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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3
votes
0answers
56 views

Advice on methods to capture lecture board and add notes [closed]

I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and ...
3
votes
1answer
215 views

Can you succeed in undergraduate math, if you can't create proofs unseen and new to you? [closed]

TL & DR. Here I only mean proofs that I personally never stumbled across, either in a book, lecture, or practice question, NOT proofs that are too hard for even the best math undergrads. I ask an ...
0
votes
2answers
79 views

Question about proving something is a group: in general not a specific structure

I could use some clarification, this isn't that difficult of a concept but I feel it's easily screwed up when doing so If you have a structure with a binary operation. First thing to do is check ...
4
votes
0answers
910 views

Can I get a PhD in Stochastic Analysis given this limited background?

General advice on PhD apps welcome Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic? 1/4 I ...
18
votes
3answers
392 views

Good examples of mathematical writing (structural organization, style, typesetting, and so on)

A very famous question on MathOveflow asks for examples of good mathematical writing. Here, I'd like to narrow down the topic and ask: $\color{#c00}{\text{Question:}}$ Could you point ...
3
votes
1answer
102 views

Should I drop a class which I may not be ready for in order to pursue more time for personal study [closed]

This is my first time asking for advice on here, but I have seen some great advice given here. I am a first year student in a graduate program and I am currently enrolled in a course on advanced ...
4
votes
1answer
114 views

Opportunities for Mathematicians to Work in Biological/Disease Areas

Yesterday, I was reading some of the question Can I Use My Powers for Good? and it got me thinking. It's quite an old question (3 years), so I don't want to resurrect it and also my own question's ...
7
votes
2answers
317 views

Am I wrong for wanting to give up studying analysis? [closed]

I am writing this because I'm having a hard time studying for analysis. This is my second time taking a real-analysis course and from the beginning, somewhere deep down I thought that I might be ...
3
votes
1answer
105 views

Suggestions for calculus review for mGRE

I'm currently studying for the mGRE that will be given in October of this year and I'm having trouble deciding which books to use for the calculus review. I'm currently brushing up in Stewart's ...
6
votes
2answers
187 views

suggesting books on Field/galois theory

I have finished courses on group theory and ring theory and linear algebra and abstract algebra(inrroducton with fraleigh's book) im about to take field/galois theory this semester any good book not ...
4
votes
4answers
329 views

Starting learn Mathematics [closed]

I'm a 21 years old Computer Science Student. I am falling in love with mathematics newly, and I want to start dating mathematics (learning mathematics :)). Because I don't have any knowledge in ...
2
votes
4answers
205 views

Book recommendation for Measure Theory

What book would you recommend me to read about measure theory and especially the following: Measure and outer meansure, Borel sets, the outer Lebesgue measure. The Cantor set. Properties of ...
4
votes
3answers
316 views

What things should one know in order to enjoy their undergraduate degree? [closed]

From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is grueling. However I'm certain that there are ...
3
votes
5answers
330 views

Does taking courses in mathematics give any help for mathematical logic?

I'm undergraduate student of philosophy department and I think I'll major in mathematical logic. For studying mathematical logic, I thought studying math lectures would give help to logic. So I ...
2
votes
2answers
670 views

Preparation for STEP Mathematics Examinations [closed]

First I will give some background, to put my question in context. I am currently in my final year of school, and in order to meet my university offer to study Mathematics this Autumn, I am required ...
2
votes
1answer
359 views

Can I Start Analysis? Seeking Your Advice on My Journey to Mathematics! [closed]

I am a college sophomore with double majors in mathematics and microbiology, and I have been doing independent research in the mathematical/computational biology, which really led me to love the ...
1
vote
1answer
46 views

Find $f'(x)$ given that $2f(x) + 3f(-x) = x^2 -x + 1 \space \space\forall x \in \mathbb{R}$

Find $f'(x)$ given that $2f(x) + 3f(-x) = x^2 -x + 1 \space \space\forall x \in \mathbb{R}$ My solution Substitute $x \rightarrow -x$ to get $2f(-x) + 3f(x) = x^2 +x + 1$. We now have 2 equations in ...
3
votes
2answers
120 views

Advice on how to use previous exams to study [closed]

I have two big (graduate) exams in mid-January (one in D. Geometry and the other one in Algebra) and I'm not sure how to study for them. I have access to all the previous exams (more than 10 of each), ...
0
votes
1answer
29 views

If $\alpha\in X/R$ is an equivalence class, then $F:X/R\to Y$ defined by $F(\alpha)=f(a)$, is well-defined, 1-1 and onto.

Let $f:X\to Y$ be a surjection. Let $R$ be the subset of $X\times X$ consisting of those pairs $(x,x')$ such that $f(x)=f(x')$. Then $R$ is an equivalence relation. Let $\pi:X\to X/R$ be the ...
-1
votes
1answer
468 views

I need help organising these books by topic [closed]

Okay, this should be a quick and easy question for those of you who've studied calculus. I have a list of books that I want to order by topic, the books are as follows: Michael Spivak - ...
1
vote
0answers
552 views

Partial Differential Equations Course And Differential Geometry Prerequisites

Is the ordinary differential equations course a prerequisite for the partial differential equations course for a person who has passed the integral calculus course? Is it really required to have ...
44
votes
2answers
872 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
698 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
102 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
50 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
75 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
82 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
80 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
104 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 ...
10
votes
3answers
520 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. ...
91
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 ...
46
votes
14answers
5k 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 ...
5
votes
1answer
340 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
70 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
394 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 ...
2
votes
1answer
208 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
509 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
105 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
3answers
4k 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
450 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
136 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
1answer
104 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 ...
20
votes
6answers
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
362 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
114 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
649 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 ...
74
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 ...