Mathematics Textbooks

In his list of knowledge needed by good theoretical physicists, Nobel laureate Gerard ’t Hooft refers to mathematics and physics textbooks on the Web.

Mathematical Tools for Physics by James Nearing is a practical and friendly textbook.

Geometry and Imagination is a fancyful hands-on course on geometry.

Theoretical Computer Science Cheat Sheet [PDF, 154 KiB, 10 pp.] contains formulas from discrete mathematics, calculus, etc.

Linear Algebra

Jim Hefferon’s introductory Linear Algebra treats vector spaces, linear mappings, determinants, eigenvalues and eigenvectors.

Mathematical Analysis

Calculus by Gilbert Strang is an introduction to one variable and multivariate calculus.

Combinatorics

Generative functions, described in Herbert S. Wilf’s generatingfunctionology, bridge the gap between discrete mathematics and (complex) analysis. With generative functions, problems in combinatorics can be solved by means of analysis.

The Theory of Probability

Introduction to Probability by Charles M. Grinstead and J. Laurie Snell considers discrete as well as continuous probability theory, and concludes with generative functions, Markov chains and Brownian motion.

Lie Groups

“Lie Groups and Quantum Mechanics” by Michael Weiss gives an intuitive overview of Lie groups, Lie algebras, and spin in quantum mechanics.

An Elementary Introduction to Groups and Representations by Brian C. Hall treats Lie groups, Lie algebras and their relations, basics of representation theory; the SU(3) group is studied in detail.

Lie Groups and Representations by Peter Woit treates Lie groups, their representations, and connections with physics.

Special Functions

Gerard ’t Hooft reviews most used special functions [PDF, 134 KiB, 11 pp.] and their more important properties.