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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33
votes
10answers
4k views

How to be a successful math undergraduate student? [on hold]

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 ...
11
votes
4answers
2k views

Topics on Number theory for undergraduate to do a project

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
5
votes
1answer
95 views

Breaking Out of Algorithmic Thinking

I have been taught my whole life to solve math with an algorithm or method. My teachers in school trained us to identify patterns in equations and then use a method to solve it. No one has ever ...
6
votes
4answers
737 views

Some Questions regarding preparing for Math Olympiads (searched but didn't get answers)

Many questions have been asked on this site regarding preparation for olympiads like the Putnam. I've read those questions and accordingly decided to start with Engel's "Problem Solving" but I have a ...
103
votes
18answers
10k views

How do you describe your mathematical research in layman's terms?

"You do research in mathematics! Can you explain your research to me?" If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure ...
7
votes
6answers
586 views

Thinking of mathematics in terms of analogs

I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical ...
6
votes
1answer
372 views

best book for real analysis for undergraduate [duplicate]

I am in under graduate first year. I want to learn some advanced real analysis. Can you give me some suggestions? One suggestion I got is Rudin's mathematical analysis. Can I buy that?
3
votes
1answer
77 views

Writing mathematics one is only slightly familiar with

Reading Paul Halmos' book I want to be a mathematician, he emphasizes early his personal experience with writing mathematics - using long, clear sentences, claiming that it is more beautiful, engages ...
3
votes
1answer
173 views

Literature on Chern-Weil Theory and the Chern-Gauß-Bonnet Theorem

At my university there are plans for a graduate seminar on Chern-Weil Theory and Chern's generalisation of the Gauß-Bonnet Theorem. Unfortunately I am having a though time in finding adequate and ...
4
votes
3answers
194 views

How to write for phd? [closed]

I'm a professor in high school and I would like to get a phd but I don't know how to do research for some phd topic. Could you guide me how to do this? When I was a student I was very interested in ...
0
votes
2answers
510 views

Binomial Theorem Practical Problem

I have been studying the 'Binomial Series', Chapter 16, Pg.125 within the Engineering Mathematics Book by John Bird. After completing this section I have attempted to complete the exercises for ...
4
votes
2answers
217 views

Surveys of Current (last 50 years) Mathematics at Graduate / Research level?

I'm wondering if there are any books or broad survey articles that survey current mathematical areas, i.e. mathematics of the last 50 years. Ideally, these would continue in the style of the various ...
11
votes
7answers
2k views

How to test whether I am suitable to pursue mathematics? [closed]

I am a high-school student. I have developed a recent affection towards mathematics (especially proofs), although I was always into logic (I've been a programmer since the age of eight). Now I am ...
7
votes
1answer
541 views

What pure mathematics foundations should an applied mathematician have?

I'm studying mathematics, with some statistics also, and I've always chosen applied courses. I'm getting to the point where I'm studying 3rd year undergraduate to graduate level material. My first ...
4
votes
0answers
308 views

start studying advanced topics in number theory

I am a first year undergrad and have had elementary course in Number Theory which includes only basic introductory topics like: divisibility,gcd-lcm,primes,congruences, number theoretic functions etc. ...
4
votes
1answer
413 views

Mathematical logic book with answers to exercises

I'm sure a question similar to mine has been asked before, but I am looking for a mathematical logic book with answers to the exercises. I am studying independently and although I have good logic ...
3
votes
2answers
158 views

What will I be doing? [closed]

I'm a freshman studying discrete mathematics B.sc. It's easy to google ''typical mathematician jobs'' and get an idea of what mathematicians do for a living, but what sort of jobs can I expect to work ...
11
votes
1answer
351 views

How often should math students take day breaks and longer breaks or vacations? Any research?

