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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0
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0answers
21 views

Algebra required for doing number theory [on hold]

How much homological algebra and representation theory are needed for doing number theory and what are the best possible references for learning these two fields?
26
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4answers
1k 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
66 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
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0answers
24 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
279 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
83 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
59 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
6answers
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 ...
1
vote
3answers
50 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 ...
8
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 ...
91
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
54 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
48 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
288 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
65 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 ...
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
39 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
52 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
62 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
143 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
102 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
78 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
89 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, ...
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
4k 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
39 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
102 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 ...
15
votes
12answers
10k views

Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...
6
votes
3answers
235 views

How to Catch Up?

I am finishing up my bachelor's degree in mathematics at the University of North Florida, and I plan on going to graduate school, but I feel very behind. One of my professor's gave us this problem: ...
28
votes
6answers
5k views

Is a good GRE score enough for a non-math graduate to be accepted in a decent pure mathematics graduate program?

I have a computer engineering degree , and i have studied several mathematics courses like single variable and multiples variables calculus , complex variables , probability , numerical analysis ... ...
19
votes
7answers
4k views

Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
73
votes
8answers
8k views

What made you choose your research field?

I was wondering how come modern mathematicians do not seem to discover as many theorems as the older mathematicians seem to have done. Have we reached some kind of saturation limit where all commonly ...
4
votes
3answers
547 views

Independent math learning

I'm an undergraduate math and econ major and I'm planning on graduating relatively soon and I am very limited to the number of math classes I have left (very sad about this fact). So far I have ...
9
votes
6answers
11k 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 ...
34
votes
4answers
6k views

Learning Roadmap for Algebraic Topology

I am now considering about studying algebraic topology. There are a lot of books about it, and I want to choose the most comprehensive book among them. I have a solid background in Abstract Algebra, ...
1
vote
1answer
109 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 ...
0
votes
2answers
132 views

Textbook for Mathematical Logic

I am about to take an undergraduate course in Mathematical logic any textbooks to recommend.Want it to be rigorous and not missing things. I am an Math undergraduate. Got still 2 years for my degree. ...
6
votes
2answers
188 views

suggesting books on Field/galois theory

I have finished courses on group theory and ring theory and linear algebra and abstract algebra(inrroducton with fraleigh's book) im about to take field/galois theory this semester any good book not ...
2
votes
2answers
56 views

How to write this non-linear Epsilon-Delta proof w/ a radical?

The question: Prove that $\lim \limits_{x \to 9} 2+\sqrt{x} = 5$. After reading this link from Milefoot on how to construct a non-linear delta-epsilon proof (second example), this is what I came up ...
5
votes
2answers
402 views

Numerical analysis, differential equations, complex analysis for statistics

I am a student of the Statistics Department. And now I can choose a subject from such list: numerical mathematics (analysis), differential equations, complex analysis, real analysis. Can you please ...
2
votes
1answer
133 views

Can you recommend a mathematical logic textbook that is easy to understand?

I started studying "Introduction to Mathematical Logic, Sixth Edition" by Elliot Mendelson. I tried to not read solutions as long as possible, but most exercises were awfully difficult to me, and the ...