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.

  1. What are some of the good practices, tips for an undergraduate mathematics student?
  2. To gain more proficiency, do I do many exercises on one topic?
  3. What is a reasonable amount of time, I should devote to mathematics every week?
  4. Vector calculus. To make it interesting, I plan to read on electromagnetism(see here). Is that a good idea?
  5. Real analysis. Is merely understanding a proof good enough, or being able to reproduce it is also equally important?

closed as primarily opinion-based by José Carlos Santos, Math1000, KReiser, mrtaurho, Lord Shark the Unknown Jan 6 at 4:49

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    $\begingroup$ Interesting. I got a PhD in math, and afterwards I've been working as a quantitative analyst at an investment firm for 5 years. However, the math I specialized in is not at all applicable to my job, and it sounds like you do want that. $\endgroup$ – Matt Samuel Jan 5 at 19:57
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    $\begingroup$ you need a solid background in real analysis and linear algebra to go beyond, so start by selecting two textbooks about these topics and complete them. Math need some time, yes. $\endgroup$ – Masacroso Jan 5 at 20:06