I am Quasar. A quick two-liner about my background - worked as programmer for five to six years, landed my first international assignment as a quantitative analyst in an investment bank, currently pursuing an open university BS mathematics (from IGNOU).
These are the courses I am taking in my second year.
- Vector Calculus
- Differential and integral calculus (of two and three variables)
- Real Analysis
- Ordinary Differential equations with an introduction to PDEs
- Numerical methods
I would like to master the content, learn undergraduate mathematics well. I want to develop confidence in my ability to prove things, without a hint. I would like to write tiny solvers in C++ for numerical algorithms. I want to lay a strong foundation for a graduate course.
To that end,
- I have begun taking rigorous notes for each subject. I motivate myself, by posting these to my blog Quantophile.com.
- I do the exercises from one or two well-known books on each subject.
- I would try my best to understand all details of all proofs, see if I can prove a result without looking at the solution or prove similar results.
I have a few questions on my mind.
- What are some of the good practices, tips for an undergraduate mathematics student?
- To gain more proficiency, do I do many exercises on one topic?
- What is a reasonable amount of time, I should devote to mathematics every week?
- Vector calculus. To make it interesting, I plan to read on electromagnetism(see here). Is that a good idea?
- Real analysis. Is merely understanding a proof good enough, or being able to reproduce it is also equally important?