Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now

Questions tagged [advice]

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...").

Filter by
Sorted by
Tagged with
51
votes
25answers
6k views

What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus. My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have ...
4
votes
3answers
343 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 ...
157
votes
8answers
10k 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 ...
737
votes
27answers
174k views

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

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 ...
10
votes
6answers
7k 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 ...
138
votes
18answers
17k 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 you've ...
51
votes
4answers
13k 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, ...
12
votes
7answers
18k views

Textbook recommendations for self-studying high school math?

I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of math without devoting too much time? This is a ...
15
votes
2answers
1k views

Is it always possible to create a intuition for abstract algebra theorems?

I am a Ph.D student in computer science, and I work on graph isomorphism. My research work requires some level of mathematics (mostly group theory ). I have done basic level abstract algebra course. I ...
3
votes
1answer
321 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) $\Sigma \frac{a_n}{1+a_n}$ diverges....
0
votes
1answer
360 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 general ...
246
votes
28answers
37k views

Too old to start math [closed]

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 ...
65
votes
2answers
26k views

What is the proper way to study (more advanced) math?

Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think ...
43
votes
7answers
11k 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 ...
53
votes
7answers
17k 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 it....
58
votes
8answers
11k 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? [closed]

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 ...
22
votes
4answers
2k views

What are some good math study methods for a high school sophomore?

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 ...
15
votes
2answers
9k 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, ...
2
votes
3answers
199 views

What is so special about $a*b^{ -1}$ equivalence?

This equivalent is used often in group theory. For example, using this equivalnce you prove Lagranges theroem and also this equivalence gives you the cosets and other things. This equivalence also ...
183
votes
9answers
26k 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 ...
88
votes
9answers
28k views

Learning mathematics as if an absolute beginner? [closed]

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 ...
14
votes
6answers
11k 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 ...
20
votes
7answers
10k views

Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
15
votes
6answers
6k views

What to self-study, after studying AP Calculus BC and finishing Rudin's Principles of Mathematical Analysis?

I am a senior in high school who has taught myself Calculus BC and I got a 5. However, I have taken all the math I can at my school. I also taught myself multi-variable calculus and much of ...
13
votes
2answers
3k views

Learning roadmap for Class Field Theory and more

I consider to study Class Field Theory and Advance Number Theory by my self this next semester. However, there are many books, lecture notes... I would like to choose the most comprehensive book to ...
12
votes
3answers
5k 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 ...
3
votes
2answers
130 views

Literature suggestions: Stochastic Integration; for intuition; for non-mathematicians.

I would like to get a good feeling of stochastic integration in a more intuitive way (to be able to easily explain it to a first year math student or a physicist). Example of what I want to understand ...
8
votes
1answer
397 views

Where to get peer-reviewed before submitting a paper to journal?

As a student where should he first approach for review of his paper, even more so a first one, before submitting to peer reviewed journal? Teachers tend to be busy with school and personal work, ...
4
votes
2answers
1k views

Textbook for Mathematical Logic

I am about to take an undergraduate course in Mathematical logic any textbooks to recommend.Want it to be rigorous and not missing things. I am an Math undergraduate. Got still 2 years for my degree. ...
1
vote
2answers
2k views

A book with simple proof exercises and full answers

I am quite bad at basic proof strategies, and in order to get some practice at this, I'm working through Daniel Solow's How to Read and Do Proofs (third ed.) Unfortunately, I'm having the problem I ...
105
votes
23answers
55k views

Complete course of self-study [closed]

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 ...
60
votes
3answers
9k views

Motivation and methods for self-study [closed]

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 ...
57
votes
12answers
8k 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 ...
33
votes
4answers
2k 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 ...
64
votes
6answers
4k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
19
votes
3answers
43k views

GRE Math Subject Test [closed]

I am studying for GRE Math. I am looking for specific tips. What types of questions usually come up? Does anyone know any tricks (e.g. integration tricks) that might be helpful? Which theorems are ...
44
votes
6answers
6k 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 ...
34
votes
6answers
3k views

Cool mathematics I can show to calculus students.

I am a TA for theoretical linear algebra and calculus course this semester. This is an advanced course for strong freshmen. Every discussion section I am trying to show my students (give them as a ...
29
votes
4answers
4k 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 ...
16
votes
3answers
21k 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 ...
23
votes
0answers
7k views

What are some strong algebraic number theory PhD programs? [closed]

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
32
votes
2answers
2k 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 ...
26
votes
5answers
4k 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 ...
21
votes
4answers
12k views

How to do well on Math Olympiads [closed]

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 ...
36
votes
2answers
5k 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 ...
31
votes
2answers
4k 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 ...
23
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 ...
19
votes
2answers
4k views

Jobs in industry for pure mathematicians [closed]

While I love research and academia and would prefer to continue there, I've found myself in industry and haven't felt it's a good match for my interests. Moreover, I'm constantly frustrated by the ...
17
votes
4answers
2k views

Proofs that involve Tricks

When I am doing a homework problem or self-studying, I can usually do proofs that only require theorems or definitions. But lately I've been trying to read more advanced texts in analysis and algebra ...
6
votes
2answers
1k views

Does set theory help understand machine learning or make new machine learning algorithms?

When I was in a university, I didn't major in math but took some math classes. However, I dropped out of math classes pretty quick. Some person recommended that I learn some ...