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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1
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1answer
30 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 [on hold]

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
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1answer
54 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
1answer
207 views
+50

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 ...
0
votes
0answers
53 views

Which kind of jobs allow time and energy for one to pursue their mathematical interests? [closed]

I would like to give some perspective on why I am asking this. I'm a undergraduate who heard the siren calling for mathematics about a year ago after struggle of finding what I wanted to do with my ...
11
votes
3answers
964 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
922 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 ...
32
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
2answers
56 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
316 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
30 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 ...
412
votes
26answers
87k 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
52 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
168 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
43 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
39 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
998 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
62 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
57 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
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0answers
22 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
30 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
8k 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
104 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
244 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
103 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
74 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
107 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
58 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 ...
14
votes
3answers
513 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 ...
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 ...
4
votes
1answer
660 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" ...
2
votes
1answer
60 views

Confusion about ODE

so I am in a class for ODE and for me is is moving a bit quick. I am one year behind most of the class but thats note anything rare. But I am feeling very stumped on something now. Because, usually I ...
160
votes
14answers
10k views

Identification of a quadrilateral as a trapezoid, rectangle, or square

Yesterday I was tutoring a student, and the following question arose (number 76): My student believed the answer to be J: square. I reasoned with her that the information given only allows us to ...
1
vote
1answer
97 views

Is it ill-advised to read books casually for entertainment? [closed]

I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis ...
3
votes
2answers
110 views

Prerequisite of Algebraic Geometry

Algebraic geometry, as far as I know, is a very important branch of mathematics, which is also very difficult. I am going to take a try to taste that. Before really going into the field, I have two ...
3
votes
1answer
234 views

Learning roadmap for mathematical biology

Which courses (undergrad level but also master's level) in mathematics and statistics should be taken by a student aiming for a PhD in mathematical biology? The basics I imagine are: Calculus ...
2
votes
2answers
70 views

How do I get good grades in an exam?

I study hard throughout the year and I am able to solve most problems in the text assigned to us and I am frequently the only one who can solve the hardest problems in the assignments or the problem ...
5
votes
1answer
63 views

How to get the most out of attending a conference talk or a research presentation?

I'll say up front that I imagine there's a resource for this somewhere, but I was unable to find it. I've been attending conference talks and research presentations for about a year at my university, ...
-1
votes
1answer
294 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 - ...
20
votes
0answers
3k views

What are some strong algebraic number theory PhD programs? [closed]

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
4
votes
2answers
139 views

Does set theory help understand machine learning or make new machine learning algorithms?

When I was in a university, I didn't major in math but took some math classes. However, I dropped out of math classes pretty quick. Some person recommended that I learn some ...
5
votes
1answer
170 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 ...
1
vote
1answer
82 views

Learning mathematical concepts

Our teacher loves to test us on pure concept based questions and test if we really know what we are doing when learning a particular lesson. For example, when we first started learning about ...
1
vote
2answers
90 views

How can I start to learn proof theory?

I'm studying computer science and I realized that I have problems in working with mathematical proofs. They are for example part of my class Formal Systems and Automata. I'm really interested in ...
0
votes
2answers
80 views

How to remember various set operations very easily?

I need an way to remember the set operations very easily. Does anybody have any idea? For example, how do you remember the distinction between Set-Intersection and Set-difference? I regularly mess ...
2
votes
2answers
74 views

Prove that $\mathbb{Q}(r+s\sqrt{t})=\mathbb{Q}(\sqrt{t})$.

Let $r,s,t\in\mathbb{Q}$. Prove that $\mathbb{Q}(r+s\sqrt{t})=\mathbb{Q}(\sqrt{t})$. Ok. So I've fallen a little behind in my algebra class, and I'm a bit confused on how to approach this ...
0
votes
0answers
15 views

Formula to convert currencies

I know this currency exchange rates: 1.000000 USD = 0.943837 EUR 1.000000 USD = 0.683463 GBP What would be the formula to find: 245 EUR = ??? GBP