The notes are aimed at introducing the mathematics required of convex modeling, rather than algorithms. Convexity is a universal phenomenon in tractable problems, but recognizing it is hard.
The material is largely synthesized from 3 sources-- I make no claim to the novelty of content:
(1) Professor Boyd and Professor Vandenberghe's Convex Optimization(primary source for my first section on Convex Sets and Functions)
(2) Professor El Ghaoui's notes, hyper-textbook, and class for EE 227 A-B (primary source for my second section on Convex Optimization, and in particular the historical anecdotes )
(3) Professor Bartlett lecture notes from CS 289 (primary source for applications in machine learning)
These sources provide go into much greater detail than I have. In particular, I have italicized technical terms. If the reader is unfamiliar with them, it would behoove her or him to search the term to learn more about it.
In the first section I cover convex functions and convex sets. I also cover the spectral decomposition theorem and the separating hyperplane theorem. In the second section I cover convex optimization models, with applications in machine learning and Boolean optimization.