I am teaching a graduate course on Advanced Mathematical Physics in Semester 2 2019/2020. The reference book used is Peter Szekeres, “A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry“. This page will host the notes for this course. Note: Readers are asked to refer to the reference book or articles for most proofs (unless it becomes essential for proper understanding).
Sets and Structures
- Logical Underpinnings of Set Theory
- Sets and Set Operations
- Cartesian Products and Relations
- Set Mappings
- Infinite Sets and Numbers
Groups, Rings and Fields
- Groups and Subgroups
- Transformation Groups – Permutations
- Transformation Groups – Matrix Groups
- Group Homomorphisms & Isomorphisms
- Cosets, Normal Subgroups, Quotient Groups and Direct Products
- Rings and Fields
- Algebraic Numbers
Modules and Vector Spaces
Ketchup Spills 