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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7
votes
1answer
150 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 ...
2
votes
0answers
46 views

A discontinuous function $f: X \rightarrow Y$ satisfying: for each closed ball $B$ of $Y, f^{-1}(B)$ is closed in $X$

Find a function $f: X \rightarrow Y$ between metric spaces $X$ and $Y$ that is not continuous but has the property that for each closed ball $B$ of $Y, f^{-1}(B)$ is closed in $X$ Solution Attempt: ...
5
votes
3answers
443 views

What is the pre-requisite knowledge for generating my own integer sequence?

I've recently come across the On-Line Encyclopedia of Integer Sequences and I'm completely fascinated by it; something about how easy integers are to grasp and yet how complex the sequences are. I ...
1
vote
1answer
91 views

Advice for a math grad student needing a sixth year [on hold]

I am a doctoral student (pure math) who might need a sixth year to complete his PhD. My school might lack the funds to allow me another year as a teaching assistant. At least, there is no guarantee of ...
33
votes
10answers
4k views

How to be a successful math undergraduate student?

I am an undergratuate student in my first year of combined bachelor of electrical engineering and bachelor of mathematics. For my mathematics degree, this year I am supposed to take two math courses ...
0
votes
1answer
61 views

Background for Graduate Real Analysis I Class

This semester, I have signed up for a graduate Real Analysis I course (really a course in measure theory/Hilbert Spaces/Lebesgue integration) and have thus far attended two lectures. However, from ...
0
votes
0answers
19 views

Adding a website in bibliography. [closed]

I have taken information from this link for my project report. I want to add the website link in the "bibliography" section. But I don't know how is to cite this. Any help is appreciated. Thanks.
3
votes
1answer
102 views

Undergraduate mathematics competitions

I am a freshman (math undergraduate) here in Argentina and I am deeply interested in mathematical olympiads but I really need some advice. Right now, my problem solving skills are good but not that ...
-1
votes
0answers
13 views

Some difference in notation in a project report

I am focusing on a specific model in my study. When I am writing my project paper, for describing the estimation procedure, can I describe it more generally with some difference in notation than my ...
0
votes
1answer
28 views

Help with Spivak's Calculus Chapter 3 Problem 6

It says: Show that the straight line through $(a,b)$ with slope $m$ is the graph of the function $f(x) = m(x-a) + b$. Since the slope in a graph of a line is determined by using similar triangles, ...
6
votes
1answer
105 views

Jobs in industry for pure mathematicians

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 ...
0
votes
0answers
10 views

Unit Impulse response vs Impulse response in ODE

I'm was watching MIT OCW lectures for Differential Equations and in lecture 23, the professor goes over impulse inputs where impulse is $\int_a^b{f(t)dt}$ where $f(t)$ can vary or be constant. He ...
11
votes
4answers
4k views

How to do well on Math Olympiads

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 ...
16
votes
1answer
1k 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 ...
2
votes
1answer
90 views

Failed Calc 2. It's the Algebra, stupid

Well, I took "Multidimensional Math" w/ Linear Algebra and Calculus 2 at the same time over a 6 week period for the Summer session. It was a disaster. I don't think my Algebra and Trig are good ...
0
votes
2answers
58 views

Next step to learn mathematics for a high school student?

I am a high school student. I would like to study mathematics at university. Because I want to be successful in my studies and in productive research so I want to learn and practice more mathematics ...
4
votes
1answer
110 views

Bridge between High School Mathematics and University-level Mathematics?

I've graduated from High School and I am going to major in math at a local University. I've finished High School Calculus and I've self-studied very very basic Multivariable Calculus, Linear Algebra, ...
79
votes
9answers
8k views

Math and mental fatigue

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
10
votes
6answers
679 views

Suggestions for topics in a public talk about art and mathematics [closed]

I've been giving a public talk about Art and Mathematics for a few years now as part of my University's outreach program. Audience members are usually well-educated but may not have much knowledge of ...
3
votes
1answer
82 views

Troubling questions about probability

Suppose we have some random phenomena. Is it true that any event concerning the phenomena has a fixed "correct" probability? That is, the correct probability is the relative number of occurrences of ...
20
votes
2answers
309 views

Is there a profitable way to read mathematical proofs

Mathematical proofs are often presented in a sequential way, i.e., presenting definitions, building lemmas based on these definitions, building further results on these lemmas and finally invoking a ...
1
vote
1answer
39 views

research in special function with Lie 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 have to research in the field of special functions with a lie ...
26
votes
5answers
4k views

Math GRE Subject Exam [closed]

I am studying for the GRE Mathematics subject exam [1]. I am looking for tips regarding how to more effectively study for it. Does anyone know of any good study materials or have any tips in general? ...
3
votes
1answer
59 views

Probability question from GRE subject test

I ran across the following problem while practicing for the GRE math subject test: Suppose $X$ is a discrete random variable on the set of positive integers such that for each positive integer $n$, ...
11
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 ...
12
votes
8answers
930 views

When trying to learn analysis from bottom up, what numbers should I first construct?

