7
votes
0answers
64 views

Value in retracing mathematicians' steps (specifically Galois)?

So I'd like to learn Galois Theory, which I am probably not "qualified" for in an ordinary sense (I've never done abstract algebra, and I'm just now learning linear algebra in my vector calculus ...
2
votes
0answers
36 views

Typical course of study chart [closed]

I am an undergraduate student in math and am very interested in the field. I have bought a few books and self-studied on my own as i have free time. The next book i found on amazon was riemannian ...
10
votes
5answers
157 views

Algebraic topology in high school?

This winter I am planning on teaching a small seminar (20 lectures 45 minutes each) for high school students. I was was given the freedom to choose the topic of the seminar, but it is supposed to be ...
6
votes
3answers
147 views

Books that you think you should have read during your undergraduate years

A quite popular question here is "If you could go back in time and tell yourself to read a specific book at the beginning of your career as a mathematician, which book would it be?" I would like to ...
2
votes
1answer
63 views

Math required for medical statistics

I have never been good with Math. I talk to many of my medical colleagues and it seems to me that most of them have a poor understanding of statistics. Many of them claim to understand it but actually ...
12
votes
5answers
358 views

I need help finding a rigorous Pre-calculus textbook

I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor ...
1
vote
1answer
85 views

A tenth grader's starting point on mathematics

This question primarily concerns the elementary books a Canadian high school student could read and work through to gain further insight into mathematics and be attracted to it. My brother, who has ...
3
votes
1answer
56 views

Re professional mathematicians working on several problems at once. Source needed.

Recently I read a quote from a working mathematician where he pointed out that professionals have to get used to carrying around several unsolved problems at once. Can anyone help me with the source ...
4
votes
0answers
90 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 ...
0
votes
0answers
95 views

Multivariable calculus and real analysis in one semester. What is the best way to study for such course?

I am in my first year of EECS and planning on taking a lot of maths classes. I have already taken single variable calculus and linear algebra and did well in them and decided to take multivariable ...
8
votes
3answers
1k 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 ...
7
votes
1answer
94 views

Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
0
votes
2answers
211 views

List of Advanced Math Text Books with answers

Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of ...
1
vote
1answer
83 views

Book: Functional Calculus

Is there a good book that investigates in detail the various kinds of functional calculus? I'm having now some knowledge about unbounded operators and integration but I would like to understand ...
2
votes
1answer
126 views

What should a student (with algebraic-geometry minded) study in differential geometry?

One of my friend who is an undergraduate student, has known something about algebraic geometry (equivalent to chapter 1 and a little bit chapter 2 in GTM 52 by Hartshorne). He is now has to study a ...
28
votes
27answers
2k views

Gift advice: present for high school graduate interested in math

I am a PhD student in mathematics who recently found out that I will be attending my girlfriend's cousin's high school graduation party. I have never met the cousin, but hear that he is very ...
2
votes
1answer
104 views

Learning Advanced Mathematics

I'm a 12th grade student and I've recently developed a passion for mathematics . Currently my knowledge in this particular area is comprised by : single-variable calculus , trigonometry , geometry , ...
11
votes
6answers
1k 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 ...
1
vote
1answer
58 views

Where can I find good examples about Algebra (but not only): Usual counter-examples, but also limit cases, rare ones, etc [duplicate]

I recently discovered the importance of examples and couter-examples in mathematics. Where could I find good examples books or anything related to it ? I am particularly looking for rare limit-cases, ...
4
votes
2answers
156 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 ...
4
votes
0answers
187 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
260 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 ...
2
votes
1answer
405 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
387 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 ...
8
votes
0answers
306 views

How much time is reasonable to complete baby Rudin?

