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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3
votes
1answer
94 views

Are there any modern mathematicians whose research interest is in “Probability Theory”?

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
1
vote
0answers
39 views

Is it wise to select a research topic first and then choose an advisor? [on hold]

I am a student of Pure Mathematics. I am interested in Linear Algebra and Abstract Algebra. As I was browsing the Internet for some good research topics which contains a flavor of linear algebra ...
81
votes
9answers
26k views

Learning mathematics as if an absolute beginner? [closed]

I dread mathematics, and I believe it's because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the ...
6
votes
1answer
178 views

How to know if you are “tough enough” to study Algebraic Topology [closed]

I am graduating with a BA this summer and I am very interested in topology. I admit it, I never went that deep into topology and all I know is about point-set topology (metric spaces etc.) but from ...
20
votes
4answers
838 views

How do I tell if I am able to go to graduate school in math? [closed]

This is my first question on this site, and this question may sound disturbing. My apologies, but I truly need some advice on this. I am a sophomore math major at a fairly good math department (top ...
4
votes
2answers
281 views

Too “young” for advanced mathematics?

Is it harmful to try to learn an advanced topic that is way beyond your mathematical maturity, even if you're really interested in it? Should I focus only on standard material for undergraduates and ...
2
votes
0answers
29 views

GRE Math Resources

I am planning to give the MATH GRE. I intend to go to physics graduate schools but I may have to given the MATH GRE according to my college's requirement. I very much like maths, but I'm overloaded ...
0
votes
1answer
27 views

Number theory text.And advices.

What do you suggest as a must number theory text maybe leaning towards diophantine equations.I think im gonna do a project as an undergraduate.And my topic i think it will be " Aplications of ...
0
votes
1answer
126 views

Any advice to help visualizing/understanding theorems in Real Analysis?

I am currently taking a real analysis course and sometimes I can't really get the complete meaning/details of certain theorems. For example, one of the statements in the Heine-Borel Theorem saying ...
3
votes
2answers
666 views

Two sets can be separated by a hyperplane iff their convex hulls do not intersect

So I am supposed to prove that two sets of points in $\mathbb{R}^n$ are linearly separable in an n-dimensional space if and only if their convex hulls do not intersect. I understand the concept ...
1
vote
1answer
46 views

Spivak's Calculus for a soon to be physics undergraduate.

I'll soon start my undergrad. studies in physics and because of that I picked up Spivak's Calculus a while ago to get a solid foundation in single-variable calculus before I start my studies. However, ...
2
votes
2answers
76 views

Studying mathematics as an Undergraduate [closed]

This is not a question related to a certain topic in mathematics, but more a question about studying mathematics generally. (please forgive me if my vocabulary isn't appropiate, I'm not a native ...
3
votes
1answer
59 views

Calculus by Spivak - looking for a piece of advice from someone who has been through it.

I am currently self-studying Calculus by M. Spivak and before I started I was well aware of the fact that it is not an easy read. Right now I am going through the problems at the end of the very first ...
1
vote
4answers
69 views

Mathematics for Guidance, navigation and control

I'm finishing my math degree this week and have been looking for some subject to practice and study on my own while I'm doing some work as a programmer. I'm interested in getting my master's later but ...
0
votes
0answers
5 views

Reference for $L$ functions

What is the best possible reference to study $L$ functions for a beginner in this field? I have studied up to the Chebotarev Density Theorem in Algebraic Number Theory. Depending on that, which book/...
26
votes
4answers
2k views

How much time is too much (to put into a single problem)?

As a self-studier, I have no due dates and no time pressure. This is partly a good thing since I do have a life outside of my pursuit of mathematics. However, the lack of pressure is also a bad ...
3
votes
2answers
73 views

Dissertation on Integrals

I'm considering doing a dissertation on Integrals: Riemann, Henstock-Kurzweil, Lebesgue and more I'm wondering if I can do it. This is usually a masters level dissertation (while I'm an undergraduate ...
0
votes
0answers
27 views

Advice on Research topics in Linear Algebra

I am a rising senior undergraduate student. I have taken following courses and I have an opportunity to do a project in Applied Linear Algebra at a fairly good Mathematics department. I am trying to ...
54
votes
6answers
3k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
4
votes
2answers
284 views

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

What books or broad survey articles survey the mathematics of the last 50-100 years? The ones I've read do a good job conveying mathematics from the ground up but typically assume a complete beginner ...
0
votes
1answer
89 views

How to do complicated problem without messy mind?

I have trouble when doing complicated problem, when I look at a problem with so much information. (e.g. deal with some concrete example such as proving a 'ugly' space is homeomorphic to another 'ugly' ...
4
votes
0answers
66 views

Concrete Mathematics: Not taught how to solve problems.

I've read and studied the first 3 paragraphs from Concrete Mathematics and now I've made the first couple of problems. When I got to the actual homework problems I was lost because I tried to solve ...
20
votes
5answers
2k 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 ...
9
votes
4answers
1k views

Where can one find (freely, online) mathematical articles with a fighting chance to be understood by high school students and undergraduates?

