Plan:

学点基本的范畴论，以预备未来学习代数拓扑和同调代数更顺畅。

Basic Algebra:

Abstract algebra & basic category theory:

• Algebra: Chapter 0
• 代数学方法
• Category theory_S.Awodey,Category theory in context_Emily Riehl
• Algebra_S.Lang
• Basic algebra_Jacobson
• …

Physical literacture:

• Unitary Group Representations in Physics, Probability and Number Theory
• Group theory: application to group theory
• Moore系列notes：Abstract group theory, representation theory,Lie group,Clifford algebra,…
• Woit: Quantum theory,groups and representation
• …

Representation theory

• …

Commutative algebra and homological algebra:

• …

Group cohomology

• …

Algebraic topology

• Algebraic topology_Hatcher
• Rotman: introduction to algebraic topology
• Differential Forms in Algebraic Topology_Bott

Physical literature:

• Nakahara

K-theory:

• K-theory: an introduction