UF’s PhD in Mathematics provides advanced training in pure and applied mathematics, including algebra, analysis, topology, differential equations, and mathematical modeling. Students work closely with faculty on original research, theoretical proofs, and real-world applications. Graduates pursue academic, industrial, and governmental roles requiring deep mathematical insight.
Thesis on stability analysis of solutions to nonlinear partial differential equations
Research on symmetry groups in complex algebraic surfaces
Topological methods in fixed-point theorems and dynamical systems
Mathematical modeling of fluid dynamics in biomedical contexts
Spectral theory of differential operators in quantum mechanics applications
Proof of novel identities in analytic number theory and their implications
Graph theory analysis of network connectivity and resilience
Functional analysis of Banach spaces and compact operator behavior
Study of combinatorial optimization problems with graph coloring constraints
Numerical solution of inverse boundary value problems using finite element methods
Thesis on elliptic curves and cryptographic algorithm security
Research on knot invariants in low-dimensional topology
Mathematical epidemiology models for vector-borne disease control
Asymptotic analysis of special functions in applied physics
Study on non-Euclidean geometry applications in modern data science
Probabilistic modeling of random walks and Markov chain behavior
Thesis on curvature flow problems and geometric evolution equations
Optimization of PDE solvers for computational fluid mechanics simulations
Mathematical logic and model theory in proof complexity analysis
Study on linear algebraic groups and their representations in physics
Push the boundaries of mathematics through abstract reasoning, analysis, and problem-solving.
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