[Home] Mathematical Resources
Advice and Stories
“Contemporary Linear Algebra” by Howard Anton and Robert C. Busby.
Essense of Linear Algebra by 3blue1brown. “Finite-Dimensional Vector Spaces” by Paul R. Halmos.
“Numerical Linear Algebra” by Lloyd N. Trefethen and David Bau, III.
“Abstract Algebra: Theory and Applications” by Thomas W. Judson.
A Sage-based introduction to abstract algebra. A lot of interesting exercises. “Algebra: Chapter 0” by Paolo Aluffi.
Category-flavored introduction to algebra with a bit of humor. Commutative Algebra and Algebraic Geometry
“Naive Lie Theory” by Stillwell.
Very accessible, with many interesting historical remarks. “Lie Groups, Lie Algebras, and Representations” by Brian C. Hall.
“Representations of Compact Lie Groups” by Theodor Bröcker and Tammo tom Dieck.
“Lie Groups Beyond an Introduction” by Anthony Knapp.
“Representation Theory” by William Fulton and Joe Harris.
Lecture notes by Thomas Krämer. “Introduction to Representation Theory” by Pavel Etingof et al.
“Quantum Groups” by Christian Kassel.
“An Introduction to Homological Algebra” by Joseph J. Rotman.
80 minutes introduction to homological algebra by Rishi Vyas. The
snake lemma makes a short (and perfectly accurate!) cameo in It's My Turn (1980). “A User's Guide to Spectral Sequences” by John McCleary.
“Differential Geometry of Curves and Surfaces” by Kristopher Tapp.
“Introduction to Smooth Manifolds” by John M. Lee.
“Riemannian Geometry” by Sigmundur Gudmundsson.
Lectures on Geometrical Anatomy of Theoretical Physics by Fredric Schuller. “Riemannian Manifolds: An Introduction to Curvature” by John M. Lee.
“Riemannian Geometry” by Manfredo do Carmo.
“A Comprehensive Introduction to Differential Geometry” by Michael Spivak.
“Introductory Functional Analysis with Applications” by Erwin Kryszig.
“A Course in Functional Analysis” by John B. Conway.
Lecture notes by Alan Sokal. Mathematics and Society
“Mathematics++” by Ida Kantor, Jiří Matousek and Robert Šámal.
Computer-scientifically flavored introductions to measure theory, Fourier analysis, representation theory, algebraic geometry and topology.
notes collection on a wide array of subjects.
An Infinitely Large Napkin by Evan Chen. “Introduction to Experimental Mathematics” by Søren Eilers and Rune Johansen.
Just for fun