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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20
votes
3answers
2k views

Why should “graph theory be part of the education of every student of mathematics”?

Until recently, I thought that graph theory is a topic which is well-suited for math olympiads, but which is a very small field of current mathematical research with not so many connections to ...
119
votes
9answers
14k 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 ...
2
votes
1answer
254 views

Will I have learned the prerequisites for self learning stochastic calculus and monte carlo method?

I'm an undergraduate econ major, and my main focus is in actuarial sciences, which as you may or may not know it's pretty mathematical. Some of the topics I will have to learn at some point on my own ...
10
votes
3answers
6k views

Choosing a PhD topic [closed]

My supervisor and I recently had a long chat about PhD related stuff. He said something to the extent that your chances of employment after finishing your PhD among other factors depends on the topic ...
37
votes
7answers
7k 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 ...
11
votes
7answers
925 views

Making up for wasted high school years - where should I begin?

I realize this question is long and quite personal but any help will be greatly appreciated. I'm a senior high school student. I've learnt maths at precalculus level. I have had little exposure to ...
31
votes
8answers
2k views

How to use math textbooks

I'm a higher schooler who was recently gifted a book by my teacher (Schaum's outline of advanced calculus) which is really awesome and I've started working my way through it. I have run into a ...
16
votes
3answers
755 views

What's next for me?

I'm in my last year of undergrad, and I would like to do original research for my senior thesis. I am already published in finite group theory and am looking for a new topic to study. I have taken ...
3
votes
1answer
704 views

Taking an exam in math analysis course.

So I'm taking my first midterm exam in math analysis soon and I'm confused on how to study for it. I mean in calculus one would be able to just go into the book and take derivatives and integrals ...
6
votes
1answer
406 views

What courses should I take in order to understand Navier-Stokes equations?

I've recently been interested in the Navier-Stokes equations. I would like to understand them deeply from a mathematical point of view. What courses in advanced mathematics (and physics?), and in ...
3
votes
1answer
645 views

Two sets can be separated by a hyperplane iff their convex hulls do not intersect

So I am supposed to prove that two sets of points in $\mathbb{R}^n$ are linearly separable in an n-dimensional space if and only if their convex hulls do not intersect. I understand the concept ...
2
votes
2answers
174 views

Recommended topics for Chemical Engineering grad. [closed]

I'm a Chem. Eng. grad. I did well in my math courses and I really like math. I've started digging for some more to learn on my own. I like applying math but I'm most satisfied when I have a deep ...
47
votes
6answers
10k views

What is mathematical research like?

I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research sounds strange to me. What does math research entail ...
14
votes
3answers
1k views

How to take the most of math lectures in college?

I am trying to become more effective in my study habits and in my case, I feel that attending classes is a huge waste of my time. The lecturer just keeps writing formulas on the board and to be ...
6
votes
2answers
1k views

start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
12
votes
4answers
228 views

Transitioning to Elementary School teaching and need some advice on bolstering my math skills

I'm an English major trying to make the transition to Elementary School teaching. For as long as I can remember, I've been extremely math-anxious and I've only done the bare-minimum level of Math work ...
1
vote
1answer
701 views

How to approach the problems in the Hoffman Kunze book?

I’m considering the idea to solve the entire set of problems contained in the Hoffman-Kunze text. The standard results of Linear Algebra are known to me. I don’t have much time to read the textual ...
3
votes
3answers
109 views

Advice reviewing academic paper

For a piece of university coursework, I have been asked to review a paper of my choice. It is a computer science course, but since it is very mathematical, I thought it was worth asking here. I was ...
44
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? [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 ...
6
votes
6answers
1k views

Is it possible to learn ring theory if one's familiar, but not good at group theory?

Is it possible to learn ring theory if one is familiar with but not good at group theory? Background: I’m using Dummit and Foote's Abstract Algebra, and I am an undergrad.
7
votes
5answers
3k views

Relearning Mathematics

First post, I'll try to make it clear and concise. I've been spending the past few weeks watching all sorts of space and science documentaries and it's ignited my eagerness to learn more about these ...
17
votes
4answers
1k 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 ...
2
votes
3answers
108 views

easy activity to train finding pattern ability? [closed]

I realize that my math learning go wrong way. Wikipedia says math is finding pattern, formulating conjectures, and proving it. but my math learning didn't focus on them. memorizing formula doesn't ...
8
votes
5answers
4k views

What are the prerequisites for taking introductory abstract algebra?

I am a maths student in my second year of university. I have taken and done quite well in Calculus I, II, III as well as a linear algebra (application focused) class. I have not worked much with ...
9
votes
5answers
1k views

Differential Geometry past an introductory course?

