References on probability theory, stochastic processes, Monte Carlo and convex optimisation, with similar writing style to Terence Tao

Question

I learned a lot from prof Tao's notes and books because unlike many authors, he seems to prefer writing more words, explanations and intuitions rather than just mathematical formulae. His approach is also very pedagogical, and quite often, when talking about one concept, he also talks about similar concept in other fields, like group theory, differential geometry, etc. (due to his very broad areas of expertise). This makes me understand (superfically) how mathematical concepts are related to each other.

I would like to know if there are some books or blogs on probability theory, stochastic processes, Monte Carlo and convex optimisation, with similar writing style and approach.

Many thanks!!!

Answer 1

It's hard to tell what you need, since this depends on the level of complexity and sophistication you're targeting, and most importantly, what you aim to learn from these books. Here are a few references that might help.

Convex analysis (in increasing order of "difficulty"):

• "Convex Optimization", S. Boyd et al.
• "Introductory Lectures on Convex Optimization", Y. Nesterov
• "Lectures on Modern Convex Optimization", A. Nemirovski et al.
• "Convex analysis and monotone operator theory in Hilbert spaces", H. Bauschke et al.

Probability theory:

• "An introduction to probability theory and its applications", William Feller.

Answer 2

Here is a good link for books to learn on the probability theory. Some are more in depth while others meant for more casual reading. There are also a bunch of puzzles on the blog along with some that have code on them, that help with understanding the concepts.