Ken C. Y. Leung
About me
I obtained Mathematics BSc from the Chinese University of Hong Kong and Master of Data Science from the University of Hong Kong.
Book Recommendations
Abstract Algebra
Dummit, Foote - Abstract Algebra (Third Edition)
Morandi - Field and Galois Theory
Algebraic Geometry
Cox, Little, Schenck - Toric Varieties
Fulton - Algebraic Curves
Algebraic K-Theory
Magurn - An Algebraic Introduction to K-Theory
Rosenberg - Algebraic K-Theory and Its Applications
Differential Geometry
O'Neill - Semi-Riemannian Geometry With Applications to Relativity
Tu - An Introduction to Manifolds (Second Edition)
Tu - Differential Geometry: Connections, Curvature, and Characteristic Classes
Lie Theory
Hall - Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Second Edition)
Knapp - Lie Groups Beyond an Introduction (Second Edition)
Varadarajan - An Introduction to Harmonic Analysis on Semisimple Lie Groups
Mathematical Finance
Björk - Arbitrage Theory in Continuous Time (Third Edition)
Mathematical Physics
Hall - Quantum Theory for Mathematicians
Number Theory
Diamond, Shurman - A First Course in Modular Forms
Marcus - Number Fields (Second Edition)
Neukirch - Algebraic Number Theory
Operator Algebras
Blackadar - Operator Algebras: Theory of C*-Algebras and von Neumann Algebras
Davidson - C*-Algebras by Example
Murphy - C*-Algebras and Operator Theory
Strătilă, Zsidó - Lectures on von Neumann Algebras
Point-set Topology
Wilansky - Topology for Analysis
Links
Mathematics
Mathematics@CUHK A mathematics blog maintained by mathematics students and alumni from CUHK
Alain Connes The author of the brilliant book “Noncommutative Geometry”. The book is freely available on the web site.
Lieven Vandenberghe There are several lecture notes for the courses he taught and the book “Convex Optimization” for download
James Milne Many high quality free lecture notes and books on such areas as Algebraic Number Theory, Algebraic Geometry, etc.
K. Conrad’s Expository papers Very interesting and educational expositions to various topics in mathematics
Pete Clark Contains a set of nice lecture notes on commutative algebra
Peter Woit The lecture notes on Lie groups and on quantum mechanics are excellent