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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0
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1answer
2k 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 ...
5
votes
5answers
325 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
130 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 ...
3
votes
0answers
126 views

Group Theory Research Topics [advice]

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
85 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 ...
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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 ...
2
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0answers
39 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
320 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
96 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
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5answers
456 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 ...
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 ...
0
votes
2answers
60 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
90 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
75 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, ...
3
votes
0answers
44 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 ...
3
votes
0answers
402 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
101 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
213 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
316 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
206 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
255 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 ...
6
votes
8answers
3k 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
154 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
784 views

I need help finding a rigorous Pre-calculus 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
137 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
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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
173 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 ...
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 ...
0
votes
3answers
58 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
292 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 ...
2
votes
3answers
148 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 ...
1
vote
1answer
32 views

Is $g$ increasing?

Suppose $f:[a,b]\rightarrow\mathbb{R}$ and define $g:[a,b]\rightarrow\mathbb{R}$ as follows $$ g(x)=\sup\{f(t):a\leq t\leq x\}, $$ with $x\in[a,b]$. Someone told me that $g$ is an increasing ...
11
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3answers
537 views

A question from an engineering undergraduate

My question primarily concerns the necessary transition from an undergraduate program in electrical engineering to graduate program in applied mathematics or pure mathematics. I'm an electrical ...
3
votes
1answer
286 views

Actuarial Science or Financial Mathematics? [closed]

I’m a second year undergraduate student of Actuarial Science that equally loves finance and pure mathematics. I only knew of Actuarial Science as a career that suited best these two requirements ...
3
votes
2answers
59 views

Favorite Textbooks for introducing a subject?

I'm interested in learning more about number theory, about fractal geometry, and about probability. Anyone have any good recommendations? I've taken calculus and statistics at university if that helps ...
3
votes
1answer
61 views

Re professional mathematicians working on several problems at once. Source needed.

Recently I read a quote from a working mathematician where he pointed out that professionals have to get used to carrying around several unsolved problems at once. Can anyone help me with the source ...
41
votes
5answers
7k views

What are the work habits of the best mathematicians? [closed]

Of course I would never compare myself to, and don't expect to be, one of the great mathematicians. However, I am curious as to how my work habits, dedication and passion differs from theirs. How ...
2
votes
4answers
492 views

Should I read about Manifolds or Algebraic Topology?

I really enjoy doing maths and it fills quite a lot of my spare time. I'm starting my first year in the university on october and I probably won't have that much time for independent reading once ...
5
votes
1answer
180 views

Problem solving strategy?

This question has always bothered me, and I've never had a maths coach to guide me along the way and show me what to do next. Nevertheless, I did make top 50 nationally in my national mathematics ...
0
votes
5answers
211 views

Some examples of applications of Game Theory

I'm approaching my junior year of HS now, and I'm looking for a good science fair project to do. I love mathematics, so I decided to a category of mathematics that can help base logical conclusions to ...
16
votes
5answers
818 views

Understanding mathematical texts

Please could you comment on following: I always wanted to know what mathematicians mean by "understanding a piece of mathematics". For example, I have just finished the second chapter from Rudin's ...
21
votes
11answers
3k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
7
votes
3answers
1k views

Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
3
votes
1answer
173 views

Changing streams in PhD

I've a masters degree from a reputed Indian university in pure mathematics, with a specialization in Algebraic Number Theory. However, I'd like to apply for a PhD in computational math/theoretical ...
3
votes
2answers
432 views

What's after undergrad? Advice needed.

I'm currently a rising senior at a small, yet well ranked liberal arts college studying Pure Mathematics. I've taken multiple high level mathematics courses and plan on doing a few more independent ...
6
votes
2answers
257 views

Advice for self-studying Inequalities and Calculus

I'm interested in self-studying the following books over the next year or so: Spivak's Calculus (I'm already in Ch. 5 and it is very slow going) The Cauchy-Schwarz Master Class by J. Michael Steele ...
9
votes
3answers
2k views

Is it bad to keep aside Lang's Algebra in graduate school?

Question is as it is stated in title. I will be joining for PhD program in this July 2014. I am interested in working in Algebra/Algebraic Geometry/Algebraic Number Theory. I tried to learn algebra ...
2
votes
3answers
613 views

What languages to learn for maths? [closed]

For people with "hands-on" experience in mathematical research, what languages are the most beneficial to learn? I know that many graduate programs require some degree of non-native lingual ...