Below there are some pdfs with my mathematical notes on different subjects. I constantly update them and some are partial because I didn’t finish typing all the content. They are very concise and more useful if your already know the underlying theory. Few of them present the intuition behind the concepts as well. I have found these notes useful when I needed a quick refresh of some concepts. If you find any incorrection or have any suggestion please send me an e-mail. The latex templates that I use to create such notes and the explanation of how I create them using tools I use in my workflow can be found here.
Set theory, Logic, and Proof: these are some of the building blocks of modern mathematics.
Measure Theory: Thanks to Kolmogorov (1933), the mathematical theory of probability is defined in terms of measure theory and Lebesgue theory of integration. Here are some notes on measure theory.
Topology: continuity and convergence concepts in its highest abstraction
Real Analysis: some notes on concepts of metric space, convergence of sequences, and continuity
Convex Optimization: if the objective function is convex, there is a beautiful analytic solutions for the optimization problem. Here are some concise notes on the underlying theory.