The PhD in Mathematics at the University of Wisconsin–Madison trains scholars in fundamental and applied mathematical disciplines. Students engage in original research across pure and applied fields such as algebra, topology, analysis, and computational mathematics, preparing for careers in academia, research, finance, and technology.
Algebraic Structures in Cryptographic Systems
Geometric Topology and Knot Theory Applications
Nonlinear Partial Differential Equations in Fluid Dynamics
Category Theory and Homological Algebra Connections
Numerical Methods for Solving High-Dimensional PDEs
Mathematical Modeling of Infectious Disease Spread
Proof Complexity in Formal Logic Systems
Analytic Number Theory and Distribution of Primes
Spectral Graph Theory and Network Analysis
Mathematical Foundations of Machine Learning Algorithms
Ergodic Theory in Dynamical Systems
Applications of Lie Groups in Quantum Mechanics
Combinatorial Optimization and Integer Programming
Algebraic Geometry in String Theory
Variational Methods in Image Processing
Symplectic Geometry in Hamiltonian Systems
Stochastic Calculus in Financial Mathematics
Theory of Computability and Undecidability
Functional Analysis in Control Theory
Mathematical Statistics in High-Dimensional Data
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