Fermat's Little Theorem
Braid Groups
Quadratic Reciprocity
Unique Factorization and the Class Number
Insolvability of Quintics
Modular Forms
Error Correcting Codes
Representation Theory
Combinatorial Design Theory
Introduction to Tensor Products
Group/Galois Cohomology
Sylow's Theorems
Affine Algebraic Groups
Kummer Theory
Galois Theory
Matroid Theory
Generating Functions
Homological Algebra
Cayley Graphs
The Contraction Mapping Theorem
The Lorenz System and dynamics
Poincare-Bendixson Theorem, Recurrence
The Cantor set and Lebesgue measure
The Fourier Transform
Spectral Theory
The Gelfand-Mazur Theorem
Introduction to Measure Theory
Continuous Nowhere Differentiable Functions
Maxwell's Equations and Geometry
Lie Groups and Algebras
Projective Geometry
The Fundamental Group
Knot Polynomials
Dynamical Systems and Chaos Theory
Quaternions and Spatial Rotation
Isoperimetric Inequality
de Rham Cohomology
Classification of Surfaces
The Lorenz Attractor
Geodesic Equations
Lagrangian Systems
Variational Calculus
General Relativity
Introduction to Topology
Celestial Mechanics
Simplicial Homology
Hopf Fibrations
Riemann Surfaces
Morse Theory
Seifert-Van Kampen Theorem
Category Theory
Functor of Points and Affine Schemes
λ-Calculus and Cartesian Closed Categories
Model Theory
Lean
Persistent Homology
SIR Models in epidemiology
Signal Processing, Fourier Analysis
PageRank algorithm and Markov chains
The Capital Assets Pricing Model
Public-key cryptosystems
Elliptic Curve Cryptography
ODEs and Cancer Modeling
Natural Language Semantics
Fluids
Game Theory
Decision Trees