Here you will find notes I have written, made primarily from courses I have taken. I initially created these simply so that I could look up results easily and did not have to worry about taking my notes with me, and then it made sense to make them available for others to use. Many people like to have a second source they can refer to when taking a course, or to study independently. Whatever your reasons: please feel free to use these notes to aid your own learning. Often it is useful to learn from multiple sources, so that you can see different viewpoints and presentations of the same material. Be careful of any typos/errors — almost certainly they are my own — and feel free to let me know of any via email.
Undergraduate Analysis
Analysis I
Analysis II
Metric and Topological Spaces
Complex Analysis
Linear Analysis
Probability and Measure
Analysis of Functions
Undergraduate Geometry
Differential Geometry (Part II)
Part III/Postgraduate
Analysis of PDEs
Elliptic PDEs (example sheets here)
Functional Analysis
Distribution Theory
Differential Geometry (Part III) (example sheets here)
Complex Manifolds (example sheets here)
Algebraic Topology (Part III) (example sheets here)
Logic and Set Theory
Logic and Set Theory
Large Cardinals
Infinite Games
Miscellaneous/Graduate
Princeton Summer School in Geometric Analysis (2019)
The Minimal Surface Equation and Related Topics (Cambridge Easter 2021)
Regularity Techniques in Geometric Measure Theory (Princeton, Spring 2024)
Compactness 