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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420
votes
26answers
91k views

How to study math to really understand it and have a healthy lifestyle with free time?

Here's my problem. I'm studying math and when I really work hard, I think I understand things very good, but that comes at a big cost: in the last few years, I've had practically zero physical ...
183
votes
28answers
23k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
4
votes
3answers
286 views

I need some advice for $ \; “ \; 3xy+y-6x-2=0 \;”\, $

PS: I edited the title again and I think, it's better now... :) Actually, almost the whole solving way is wrong but, I understood why... :D :) You can check that or add some more useful links about ...
31
votes
4answers
5k views

Learning Roadmap for Algebraic Topology

I am now considering about studying algebraic topology. There are a lot of books about it, and I want to choose the most comprehensive book among them. I have a solid background in Abstract Algebra, ...
7
votes
6answers
2k views

Which topics of mathematics should I study? [closed]

I'm a first year econometrics student with a great interest in mathematics. I very much enjoy my study, but still I am interested to learn about more topics in mathematics which are not part of my ...
109
votes
9answers
11k views

How do I sell out with abstract algebra?

My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...
103
votes
18answers
10k views

How do you describe your mathematical research in layman's terms?

"You do research in mathematics! Can you explain your research to me?" If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure ...
74
votes
5answers
3k 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
3answers
5k views

Motivation and methods for self-study [on hold]

First, a little background: Beginning with calculus in my first semester of college, I fell in love with mathematics. That was the point at which the concepts became interesting to me, and I started ...
77
votes
8answers
23k views

Learning mathematics as if an absolute beginner?

I dread mathematics, and I believe it's because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the ...
33
votes
7answers
4k views

What are some good math specific study habits?

What are/ were some of your good mathematician's study habits that you found really worked for you? I'm a CS major at a respected school and have a solid GPA... However, I definitely lack when it ...
11
votes
6answers
8k views

In what order should the following areas of mathematics be learned?

I am in a biological field (medicine) but I have genuine passion for mathematics. I want to learn it on my own , in my spare time. Mathematics , as I gather, is learned best when you have grasped ...
17
votes
4answers
1k views

Grasping mathematics

First, I'm not trying to make this sound like a "poor-me" story. I understand fully that every decision I've made leading to this is my fault. I am genuinely looking for advice. So, I am a high ...
6
votes
4answers
9k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
2
votes
1answer
178 views

Rudin: Problem Chp3.11 and need advice.

I am working on the following problems and I have a couple of questions. Suppose $a_n>0, s_n = \sum_{i = 1}^{n}$ and $\Sigma a_n$ diverges. RTP (a) $\Sigma \frac{a_n}{1+a_n}$ ...
8
votes
2answers
3k views

Rudin against Pugh for Textbook for First Course in Real Analysis

So as I have said before in a previous question, I am taking a first course in Mathematical Analysis, and I'm quite excited. I just found out though that unlike the other professors at my university, ...
0
votes
1answer
85 views

Linear Congruence Theorem - Are these solutions too? Where'd they hail from?

(1) Can't the signs - I colored them in red - of x and y be switched? Aren't $x = x_0 - bn/d$ and $y = y_0 + an/d$ also solutions? They satisfy $ax + by = c$? (2) How can I remember these ...
77
votes
23answers
23k views

Complete course of self-study

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
160
votes
14answers
10k views

Identification of a quadrilateral as a trapezoid, rectangle, or square

Yesterday I was tutoring a student, and the following question arose (number 76): My student believed the answer to be J: square. I reasoned with her that the information given only allows us to ...
46
votes
12answers
4k views

I almost quit self-studying mathematics, but should I continue?

Before I move on to the main idea of this post, I need to tell you some background information about myself. Hopefully, it proves useful for you in giving me advice. I'm a 16 year old high school ...
41
votes
8answers
5k views

How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards?

I'm a computer science student who is a maths hobbyist. I'm convinced that I've proven a major conjecture. The problem lies in that I've never published anything before and am not a mathematician by ...
13
votes
6answers
4k views

Advice for Self-Study

I am a senior in high school who has taught myself through Calculus BC and I got a 5 on the exam. However, I have taken all the math I can at my school. I have also taught myself multi-variable ...
11
votes
3answers
9k views

I want to start mathematics from scratch. What should I begin with?

I've just finished high school but I don't feel my knowledge of mathematics is good enough. I'd like to start again from scratch, possibly adding a bit (a lot) of problem solving to it. What is the ...
8
votes
3answers
685 views

Which of these courses to take if one intends to go to grad school in pure math (rank please)

could you rank these classes in terms of necessity to take if I intend to pursue a Ph.D in pure math? I don't know if I can fit everything, but I want to make sure I take the most important ones: ...
66
votes
7answers
7k views

What made you choose your research field?

