Comprehensive math books for summer self-study

[ahmed markhoos]

Hello,

I'm planning to spend my summer studying some physics and maths books.

Physics books aren't my problem, math books are. I took " calculus 1/2 & differential equations " till now and a material of mathematical methods (vector analysis/general coordinates/complex/gamma-beta functions/ differential equations).

I was thinking about one of two books:
1- Mathematical methods in the physical sciences By: Mary Boas (We used it for mathematical methods).
2- Mathematics: Its content, methods and meaning By: A. D. Aleksandrov , A. N. Kolmogorov ,M. A. Lavrent’ev.

They say they are both good, but I'm really hesitated between the two and between other good books.

 

[micromass]

Those are very very different books, both in style and in contents. Maybe you should tell us what your goals are? Why do you want to learn math?

 

[ahmed markhoos]

Those are very very different books, both in style and in contents. Maybe you should tell us what your goals are? Why do you want to learn math?

Thank you for your reply.

I have actually two main goals:
1- I want to prepare myself mathematically for subjects like quantum/statistical and physics as whole.
2- I'm interested in math even if it's not related with physics.

-- Sometimes I get really lost when I try to recognize my feelings toward math. I really like it as a subject that has no boundaries except rationality, but at the same time most of what they teach in math majors "or maybe a big branch of math" are bunch of meaningless formulas and rigid symbols-- at least this is their way of teaching. I really don't like that kind of math, things like Brouwer fixed point theorem, combinatorics really attract me to math. actually I think this is why I'm majoring physics. LoL, anyway it's just thoughts.

 

[micromass]

If you want to prepare for QM or stat mech, then I recommend studying linear algebra and probability. Boas should be good for that. But you might also want to study it more rigorously (which would be helpful for QM). Treil has a free textbook that is really good: http://www.math.brown.edu/~treil/papers/LADW/LADW.html (I hope you are a bit familiar with matrices and basic vectors).