I am Quasar. A quick two-liner about my background - Computer science undergraduate, with a standard curriulum(single & multi-variable calculus, linear algebra, elementary probability and statistics) worked as programmer for five years before switching fields and now a risk analyst at an investment bank.
I like to self-learn. I enjoy solving probability problems(from Joe Blitzstein's book, William Feller is an awesome read!), or reading about elementary analysis; it makes me tick. I have about 3-4 hours of study time in the evenings.
I am enrolling myself in for a two-year graduate level course(MSc. in mathematics) through distance mode at a local university here. The course material gets delivered to your home, and I would be required to self-learn.
I know, there are no shortcuts. I am dilligent, energetic and determined to take serious efforts, learn as much as possible, get to a point, where I can write mathematical proofs myself, learn new areas like measure theory, functional analysis, solve ODEs and PDEs and gain mathematical maturity.
Here's the course curriculum:
- 110 Modern Algebra
- 120 Real Analysis
- 130 Differential geometry and differential equations
- 140 Analytical mechanics and Tensor analysis
- 210 Complex Analysis
- 220 Set Topology and Functional Analysis
- 230 Graph Theory
- 240 Mathematical Statistics
I know that, topics like real analysis are introduced to students of pure mathematics at an undergraduate level. I would like to therefore, specifically ask, given that I am not a pure math undergrad, what are some of the best books I can buy to self-learn these subject areas? Also, how do I know, that I've mastered a topic for sure?
It would be real nice, if you could suggest two books on each topic - one which provides great intuition and another which is more rigorous.
Thanks a tonne!