I was wondering how come modern mathematicians do not seem to discover as many theorems as the older mathematicians seem to have done. Have we reached some kind of saturation limit where all commonly ...
66
votes
11answers
12k 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 ...
26
votes
5answers
4k views

Math GRE Subject Exam [closed]

I am studying for the GRE Mathematics subject exam [1]. I am looking for tips regarding how to more effectively study for it. Does anyone know of any good study materials or have any tips in general? ...
35
votes
7answers
4k views

Should I be worried that I am doing well in analysis and not well in algebra? [closed]

I attend a mostly liberal arts focused university, in which I was able to test out of an "Introduction to Proofs" class and directly into "Advanced Calculus 1" (Introductory Analysis I) and I loved ...
28
votes
4answers
1k views

Understanding mathematics imprecisely

For a long time, it has been a complete mystery to me how any of my peers understood any math at all with anything short of filling in every detail, being careful about every set theoretic detail down ...
33
votes
10answers
3k views

Becoming Better at Math

How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up. EDIT: Could anyone suggest books for someone with a math education that just ...
23
votes
3answers
1k views

How much time is too much (to put into a single problem)?

As a self-studier, I have no due dates and no time pressure. This is partly a good thing since I do have a life outside of my pursuit of mathematics. However, the lack of pressure is also a bad ...
20
votes
4answers
1k views

Perspectives on Riemann Surfaces

So, I have come to a somewhat impasse concerning my class selection for next term, and I have exhausted all the 'biased' sources. So, I was wondering if anyone in this fantastic mathematical community ...
24
votes
2answers
1k views

Efficient ways to read and learn a new topic [closed]

I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material ...
21
votes
6answers
1k views

What am I losing if I decide to perform all math by computer?

I solve mathematical problems every day, some by hand and some with the computer. I wonder: What will I lose if I start doing the mathematical problems only by computer? I've read this text and the ...
15
votes
5answers
1k 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 ...
11
votes
3answers
2k views

Is Foundational Research a Dead Field?

I'm a second year mathematics major at a pretty good school. Ever since I became a math major I have been most interested in set theory and logic, which I guess can be lumped into the category of ...
11
votes
4answers
4k views

How to do well on Math Olympiads

I'm a high school student who really likes maths and I'm quite good at school. I want to start training maths by myself but I think I need some guidelines. I want to do well on IMO but I don't know ...
7
votes
2answers
482 views

What is the best approach when things seem hopeless?

I'm finding that I am getting to the point of being hopelessly behind in one of my courses. What is the best thing to do when it feels impossible to get caught up in the literal sense. Being "caught ...
12
votes
5answers
454 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 ...
11
votes
4answers
2k views

Topics on Number theory for undergraduate to do a project

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
8
votes
4answers
4k views

Advanced Linear Algebra courses in graduate schools

After studying general a linear algebra course, how would an advanced linear algebra course differ from the general course? And would an advanced linear algebra course be taught in graduate schools? ...
5
votes
7answers
1k views

What should I learn next for pure math?

I can do basic single variable calculus which is essentially all you do at A Level in the UK. I also just read "What is mathematics?" by Richard Courant which I found very good. I would like to know ...
19
votes
2answers
2k views

Spotting crankery

Underwood Dudley published a book called mathematical cranks that talks about faux proofs throughout history. While it seems to be mostly for entertainment than anything else, I feel it has become ...
16
votes
1answer
1k views

Strategies and Tips: What to do when stuck on math?

Since math students will be stuck on some math at some point, what strategies or tips can help (to assuage this recurrent reality of maths)? Certainly, this wonderful website helps; here: one can ...
6
votes
4answers
1k views

Self-learning Mathematics

My question is very elementary, but I hope that you will endure it. I am currently in a CS Master's program and I notice that my skills in mathematics are lacking. My calculus course was 10 years ...
5
votes
4answers
363 views

What sequence should I study these topics in?

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 ...
3
votes
2answers
2k views

What makes Probability so difficult to get it right in the first place? [closed]

I took two classes of Probability, I did very well and was confident on the subject. Now I meet it again in my Combinatorial Algorithm course, and guess what? I feel completely blank again! I have to ...
13
votes
2answers
932 views

Studying mathematics efficiently

I am particularly angry at myself for the last few days. I noticed how inefficiently I work. Here is the general scenario: I decided to study abstract algebra and analysis some days back. I tried ...
11
votes
0answers
611 views

Prerequisite of Projective Geometry for Algebraic Geometry

I studied Euclidean Geometry in high-school, and I have not studied anything relates to geometry since I started studying in university. I am now intending to study Algebraic Geometry, however, I ...
10
votes
0answers
317 views

Big geometry grad schools - for an average applicant [closed]

What are some schools that have a lot of geometry going on, but that might accept some middle-of-the-range applicants? Let me add some context... I left grad school (UC Davis) with an MS in 2012 ...