Self-learning university mathematics

Basic

• Set theory
• Logic

Analysis

• Complex Analysis
• Real Analysis
• Functional Analysis
• Ordinary/Partial Differential Equation
• Fourier Analysis
• Wavelets
  • A First Course in Wavelets with Fourier Analysis by Albert Boggess, Francis J. Narcowich
• Measure theory

Algebra

• Linear Algebra
• Abstract Algebra
• Galois Theory
• Representation Theory for Group and Algebra
• Algebraic Number Theory
• Algebraic Topology
• Coding and cryptography

Geometry

• Topology
• Differential Geometry
• Differentiable Manifold
• Lie Group and Lie Algebras
• Riemannian Geometry
• Graph theory
• Fractal
• Algebraic Geometry

Statistics

• Probability
• Multivariate Statistics
• Stochastic Process
• Time Series

Programming

• Optimization
  • Introduction to nonlinear optimization: theory, algorithms, and applications with MATLAB
• Operations Research
• Combinatorics Mathematics
• Optimizing Controls

Computational Math

• Discrete Mathematics
• Numerical Methods
• Parallel Computing
• Nonlinear Mathematical Physics Method
• Computational Fluid Dynamics
• Numerical Solution of Partial Differential Equation
• Intelligent Computation

Finance

• Financial information analysis
• Quantitative Economics
• Mathematical Finance