested in Abstract Algebra, specifically Group Theory (I've taken a course that dealt entirely with Fields, but I enjoy Groups a bit more) ...
3
votes
1answer
101 views

Self-learning Book recommendation for topics in ring-theory

I failed badly in my Internal examination in ring theory , and at any cost want to improve upon my grades in the final eamination,with a month and a half to go .... I haven't yet covered the below ...
18
votes
5answers
2k views

Bad at computations… but not math?

Very generally, the question I'm trying to ask is: Can someone be a good professional mathematician without being particularly good at (or even being - relatively - bad at) computations? More ...
2
votes
0answers
40 views

How to relate two integration contour?

How one can relate two integration contour? For example if I have an integration contour like $\int_{-a}^{a}f(x)dx$ here let say a=infinity. How I can say that the integral $\int_{2}^{3}f(x)dx$ is a ...
17
votes
4answers
345 views

Value in retracing mathematicians' steps (specifically Galois)?

So I'd like to learn Galois Theory, which I am probably not "qualified" for in an ordinary sense (I've never done abstract algebra, and I'm just now learning linear algebra in my vector calculus ...
2
votes
0answers
110 views

self-study hints

A question to those who took rigirous courses like math 25 (Harvard), MATH 295-396 Michigan and etc Being not able to collectively discuss problem sets from the course, as those who involved in ...
12
votes
5answers
571 views

Algebraic topology in high school?

This winter I am planning on teaching a small seminar (20 lectures 45 minutes each) for high school students. I was was given the freedom to choose the topic of the seminar, but it is supposed to be ...
71
votes
11answers
13k views

Am I just not smart enough? [closed]

When I was doing math, let us say for example, introductory number theory, it seems to take me a lot of time to fully understand a theorem. By understanding, I mean, both intuitively and also ...
0
votes
2answers
61 views

What is the relation between two integrals?

Let us suppose that we have two integrals, $I_1$ and $I_2$ with the same non negative integrand. The integration contour of $I_1$ is a subset of the the integration contour for $I_2$. What can we say ...
1
vote
1answer
116 views

Interesting and not too difficult topics in geometry

I was asked to give a talk to a mixture of undergraduate and graduate students on a topic of my choosing from differential geometry. The students will mostly not be in geometry; however, I believe I ...
1
vote
2answers
80 views

Enlightening ideas and methods that change one's appoach to problems, theorems or mathematics as a whole

I would like to collect a "big-list" of ideas and methods from different areas (although I'm particularly interested in elementary number theory, algebra, calculus, linear algebra, geometry, physics, ...
2
votes
0answers
49 views

My attempt to gather mathematical spaces in a drawing

There are many spaces (Sobolev, inner product spaces, etc.) that I am not using on a daily basis, but have to recall their definition from time to time. So I decided to draw a synthetic scheme of the ...
4
votes
0answers
703 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 ...
2
votes
1answer
124 views

How to conceptualize unintuitive topology?

I found Project Origami: Activities for Exploring Mathematics in my university's library the other day and quickly FUBAR'd (folded-up beyond all recognition) the couple sheets of paper I had with me ...
6
votes
1answer
281 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 ...
12
votes
2answers
2k views

I'm feeling demotivated in my undergraduate course

I was a very good math student in high school. I was in the national level Olympiad team. Now I'm studying at the best college in my country with really good mathematicians. I've all almost all of my ...
9
votes
3answers
341 views

How do you go about formalizing a concept?

I am reading Godel Escher Bach. I love it. In the first few chapters, the author shows what a formal system is and gives examples that eventually lead to a typographical formal system of strings that ...
2
votes
0answers
246 views

A Compact Real Analysis book for a graduate student, who is short of time.

I am a Phd student in Computer Science and I want to focus on Machine Learning, especially on statistical methods. My problem is, I always keep hitting the wall when it comes to studying underlying ...
2
votes
2answers
57 views

Combinations: People want a beer, there are certain kinds of beer, but limited numbers of each kind

Four people go to a pub and each wants to drink a pint of either the lager, ale, or porter. However, there are only 2 pints of lager, 1 ale, and 1 porter available to drink. How many combinations of ...
4
votes
2answers
284 views

How much set theory is necessary for serious logic?

I'm currently studying logic at my university and I have been trying to squeeze in as much set theory on the side as possible. Considering that I am spending quite a lot of time studying set theory ...
8
votes
8answers
5k views

How should I self-study calculus? [duplicate]

So I already took Pre-Calc, and ended up with a B both semesters. I am an incoming senior in high school. My special-ed case manager won't let me take it because she doesn't want to see me panic ...
2
votes
2answers
172 views

Going Back to Grad School After Being Away from Math

I graduated with a degree in Math-Computer Science(dual degree) from a college in the US in 2012, and have been working in the Software industry ever since. From 2012 to mid 2014 I was a software ...
13
votes
5answers
994 views

I need help finding a rigorous precalculus textbook

I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor ...
0
votes
1answer
153 views

Dealing with questions with unknown answers

The vast majority of textbook exercises are worded essentially in the format: This assertion is (true/false). Prove this or find a counterexample. This, of course, is not how mathematics is ...
41
votes
6answers
4k views

What should an amateur do with a proof of an open problem?

Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for ...
1
vote
3answers
180 views

Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
6
votes
4answers
430 views

What sequence should I study these topics in? [closed]

I will shortly list a series of topics that amount to what is essentially the first two years of an undergraduate degree. I'd like to know what is considered best order in which to study these ...
0
votes
3answers
65 views

What are the concepts that I need to understand before studying Fourier Analysis?

Background ( Long Story Short ) : For some reasons, I am taking a class in my university that focus on Fourier Analysis Laplace Transform, and Partial Diffiential Equations Problem : I have done ...
7
votes
1answer
330 views

How much mathematics should a student of mathematical logic know?

I would like to know what areas of mathematic are directly related to mathematical logic, besides the usual courses on model theory, proof theory and computability. If you suggest only one book on ...