# Suggestions for self-studying Mathematical analysis from Vladimir Zorich

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?