John Edensor Littlewood wrote in page 197 of Littlewood's Miscellany "For a week without teaching duties - and here I think I am preaching to the converted - I believe in on afternoon and the ...
10
votes
0answers
318 views

Big geometry grad schools - for an average applicant [closed]

What are some schools that have a lot of geometry going on, but that might accept some middle-of-the-range applicants? Let me add some context... I left grad school (UC Davis) with an MS in 2012 ...
3
votes
0answers
312 views

Bachelor Thesis - Galois Theory Research Topics?

I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was ...
7
votes
1answer
172 views

General Topology: “Follow your Nose Approach”

So, this is definitely a soft question and I apologize. I've been in point set topology for about a week and I have two questions, Everything spews from definition, so should I dismiss my geometric ...
2
votes
2answers
106 views

Greedy algorithm for reading a single paper in Dutch

I want to read the paper of Freudenthal and van der Waerden that proves there are only 8 convex deltahedra. (“Over een bewering van Euclides” Simon Stevin 25 (1946–7), pp. 115–121.) I have a copy of ...
2
votes
1answer
605 views

Mathematical Background for Computer Vision [closed]

I am a PhD student and would like to do deep research in the area of computer vision and pattern recognition. I know to be successful I need strong mathematical background. Could you please introduce ...
8
votes
1answer
610 views

Preparing for “differential forms in algebraic topology”?

I'd very much like to read "differential forms in algebraic topology". Apart from background in calculus and linear algbra I've thoroughly went through the first 5 chapters of Munkres. I'm thinking ...
0
votes
2answers
90 views

What textbook and chapters should I go through to study for a probability qualification exam?

In 7 months I will have to take a "Probability" qualification exam similar to the ones shown here: Fall 2013 Spring 2013 Fall 2012 Spring 2012 Fall 2011 Could somebody please recommend the best ...
3
votes
2answers
242 views

What's the right moment to learn Set Theory?

I've seen a question in which the OP asked when is the right moment to learn Category Theory, it seems this moment comes a little after a course of algebra, and indeed some books on abstract algebra ...
14
votes
3answers
419 views

Being mathematically critical: how should a student approach statements that appear to be obvious?

Very occasionally, I will read or hear a theorem, and think: isn't that obvious? Not in a contemptuous "I can immediately see how to prove this" way, but rather in a "I would have thought this was ...
3
votes
4answers
96 views

Let $x,y,z$ be integers and $11$ divides $7x+2y-5z$. Show that $11$ divides $3x-7y+12z$.

Let $x,y,z$ be integers and $11$ divides $7x+2y-5z$. Show that $11$ divides $3x-7y+12z$. I know a method to solve this problem which is to write into $A(7x+2y-5z)+11(B)=C(3x-7y+12z)$, where A ...
2
votes
1answer
238 views

Is it possible to learn differential topology before analysis?

Currently I'm self studying for my own enjoyment topology and algebra (munkres and herstein). Since I start at the university next year everything I'm learning now is for my own enjoyment and I will ...
5
votes
2answers
166 views

Is it better to teach or to grade?

As a graduate student at my university, I have the option many times of deciding what type of work I do for support. The two basic options are to teach either a calculus or college algebra course, or ...
20
votes
6answers
622 views

Generic elementary group theory problems.

This question is about generic group theory problems. here are examples for what I’m referring to: Prove that any group of order $p^2$, where $p$ is a prime, is abelian. Let $G$ be a ...
3
votes
0answers
94 views

What is the most relavant math for statistics students?

As they say "the more math you learn the better". Unfortunately, I did not have a lot of mathematical training in my undergraduate. Now I am doing a master in mathematics, mainly to make up some ...
1
vote
1answer
139 views

Is it good that I feel embarrassed when I can't find solution to a problem? [closed]

Is it good that I feel embarrassed when I can't find solution to a problem and then I have to check the solution manual?
4
votes
1answer
126 views

Advice regarding best-practice mathematics / categorial logic.

