Brief book that introduces you to Zermelo-Fraenkel set theory. Anyone that has studied combinatorics / algebra / analysis is probably familiar with “naive set theory”, eg: union, intersection, complement, etc. But despite the book’s name, it introduces you to axiomatic set theory. The problem with naive (non-axiomatic) set theory is it allows you to construct…
Category: Mathematics
Information Theory: A Tutorial Introduction by James V. Stone (8.0/10)
Ch1: What is Information? Information is quantified using bits, not to be confused with binary digit. A binary digit contains at most one bit of information, but may contain less (if it’s not equally likely to be 0 and 1). Ch2: Entropy of Discrete Variables Definition of entropy H(x) for discrete random variables. Entropy can…
How Not to Be Wrong by Jordan Ellenberg (6.8/10)
Kind of like the Freakonomics of math, describes a variety of situations where math (mostly statistics) is useful in real life. Some of it is heuristics to avoid common fallacies, then a mix of random topics with tenuous connection to real life events, but the author doesn’t have much of a coherent point to make….
Fifty Challenging Problems in Probability by Frederick Mosteller (6.6/10)
A classic book with a bunch of random problems in elementary probability (but not statistics). They are not very difficult, ranging from easy to moderate in difficulty. Some of them touch on significant ideas (like random walks, coupon collector problem, German tank problem), but the majority are quite arbitrary (maybe suitable for a contest problem)….
Birth of a Theorem by Cedric Villani (7.4/10)
Memoir by Fields medalist Cedric Villani describing the process of discovering a mathematical proof. It’s inspiring that even for somebody as smart as him, math is difficult and he doesn’t always know what he’s doing. However, he does a poor job of explaining the math — his expositions are way too technical, aimed at the…