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I am studying the pre-requisites for applying to a mathematical finance course. I am a Comp Sci. engineering graduate.

For basic high-school Calculus, I mastered the material and solved examples from the book Differential calculus by N. Piskunov.

For Real Analysis, my plan is to study from Mathematical Analysis by Vladimir Zorich(volume I), which I find rigorous, but interesting. To supplment my understanding further, I intend to read Understanding Analysis by Stephen Abott.

I haven't taken a theorems or proofs based course in college. I think it is fair to assume, that it would take me atleast 6-8 months or more to learn these concepts.

  • That I am self-learning, would you have any suggestions, tips for understanding and studying real analysis?
  • Should I have my solved exercises, proofs typed in Latex for future reference?
  • There are some proofs, I can construct without much difficulty. For example, to prove that a set $A$ is countably finite, requires me to prove that there is a bijection from $N\rightarrow{A}$. But there are other theorems, which I understand, but often, I am not able to reproduce them. Would a student of mathematical analysis encounter such difficulties?
  • Are there any other videos on the internet (lectures) that use Vladimir Zorich as the text?
  • How do hone your skills in constructing proofs?

Thanks a tonne in advance,

Quasar C.

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Even the best mathematicians out there have all struggled when they first started a proof based course. It takes time and extreme patience. There are free courses to check out on Youtube for Real Analysis that I think could be helpful. If you have the time to write out you proofs in Latex then I think it would be helpful for future reference. Do not get bogged down with proofs that are difficult for you to prove, it is best to be able to extract the tricks and techniques of solving those proofs you find more challenging. Meaning knowing the key steps in solving the problem without actually solving it. As advice, I would say really try to do the proofs on your own without referring to a solution, I know that can be difficult but spending a few hours of thinking and trying to solve the problem is the best way to get better at doing proofs. Be patient, know the theorems and definitions and really try to understand their deeper meaning and why they are useful. With enough time and practice you will get better and better, keep up the good work.

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