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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4
votes
0answers
212 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. ...
3
votes
1answer
273 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
146 views

What will I be doing?

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 ...
4
votes
0answers
102 views

How can math students (not instructors) improve studying by Learning through Testing?

I hit upon Alex K. Chen's answer on What learning strategies do people who are "quick learners" follow? which links to this New York Times article To Really Learn, Quit Studying and Take a Test . ...
4
votes
0answers
167 views

For maximum productivity, how many math subjects or subfields should be studied daily? [closed]

I quote Ben Baert on Quora at http://qr.ae/hkuCd: Study every subject only for short periods and take regular breaks: during my 5 or 6 hours - preferably spread out over the course of the day, I try ...
16
votes
1answer
263 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 ...
9
votes
0answers
262 views

Big geometry grad schools - for an average applicant

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
205 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 ...
6
votes
8answers
541 views

How t0 stop being obsessive about small, trivial things [closed]

I'm a student of math, my problem is that I tend to overformalize and overanalize some things and definitions and so I keep wasting time and effort in pointless things. For example, one often finds ...
1
vote
0answers
125 views

Soft question - having difficulty with rigorous proofs

What exactly is in your opinion the best way to understand rigorous proofs?I seem to be having a number of problems when it comes to learning mathematics. .While I easily get the intuitive part, the ...
7
votes
1answer
161 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
98 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
437 views

Mathematical Background for Computer Vision

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 ...
10
votes
1answer
445 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
85 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 ...
-1
votes
2answers
76 views

What textbook and chapters should I go through to study for basic math qualification exam?

In 7 months I will have to take a "Basic Math" qualification exam similar to the ones shown here: Fall 2013 Spring 2013 Fall 2012 Spring 2012 Fall 2011 Could somebody please recommend the best ...
2
votes
2answers
201 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 ...
13
votes
3answers
357 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
92 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 ...
4
votes
1answer
185 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
163 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 ...
22
votes
6answers
472 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 ...
7
votes
0answers
341 views

How much time is reasonable to complete baby Rudin? [closed]

I've been teaching myself math for more than a year. My current aim is towards algebraic topology and differential geometry. Apart from a messy (by which i mean some rigorous and some not) ...
2
votes
0answers
158 views

As a high school student, how do I go about doing research and writing a research paper?

I am currently a high school junior living in India and have already taken Differential Calculus and will be finishing Integral Calculus in 2 months time. I am interested in doing some research and ...
3
votes
0answers
83 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
votes
1answer
119 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?
2
votes
0answers
97 views

How do I approach the foreign language requirement for PhDs in pure mathematics?

I see that many PhD programs require students to demonstrate students’ abilities to translate English mathematics papers to two of French, Russian, and German and different papers in those languages ...
4
votes
1answer
115 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
161 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
232 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
75 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 ...
1
vote
1answer
176 views

What major to choose, out of three possible math majors?

I need help with trying to figure out which major I should try to graduate with. Currently, I am a senior undergraduate student with an actuarial science major. I have three actuarial exams finished, ...
0
votes
1answer
541 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
124 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 ...
1
vote
0answers
143 views

Transitioning From Pure Maths To Applied.

I was wondering if anyone had any experience transitioning from pure mathematics to applied mathematics? I am currently doing an Msc in pure maths and my background is mainly algebraic. I was ...
13
votes
5answers
1k views

Do you memorize all the proof when you study for final exam?

I want some good tips to study mathematics efficiently and effiectively. I know there is a no royal way to master mathematics, however, I want to put more time on studying 'more useful things'. I ...
-2
votes
4answers
147 views

Linear Algebra and Set Theory book recommendations.

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

Need advice on whether I should take Algebra 2 next semester

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
63 views

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

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
260 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 ...
2
votes
4answers
372 views

How to choose math courses at uni

I don't know what kind of job I want, but I know I like pure math. It seems people study pure math and then, in the end, realise there is nothing out there for them (jobwise). I don't want this to ...
2
votes
0answers
267 views

Math gre subject test scores and results?

I took the math gre scores back in October and did terribly (52%) even though I was scoring in the 70-80% on practice exams. I am interested in applying to Stanford's ICME and Berkeley's Stats ...
1
vote
0answers
37 views

Senior Research Group

I have been elected to participate in a senior research group where each undergrad has the freedom to choose any advanced topic in mathematics. As far as background, I've taken multivariable calculus ...
39
votes
12answers
3k 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 ...
1
vote
0answers
34 views

Question pertain to graduate programme in astronomy from mathematical background

I am currently an undergraduate student in mathematics, and wanted to pursue a career in astronomy area. What graduate programme should i take? is applied mathematics sufficient? I am currently ...
5
votes
2answers
137 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 ...
17
votes
1answer
500 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
86 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, ...
3
votes
2answers
141 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 ...
2
votes
2answers
173 views

How important are tests in math study?

I'm currently trying to teach myself math through reading. I've made a schedule to keep my pace and to make sure I finish enough problems. Should I add to my routine a timed test now and then?