I am interested in studying more analysis and related topics. However, I want to make sure I do so well and without making too many broad jumps in my learning. In some books I have seen, the author ...
0
votes
2answers
59 views

Rudin's Chain Rule

Rudin's chain rule theorem goes like this: Suppose $f$ is continuous on ${[a,b]}$, $f'(x)$ exists at some point $x\in [a,b], g$ is defined on an interval $I$ which contains the range of $f$, and ...
9
votes
1answer
329 views

Balancing Coursework with original research

I am a first-year graduate student in a US university pursuing a PhD in mathematics. I am a bit frustrated in trying to balance coursework with original research. I saw students who spend most of ...
1
vote
0answers
32 views

Dihedral group and symmetry group of icosahedron

I am studying abstract algebra at the moment, but I have several troubles picturing the dihedral group $D_n$ and the symmetric group of the icosahedron. For instance, I find it really hard to solve ...
417
votes
26answers
90k views

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

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 ...
2
votes
1answer
55 views

literature on advanced calculus [closed]

I need your opinions on this particular textbook: Advanced Calculus by Robert C. Buck. In my first year in college I finished two semesters of single-variable calculus and now I'm looking for a proper ...
0
votes
0answers
46 views

How to effectively learn from and use Ramanujan's notebooks? [duplicate]

I will come back and elaborate on the question if necessary (I must be off for a while...). But I'll try being specific. I have all four of Ramanujan's notebooks, with their respective Errata ...
15
votes
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 ...
8
votes
1answer
175 views

Do Electrical Engineering Researchers Usually Know Higher Math? e.g. Measure and Distribution Theory, Functional Analysis

I am an EE undergraduate student, and I recently took two courses in signals and systems. We were exposed to things like the Dirac delta (without mention of distributions), Fourier series (without ...
0
votes
0answers
48 views

What journals/websites do mathematicians have to check frequently?

There are so many news and publications updated online everyday. What are some must-read journals or websites? Such as AMS notices, or Arxiv.org? On one hand, I want some comprehensive news and the ...
3
votes
0answers
41 views

Classical geometry vs. p-adic geometry

I am interested in learning more about $p$-adic analysis and some of the geometric theories that are commonly used. However, it seems that many of the tools there are developed from analogous ...
41
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?

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 ...
5
votes
5answers
1k views

Multiplicative inverse of a complex number.

Find the multiplicative inverse of $1+ 3\sqrt{2}$ in the ring $\mathbb{Q}(\sqrt{2})$ and use it to solve the equation $(1+3\sqrt{2})x=1-5\sqrt{2}$. I think that the inverse is the conjugate, so it ...
2
votes
1answer
65 views

How far can I get with graph theory?

I am an undergraduate who had recently finished his $2$nd year. I was wondering how far can I get with Graph Theory this summer. I am studying from Bondy & Murty's book. I already finished ...
1
vote
0answers
64 views

Kline, Lang, Silverman…which author provides thorough and rigorous Calculus up Multivariate & Advanced Calculus?

I know this question may appear subjective, but it is not, let me explain; note to mods --> please don't close this if it is considered too subjective, please alert me and I'll try to reword it. I ...
0
votes
0answers
28 views

How to Begin Learning/Doing Sport Statistics?

I would like to start playing fantasy sports using a statistical approach to help with picking players, setting line ups etc. I have a particular interest in football but am also interested in hockey ...
1
vote
1answer
31 views

Proving triangular inequality in general

I want some advice on approaching proofs of the triangular inequality for various metrics. I have a suspicion the answer is simply 'improve mathematical maturity' but hopefully there is a general ...
6
votes
4answers
9k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
2
votes
3answers
109 views

How do I figure out my math aspirations? [closed]

I am really confused. Here's my present situation: I'm 18. I am about to start a computer science degree this August--going there only coz my parents want me to. I know most teachers for undergrads ...
4
votes
2answers
253 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 ...
0
votes
2answers
113 views

How important is it to learn latex?

So I am currently in my senior year (Undergraduate mathematics). And I am thinking to continue on and do my masters and PHD in mathematics. I need to now how important it is to learn latex and how ...
0
votes
1answer
75 views

Is the infinitesimal approach good.

I have heard of an infinitesimal approach to calculus. Is it better than the normal approach or is it the other way around.
7
votes
1answer
108 views

Would the professor take me seriously? [closed]

I'm a pure mathematics undergraduate. I have been working since a long time, and I am finally done with my little book. It handles a particular subject (which I won't mention). It is a collection of ...
4
votes
0answers
62 views

Matrix Calculus

My school offers Matrix Calculus class next semester. I have never heard about this subject before and got intrigued. After a short chat with professor I found myself unable to get rid of suspicion ...
15
votes
3answers
529 views

Why don't I understand “What is mathematics?” by Richard Courant [closed]

I am 14 years old and can do A level maths happily. However, I want to further my knowledge of mathematics to pave my way for more discrete maths and harder analysis etc. So I decided to pickup "What ...