Notes
This page contains notes I’ve written while studying various mathematical topics.
These notes were written for personal reference, so they may not be properly referenced/formatted, and some remain unfinished. Feel free to explore them. If you spot any typos, please let me know at junaid.aftab1994@gmail.com.
| Topic | Description | Link |
|---|---|---|
| Algebraic Topology | ||
| (Co)homology & Homotopy | Topological invariants for classifying and distinguishing topological spaces. | Notes |
| Topological K-Theory | A cohomology theory for vector bundles, with applications in topology and physics. | Notes |
| Category Theory | ||
| Foundations | Categories, functors, natural transformations, and universal properties form the foundational language of modern mathematics. | Notes |
| Functional Analysis & Operator Algebras | ||
| C*-Algebras | Algebras of operators on Hilbert spaces, with applications in quantum physics. | Notes |
| Linear Analysis | Theory of infinite-dimensional vector spaces and the linear operators between them. | Notes |
| Geometry | ||
| Complex Manifolds | Smooth manifolds with complex structures, central to geometry and physics. | Notes |
| Lie Theory | ||
| Lie Groups | Smooth manifolds with a group structure, fundamental in geometry and physics. | Notes |