I'll be doing an independent study with one of my profs in differential geometry next semester (my university did not happen to offer an intro diff. geometry course next semester like it usually ...
4
votes
3answers
547 views

Independent math learning

I'm an undergraduate math and econ major and I'm planning on graduating relatively soon and I am very limited to the number of math classes I have left (very sad about this fact). So far I have ...
3
votes
1answer
846 views

Goldberg against Rudin against Pugh. Which real analysis book should I buy? [closed]

I am trying to decided which real analysis text book I should buy. I have the following in mind- 1)Walter Rudin's "Principles of Mathematical Analysis" 2)Charles Pugh's "Real Mathematical Analysis" ...
4
votes
3answers
367 views

participation in 1st year introductory pure maths classes

I have just started teaching a very elementary class for 1st year students on introductory pure mathematics. ( classes at my institution are groups up to 20 students and supplement the lectures. The ...
10
votes
2answers
4k 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, ...
11
votes
6answers
626 views

Strategies to prevent my math abilities from fading?

This is not a math question per se, but I think that it is relevant to a number of people. I am currently in the process of applying to graduate school, but not feeling super confident that I will get ...
6
votes
2answers
585 views

Advice about taking mathematical analysis class

I appologize if this isn't the place to ask, if it's not could you let me know and I will take it to meta? Anyway, so I am planning on taking a mathematical analysis course next spring, and I'm really ...
6
votes
4answers
394 views

Should I include obvious steps in mathematical paper?

I am writing a formal school paper (by formal I mean, with an abstract, a bibliography and 20 pages in length) on mathematics (it is called 'Extended Essay,' for those having knowledge of the ...
4
votes
4answers
160 views

Transition from introduction to analysis to more advanced analysis

I am currently studying intro to analysis and learning somethings about basic topology in metric space and almost finished the course . I am thinking of taking some more advanced analysis. Would it be ...
5
votes
2answers
1k views

What are the prerequisites for Stochastic Processes

I'm a first-semester mathematics student, however I already feel the need of a certain goal, or rather an area I'd like to specialize in. For a quite a while, that's been the study of stochastic ...
3
votes
1answer
877 views

Relearn mathematics

I believe that this question is well known, but since I'm not a US resident and do wish to learn math according to the U.S. school syllabus I wish that somebody can help me. At my first eight years ...
21
votes
3answers
1k views

Academic integrity [closed]

This may sound like a childish question and for all its worth, very well may be one as I am only 17, but how do I know who to trust with reviewing or looking at my work? The idea of someone stealing ...
26
votes
8answers
4k views

Math every mathematician should know [closed]

This question is meant as a companion to previously asked questions like Proofs every mathematician should know. More and more I'm beginning to see that there is just too much math to learn. ...
9
votes
1answer
2k views

Choosing a Master Thesis Topic: Logic - Model Theory

I am a first-year graduate student in maths. Around these days, I feel I must decide on which exact part of mathematics I shall go through. Infact, I have narrowed down the suitable options but still ...
3
votes
3answers
1k views

Suggestions on Real, Fourier Analysis textbooks?

I'm new here, and I hope this is within the scope of the website. I'll try to ask few advisory type questions in the future... I'm a college junior, and I was wondering if you guys could offer any ...
192
votes
28answers
27k 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 ...
6
votes
1answer
330 views

Set theorist as a physicist or physicist as a set theorist?

I'm majoring physics, but really interested in mathematics. I liked physics since it was really beautiful to have an analysis on a nature with mathematical tool. However, the more i study, the more ...
24
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 ...
1
vote
1answer
120 views

prove normality of famlity of analytic functions

I already proved normality for meromorphic functions that omit 3 values. I'm trying now to prove normality of family of analytic functions that omit two values. Is there any way to deduce any one of ...
2
votes
2answers
178 views

Numeric synaesthesia: uses of and advice for learning math.

It turns out that my adolescent son might have numeric synaesthesia-- numbers have specific colors and possibly other distinguishing characteristics for him. He has shown that he can commit long ...
3
votes
3answers
622 views

Should analysis be studied minus point set topology

I have noticed that certain texts like Terry Tao's Analysis I, Bartle and Sherbert's Real analysis as well as Michael Spivak do not use the language of topology in their exposition. A text like ...
2
votes
2answers
516 views

Study Strategy: broad/depth; abstract/intuitive

Research Interest: Chaos, Dynamical System, PDE. Study style: Shallowly Broad: Quickly absorb as many branch as possible [master more 'toolbox'] OR Narrowed Depth: Carefully focus on ...
0
votes
3answers
51 views

Example of no inclusion in set of closures

Let $(X,d)$ be a metric space and $A_j \subseteq X$ for $j = 1,2,...$ . Let $B = \bigcup_{j=1}^\infty A_j$. Find an example for which $\bigcup_{j=1}^\infty \bar{A_j} \neq \bar{B}$. Also, in general ...
10
votes
3answers
18k views

GRE Math Subject Test

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 ...
3
votes
1answer
1k views

How to work faster on the GRE.

I'm fixin' to go to grad school next year, so lately I've been studying for the mathematics subject GRE. What I have heard, from MSE and other places, is that the most important thing is to learn to ...
2
votes
1answer
972 views

Prerequisite for Differential Topology and/or Geometric Topology

What are the prerequisites to learning both or one of the items? Consider that one will have done some of the "core" classes like Differential Geometry, Real Analysis, Abstract Algebra and POint-Set ...