I am an undergraduate non-math major. I just finished my university's engineering calculus series, looking forward to linear algebra in the coming semester. To be frank, I always despised math because ...
14
votes
8answers
1k 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 ...
92
votes
5answers
4k 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 ...
5
votes
3answers
9k views

What is the most effective way of teaching mathematics to my 7 year old kid? [closed]

I want to help my kid excel in Math. I can see she has some trouble with additions,subtraction, multiplication and division. Will it help if I let her memorize the multiplication table? or use ...
44
votes
25answers
3k views

What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus. My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have ...
2
votes
2answers
67 views

Will conquering the two basic actuary exams, p and fm, be too difficult to do alone? [closed]

I'm currently a PhD student in mathematics at a decent sized graduate school, but I've been questioning my desire to continue on and finish my doctorate after I achieve my master's, which will occur ...
1
vote
3answers
4k views

James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've ...
1
vote
0answers
50 views

Good books on Algorithms for a math major without any programming experience?

I couldn't find this question anywhere else so it may not be apt. I am an undergraduate mathematics major and during my discrete math class I really enjoyed the study of algorithms and recursive ...
2
votes
1answer
300 views

A Compact Real Analysis book for a graduate student, who is short of time.

I am a Phd student in Computer Science and I want to focus on Machine Learning, especially on statistical methods. My problem is, I always keep hitting the wall when it comes to studying underlying ...
3
votes
0answers
23 views

Looking for references for learning the words and sentences used in proofs

I'm familiar with textbooks on logic, proof techniques, and sets. But I have yet to encounter a textbook that dives into the language used w/ definitions and sentence structure used in proofs, for ...
0
votes
3answers
71 views

Where to start Stochastic processes

This semester I have the course stochastic processes in university but as our instructor is awful I can't rely on him and I should study this course on my own.To start, I need a suitable book for self-...
11
votes
4answers
2k views

Is it bad to keep aside Lang's Algebra in graduate school?

Question is as it is stated in title. I will be joining for PhD program in this July 2014. I am interested in working in Algebra/Algebraic Geometry/Algebraic Number Theory. I tried to learn algebra ...
0
votes
2answers
42 views

Dealing with computations that are tedious and time consuming

In attempting mathematics homework question one of the greatest redundancies I generally face is having to deal with long winded and tedious computations. For instance, in the field of Quantum ...
0
votes
0answers
55 views

Graduate student in Number Theory, need advice on choice of courses

I am starting my MSc in Mathematics next Fall (European university) and I intend to lean more towards number theory. Each semester, in addition to some elective courses in number theory, I have to ...
3
votes
1answer
65 views

What are Stochastic Processes and Combinatorics useful for?

I am a math major and I am trying to figure out what math classes I want to take next semester. My question is what industries are Stochastic Processes and Combinatorics useful for? I haven't ...
2
votes
1answer
145 views

How to conceptualize unintuitive topology?

I found Project Origami: Activities for Exploring Mathematics in my university's library the other day and quickly FUBAR'd (folded-up beyond all recognition) the couple sheets of paper I had with me ...
2
votes
2answers
108 views

Advice for an undergraduate math major [closed]

I've recently switched into the mathematics department at my university preceding my second sophomore semester. My question is the following: What should I study over the summer to best aid my ...
1
vote
2answers
34 views

How to do large number of arithmetic operations

I'm having trouble with doing long arithmetic operations. Generally if the equation involves addition, subtraction, division and multiplication and it's larger than 2-3 lines of A4 paper, I can be ...
0
votes
0answers
35 views

*ADVICE* Intuition about techniques for disproving the existence of simple groups of given order

Looking for some feedback on how to know when to use the different techniques for disproving there are no simple groups of a given order. the techniques being: 1) counting elements 2) using ...
1
vote
0answers
79 views

Understanding Higher Orders and Levels of Mathematics [closed]

this is a more general question than the most. As a background, I'm currently a graduate student getting my masters in mathematics. I have what I believe is a strong passion for mathematics, though ...
2
votes
1answer
96 views

Stochastic processes book suggestions.

I would like to find a book that introduces me gently to the subject of stochastic processes without sacrificing mathematical rigor. It would be great if the book has lots of examples and that the ...
25
votes
6answers
3k views

How long to do math each day? [closed]

I have seen some posts math.SE (mkko's answer) indicating that it is the norm for (undergrad?) math majors to study 70-80 hours per week. I'm a little bit shocked by that. For some background on me, I'...
26
votes
4answers
4k views

Pure mathematics curriculum for self study with interests in foundational issues [closed]

I wonder if I want to make my own pure mathematics curriculum to study along the next 4 or 5 years. What topics should I include? I want it to be like one which an undergraduate student of pure ...
8
votes
5answers
5k views

What are the prerequisites for taking introductory abstract algebra?

I am a maths student in my second year of university. I have taken and done quite well in Calculus I, II, III as well as a linear algebra (application focused) class. I have not worked much with ...
0
votes
1answer
43 views

Abstraction and/or concreteness - What should be emphasized

Alexandar Grothendieck was probably a mathematician focusing on theory developement and abstraction much much more than focusing on concrete examples and/or problems. In his biography, he wrote: ...
0
votes
1answer
105 views

Question about Bachelor thesis and future lectures. [closed]

I just finished my exams one day ago but lectures will already reassume in less than two weeks. I currently finished my 5th semester and will therefore tackle my last semester of my bachelors. But I'm ...