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 | Classical 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 | Foundational language of modern mathematics. | Notes |
| Geometry | ||
| Complex Manifolds | Manifolds with complex structure with applications in geometry and physics. | Notes |
| Lie Groups | Manifolds with group structure with applications in geometry and physics. | Notes |
| Scheme Theory | Schemes generalize of algebraic varieties in contemporary algebraic geometry. | Notes |
| 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 their linear operators. | Notes |