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

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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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