Notes

A collection of my notes from in mathematics from both college and my PhD. They are organized mostly by subject and area of interest. If you have any questions or find any of the copius errors shoot me an email!

Classes Taken at UChicago

• Algebraic Number Theory, taught by Kato in 2024: The Poetry of Number Theory and the Geometry of the Primes .
• Riemannian Geometry, taught by Neves in 2024: Riemannian Geometry .
• Lie Groups and their Lattices, taught by Benson Farb in 2024: Lie Groups and Their Lattices
• Probability Theory, taught by Ewain Gwynne in 2024: Probability Theory
• The Geometry and Topology of Solutions to Algebraic equations , taught by Benson Farb in 2025.
• Persistent Homology , taught by Leonid Polterovich and Schmuel Weinberger in 2025.

Classes Taken at U(M)

• Combinatorics
  • Intro to Combinatorics: MATH 465 Notes and LaTeX zip
• Geometry and Analysis
  • Analysis in Euclidean Space: MATH 395 Notes and LaTeX zip
  • Analysis on Manifolds: MATH 396 Notes and LaTeX zip
  • Graduate Real Analysis (measure theory, Hilbert/Banach spaces, LpL^pLp spaces): MATH 597 Notes and LaTeX zip
  • Graduate Complex Analysis: MATH 596 Notes and LaTeX zip
• Probability
  • Intro: MATH 525 Notes and LaTeX zip
• Topology
  • Algebraic Topology: MATH 592 Notes and LaTeX zip
  • Algebraic Topology II: MATH 695 Notes and LaTeX zip
  • Differential Topology: MATH 591 Notes and LaTeX zip
• Algebra
  • Group Theory and Representation Theory: MATH 493 Notes and LaTeX zip
  • Honors Algebra II (rings,fields, modules, and Galois Theory): MATH 494 Notes and LaTeX zip
• Analytic Number Theory
  • Modular Forms: MATH 678 Notes and LaTeX zip
• 297 Problem Sessions INCOMPLETE
  • These notes were created for the 297 Problem Sessions I hosted as a course assistant. They cover a variety of topics, such as elementary group theory and point-set topology.

Templating

The template files I use for my LaTeX can be downloaded here . If you have any contributions to make those template files are also on Github . Also thanks to Wen for allowing me to use his preamble which can be found on Gitlab