- Single Variable Calculus - Spivak - "Calculus", Stewart - "Calculus - Early Transcendentals"
- Linear Algebra - Friedberg, Insel, Spence - "Linear Algebra"
- Multivariable Calculus - Spivak - "Calculus on Manifolds", Stewart - "Calculus - Early Transcendentals"
- Point Set Topology - Munkres - "Topology"
- Ordinary Differential Equations - Meinrenken Lecture Notes
- Basic Probability (i.e. not measure theoretic) - Rice - "Mathematical Statistics and Data Analysis"
- Abstract Algebra - Grillet - "Abstract Algebra"
- Complex Analysis - Ahlfors - "Complex Analysis", Cartan - "Analytic functions of one or several complex variables", Bierstone Lectures on Complex Analysis
- Real Analysis (metric space topology, Weierstrass approximation, Arzela-Ascoli) - Pugh - "Real Mathematical Analysis"
- Smooth Manifolds - Lee - "Introduction to Smooth Manifolds", Milnor - "Topology from the Differentiable Viewpoint", Gualtieri Lecture Notes
- Algebraic Number Theory - Milne - "Algebraic Number Theory", Marcus - "Number Fields"
- Measure Theory and Lebesgue Integration - Folland - "Real Analysis"
- Functional Analysis (Banach and Hilbert spaces, Fourier analysis, distributions) - Folland - "Real Analysis"
- Functional Analysis (Topological vector spaces, hyperplane separations, spectral theory) - Conway - "A Course in Functional Analysis"
- Riemannian Geometry - Petersen - "Riemannian Geometry", do Carmo - "Riemannian Geometry"
- Lie Groups, Lie Algebras - Meinrenken Lecture Notes, Bröcker, Dieck - "Representations of Compact Lie Groups"
- Representation Theory - Knapp - "Representation Theory of Semisimple Groups", Woit - "Quantum Theory, Groups and Representations"
- Combinatorics - Stanley - "Enumerative Combinatorics"
- Algebraic Topology - Hatcher - "Algebraic Topology", Bott and Tu - "Differential Forms in Algebraic Topology", May - "A Concise Course in Algebraic Topology"
- Partial Differential Equations - Evans - "Partial Differential Equations", Haslhofer Lecture Notes
- Characteristic Classes - Milnor and Stasheff - "Characteristic Classes"
- Bundles and K theory - Hatcher - "Vector Bundles and K-theory", Taubes - "Differential Geometry: Bundles, Connections, Metrics and Curvature", Meinrenken Lecture Notes, Kobayishi and Nomizu - "Foundations of Differential Geometry"
- Index Theory - Lawson and Michelsohn - "Spin Geometry", Meinrenken Lecture Notes, Nicolaescu Lecture Notes
- Complex Geometry - Huybrechts - "Complex Geometry"
- Symplectic Geometry - Meinrenken Lecture Notes, da Silva - "Lectures on Symplectic Geometry", Jeffrey - "Hamiltonian Group Actions and Equivariant Cohomoloy"
- Hyperbolic Geometry /Teichmüller Space - Hubbard - "Teichmüller Theory", Imayoshi and Taniguchi - "An Introduction to Teichmüller Spaces"