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
votes
1answer
331 views

Does one necessarily need an MS in Math before taking a PhD in Math? [closed]

I finished bachelor's in mathematical finance and am nearly finished with master's in mathematical finance (I am already done with thesis), and I plan to pursue a PhD not in mathematical finance but ...
3
votes
1answer
157 views

Advice on mathematical cources and profession [on hold]

I am a class 9 student studying in India. I deeply love mathematics and I am aspiring to become a mathematician ( I am aiming for research and development). My hobbies include learning and trying to ...
1
vote
0answers
28 views

Partial Differential Equations Methodology

I am currently studying PDE's i got an almost standard methodology for the First order PDe's mostly using the characteristic's Method.Now Im on the Second order Pde's .So i wanted to get some things ...
1
vote
0answers
36 views

Book Suggestion, Analysis (Multivariable Calculus)

I am doing my 4th Analysis course. Now we are doing functions from $\mathbb{R}^{n}$ to $\mathbb{R}^{m}$ And we are talking about differentiabiity . I have a lot of problems understanding the course ...
3
votes
4answers
145 views

Good way to convince a young kid that $0*0 = 0$?

My little brother (6 years old) asked me a question ("What is $0*0$?") and gave an answer to his own question which I found ridiculous so I refuted it but he still thinks he is right. He says that ...
4
votes
1answer
172 views

Quality of Videos Lectures and Lectures vs Textbooks

I am a student trying to learn different subjects by watching video lectures and reading on my own time. I was wondering if the lectures from ICTP and nptelhrd are a great use of my time. I tried ICTP ...
2
votes
0answers
57 views

What topics should I study to understand this document?

Background I'm trying to understand a document I found online. The reason I'm reading it is because I need to translate the Nedelec element into code for my research. Problem My background is in Food ...
2
votes
1answer
58 views

Ackermann Function - Book recommendation

What books would you recommend me for the topic "Ackermann Function" ?? I will have a presentation at the end of the semester for this topic and I would get some information...
1
vote
1answer
125 views

In balancing effort and advancement in what concerns learning

What's new besides showing modern advancements in modern mathematics as well as eloquently written notes also contains some good advice to young people like me in this room (career advice:!). in ...
9
votes
1answer
136 views

Mathematical Research seems daunting [closed]

Suppose you are a research mathematician. I imagine your problems are generally unlike the problems of fellow scientists in the physical sciences, because you deal with proofs, and proofs demand ...
3
votes
0answers
43 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 ...
4
votes
1answer
137 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
72 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 ...
3
votes
0answers
552 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 ...
3
votes
2answers
155 views

What is the difference between 'thus', 'hence' and 'therefore'? [closed]

When explaining and writing proofs for certain things in my notes I find myself using these words interchangeably however I'm left to wonder if there is a certain protocol to follow when using them? ...
16
votes
3answers
303 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
80 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
86 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
263 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
84 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 ...
4
votes
1answer
129 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
264 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
150 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
300 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
250 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
316 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
259 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
42 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
104 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
24 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
305 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
342 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 ...
41
votes
2answers
745 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 ...
7
votes
1answer
343 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
82 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
36 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
2answers
53 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
69 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
71 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
52 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 ...
9
votes
3answers
476 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. ...
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 ...
41
votes
15answers
2k 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 ...
3
votes
1answer
211 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
62 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
39 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
350 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 ...
3
votes
1answer
173 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 ...
7
votes
2answers
220 views
+50

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
87 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 ...