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.
Street Fighting Mathematics is a course on problem solving with approximation and dimensional analysis.
Jim Hefferon’s introductory Linear Algebra treats vector spaces, linear mappings, determinants, eigenvalues and eigenvectors.
Calculus by Gilbert Strang is an introduction to one variable and multivariate calculus.
Advanced Calculus by Shlomo Sternberg tackles mathematical analysis in normed vector spaces and differentiable manifolds. Fourier’ transform, Sturm-Lieuville theory etc. are considered.
Complex Variables and Analysis offers illustrated lecture notes and Mathematica notebooks and Maple worksheets.
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.
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. Illustrative Mathematica programs are available with the book.
“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.
Gerard ’t Hooft reviews most used special functions [PDF, 134 KiB, 11 pp.] and their more important properties.
Quick introduction to tensor analysis by Ruslan Sharipov introduces tensors via basis transformations of vector spaces. Tensors in linear as well as curved spaces are treated.
In an overview, Stefan Waner covers the differential geometry needed for understanding general relativity, and finally discusses black holes.
John Baez gives in “Categories, Quantization, and Much More” a popular review of categories, and discusses their use in physics.
The 1st chapter of Toposes, Triples and Theories by Michael Barr and Charles Wells is on category theory, the rest on topos theory.
Created: 14.08.2004
Changed: 09.03.2008