Lie Groups and Lie Algebras
Differential equations with continuous symmetries that possess both group and manifold structures
Mathematician Terence Tao’s Personal Website
This website primarily documents Terence Tao’s mathematical research progress, lectures, teaching materials, books, and other content. The material generally requires a strong mathematical background to understand, covering topics such as harmonic analysis, partial differential equations, and number theory. However, it also offers very detailed educational advice aimed at a general audience, spanning mathematics learning recommendations from elementary school through postdoctoral studies.
Calculus: An Intuitive and Physical Approach
This book is especially suited for understanding calculus from a physical perspective. Many concepts in physics become remarkably simple when approached through the ideas of calculus, eliminating the need to memorize formulas or rote problem-solving techniques.
Probability Theory: Written for the Passionate Beginner
This book covers all the standard introductory topics in probability theory, including combinatorics, probability rules, Bayes' theorem, expectation, variance, probability density, common distributions, the law of large numbers, the central limit theorem, correlation, and regression analysis. It also features 150 detailed solved problems.
What Is Algorithmic Hegemony?
When algorithms are placed in the wrong context, they cease to be neutral tools