A good heuristic is: If it doesn't cost anything, generalize. In particular, if we have a theorem, and a proof thereof, then we ought to look for a maximal generalization of this theorem, ...
6
votes
0answers
203 views

What is the best way to go about learning math?

I know this is a very subjective question, but after struggling on my own for a while I figured I might as well ask it. I did all the normal math classes in college (LinAlg, MultiVariable Calc, ...
2
votes
2answers
326 views

Ring theory : Completely lost and overwhelmed

Over the past 3( 9 sessions) weeks my professor has covered entire Part 3 - Rings from Gallian's Abstract Algebra which includes Introduction to Rings Motivation and Definition Examples of ...
5
votes
0answers
91 views

Is there a proper etiquette for asking an author for their (mathematical) software?

This may not be the correct place to ask such a question. I have read a mathematical paper on multiclass total variation clustering. I wish to use the algorithm in the contents to compare with another ...
2
votes
1answer
981 views

what prerequisite classes must I have before I take Abstract Algebra and Real Analysis at the undergrad level?

what prerequisite classes must I have before I take Abstract Algebra and Real Analysis at the undergrad level? Will these prerequisites help me with these two coursea at the graduate level? or do I ...
3
votes
3answers
158 views

Question on Rudin sequences?

In baby Rudin, Rudin shows that $$\lim_{n \to \infty}\sqrt[n]{p} = 1.$$ In the proof of limit he tries to prove that the limit is $1$. So he takes $x_n = \sqrt[n]{p} - 1$. I have never noticed this ...
-2
votes
4answers
175 views

Linear Algebra and Set Theory book recommendations. [duplicate]

I would like to studying linear algebra and set theory. Does anyone have a a good recommendation of books/resources/etc.?
2
votes
6answers
591 views

Need advice on whether I should take Algebra 2 next semester [closed]

I am an undergraduate primarily interested in pure mathematics, but recently ODE and Linear Algebra have caught my attention. As I study more applied maths, I have less time for pure math. My ...
2
votes
2answers
86 views

Important topics to cover in an intro course to algebraic number theory? [closed]

I am currently doing an independent study in algebraic number theory using Stewart and Tall's Algebraic Number Theory and Fermat's Last Theorem textbook. I have covered the material for the course ...
5
votes
1answer
313 views

Where to go from here…graduate school

I am an undergrad math major (minor in applied stats) set to graduate next month. I have been considering graduate school for a long time, and I know I want to pursue at least a Master's in the near ...
46
votes
12answers
4k views

I almost quit self-studying mathematics, but should I continue?

Before I move on to the main idea of this post, I need to tell you some background information about myself. Hopefully, it proves useful for you in giving me advice. I'm a 16 year old high school ...
5
votes
2answers
181 views

Commutative/noncommutative algebra?

I know basic knowledge of undergraduate algebra till galois theory of finite extensions. I want to learn number theory, but also like algebra. This semester I have to choose to read either commutative ...
20
votes
1answer
626 views

Learning Math Efficienctly and Succeeding in Grad School

I'm currently a second year Ph.D. student studying pure math. I've recently come to the conclusion that I must be studying wrong. Actually, more to the point, I must be thinking about mathematics ...
2
votes
2answers
93 views

Informal: What do you do when you cannot understand a proof in a book?

I have just moved to the differentiation chapter in Royden's book on real analysis. Unfortunately, many of these proofs are difficult for me to understand, and no matter how many times I read them, ...
4
votes
2answers
151 views

Real Exponentiation (help with an exercise)

Hi everyone I have serious problems with this exercise. I would appreciate any help. Thanks. (I can use freely any fact regard to real exponentiation when the exponent is a rational number, other ...
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, ...
3
votes
2answers
2k views

Learning maths as a hobby - tips and techniques not to forget

I learn math in my free time. I do it mainly as a hobby, but it also helps me as a software engineer. My main resources are MathTutor site and Stroud books. The problem I have is I can't work on math ...