I was thinking of self-studying Measure, Integral and Probability - Marek Capinski, Springer Undergraduate Mathematics Series, over the summer holidays (~13 weeks). However, I would like to know whether this proposal is feasible and would like to hear your opinions!
Some background info:
1) I finish my first year of undergraduate studies in summer
2) Formally, I have taken courses in linear algebra, single and multi-variable calculus, mathematical analysis (Introduction to Real Analysis - Bartle), calculus-based probability (A First Course in Probability - Sheldon Ross). I have previously done some self-study on Riemann integral (Elementary Analysis - Kenneth Ross) and ordinary differential equations (Paul’s notes - Lamar University) though I will have to revisit the latter two formally.
The long-term goal in mind is to learn stochastic calculus in finance by the third/ fourth year of undergraduate studies. But I know there are many prerequisites to pick up: measure theory, measure-theoretic probability, discrete stochastic processes, continuous stochastic processes and then finally stochastic calculus. As such, I have decided to start by first learning measure theory and further probability.
However, I know that this plan will not be easy, as a level of mathematical maturity is required.
So if you feel that my project is not feasible (maybe because I will find myself struggling at every step), feel free to suggest any alternatives that are along the line of mathematical finance!
- If the aforementioned text is too advanced, would A Second Course in Probability - Sheldon Ross be more appropriate? Here is the book review by the Mathematical Association of America - https://www.maa.org/press/maa-reviews/a ... robability
I hope to hear from you soon!
Galvinator