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) ...
3
votes
0answers
77 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 ...
4
votes
1answer
110 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, ...
-2
votes
4answers
140 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.?
9
votes
4answers
2k views

How to do well on Math Olympiads

I'm a high school student who really likes maths and I'm quite good at school. I want to start training maths by myself but I think I need some guidelines. I want to do well on IMO but I don't know ...
4
votes
2answers
160 views

Recommendation for learning math [duplicate]

I'm in the 11th grade. At the bachelor exam, my main focus will be on mathematics and informatics. I'm a hard working man, but due to the school norms, I can consider myself idiot at math. Why? ...
1
vote
1answer
144 views

Understand calculus

I am a computer engineering student and lately every thing I see includes math. I have taken all the math courses any one in college should have taken (high school : alg,trig & geom, -sophomore: ...
1
vote
2answers
65 views

First time writing a survey on population models

I am a graduate student trying to write a survey paper on population models. I am new to writing mathematical papers as you guessed. My professor did not give me much direction, but from what I ...
1
vote
1answer
304 views

Callahan's Advanced Calculus: A Geometric View vs Hubbard's Vector C, L A, and Di Forms vs Ad- Calculus: A Differential Forms Approach by Edwards

My friend has given me the chance to get one of the books mentioned in the title of this question for free. I've learned single variable calculus. Which one of these books do you think would best ...
5
votes
0answers
141 views

which branch of maths studies Standard Logical Matrices

In classical logic you have truthtables like: & | T | F ---|---|--- T | T | F F | F | F In many valued logic you have tables like: (this one is ...
4
votes
0answers
97 views

A partial ordering on textbooks

After college, it has been very difficult to continue learning math as a hobby, I have the time for it, but I get incredibly frustrated when I run into something that it feels like I will never ever ...
1
vote
1answer
216 views

Which topics of real-analysis should be studied if you have already done calculus

Which parts of real-analysis are worth studying if you have already taken several calculus courses? I know that real-analysis is more 'rigurous', but still I wonder whether it is worth to again go ...
5
votes
2answers
380 views

What are some reasonable things to prove about the Collatz Conjecture?

I am writing an undergraduate paper on the $3n+1$ problem, and I am looking for some theorems related to the problem that would be reasonable for someone with my mathematical background to prove. I'm ...
12
votes
1answer
474 views

Practical Tips: Mathematical research and discoveries [closed]

How to be when you are working on something innovative? What to do if there is a chance (even the $1\%$) that your work is leading you to something original? For example what have I do if I ...
11
votes
7answers
627 views

Making up for wasted high school years - where should I begin?

I realize this question is long and quite personal but any help will be greatly appreciated. I'm a senior high school student. I've learnt maths at precalculus level. I have had little exposure to ...
29
votes
8answers
2k views

How to use math textbooks

I'm a higher schooler who was recently gifted a book by my teacher (Schaum's outline of advanced calculus) which is really awesome and I've started working my way through it. I have run into a ...
16
votes
3answers
652 views

What's next for me?

I'm in my last year of undergrad, and I would like to do original research for my senior thesis. I am already published in finite group theory and am looking for a new topic to study. I have taken ...
1
vote
1answer
802 views

possible topics for undergraduate project. [closed]

i don't know whether it will be appropriate to ask this question here or not but i need help. we have to a project in either pure or applied mathematics. my supervisor told me that it should not be ...
3
votes
1answer
391 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" ...
5
votes
2answers
370 views

Advice about taking mathematical analysis class

I appologize if this isn't the place to ask, if it's not could you let me know and I will take it to meta? Anyway, so I am planning on taking a mathematical analysis course next spring, and I'm really ...
3
votes
1answer
152 views

Lattices inside matrix groups $SL_2(K)$

I am currently a second year undergraduate majoring in math and our university is offering an opportunity for undergraduates to do a project over the summer break. I have spoken to my professor who is ...
5
votes
4answers
3k views

Advanced Linear Algebra courses in graduate schools

After studying general a linear algebra course, how would an advanced linear algebra course differ from the general course? And would an advanced linear algebra course be taught in graduate schools? ...
3
votes
2answers
372 views

Advice for study plan.

I'm studying math by myself, and now I'm wondering what is the most appropriate for me to study. I think my interest goes to rather pure mathematics than applied math or math for engineers. So far I ...
68
votes
24answers
13k views

Complete course of self-study

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
5
votes
0answers
150 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-module and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, and A Primer of Algebraic D-Modules ...
13
votes
7answers
2k views

Teaching abstract maths concepts to young children.

I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) ...