**Ph.D. Programs**

** **Ph.D. degrees are also offered in both **Mathematics** and **Computer Science**, and Ph.D. students may work on any area of interest offered by the department.

**Graduate elective courses (for both M.Sc. and Ph.D. degrees):**

Aside from the above-required courses, here is a list of M.Sc. and Ph.D. courses offered by the department over the past few years:

**Combinatorics and Graph Theory: **

Combinatorial Analysis I, Graph Theory I, Algebraic Combinatorics, Algebraic Graph Theory, Graph Theory II, Combinatorial Analysis II, Topics in Combinatorics, Topics in Graph Theory, and Combinatorics.

**Algebra, Number Theory, and Algebraic Geometry: **

Topics in Number Theory, Noncommutative Rings, Number Theory, Division Rings, Homological Algebra, Algebraic Geometry II, Valuation Theory, Arithmetic Geometry, Commutative Algebra, Algebraic Number Theory II, Noncommutative Rings II, Linear Groups, Topics in Number Theory, Algebraic Number Theory, Topics in Algebraic Geometry, Homological Algebra II, Category Theory, Group Representation, Commutative Algebra II, Topics in K-Theory, Noncommutative Algebra, Lie Algebra, Homological Methods in Commutative Algebra, Arithmetic of Elliptic Curves, Character and Representation Theory, Ring Theory, Topics in Algebra, Quadratic Forms, and Finite Groups.

**Probability, Statistics, and Financial Mathematics: **

Financial Mathematics, Probability Theory, Advanced Probability Theory, Stochastic Analysis, Stochastic Differential Equations, Statistic Theory I, Numerical Solutions of SDE, Topics in Statistics, Advanced Statistics, Probability Theory II, Stochastic Evolution Equations, Topics in Probability, Numerical SPDE, and Topics in Probability.

**Analysis, Differential Equations, and Dynamical Systems:**

Theory of PDE, Harmonic Analysis I, Algebraic Geometry I, Parabolic PDE Theory, Functional Analysis, Calculus of Variations, Semigroups of Linear Operators, Theory of PDE II, Applied Functional Analysis, Applied Analysis I, Variational Methods in Analysis, Topics in PDE, Integral Equations, Elliptic Equations, Applied Analysis II, Inverse Problems, Dynamical Systems, Topics in Analysis, Topics in Biomathematics, Approximation Theory, Biomathematics, Finite Elements Methods, Dynamical Systems II, Functional Analysis II, Topics in Dynamical Systems, Hyperbolic PDE, and Numerical PDE.

**Geometry, Topology, and Complex Analysis: **

Topics in Geometry of Manifolds, Topics in Algebraic Topology, Differential Geometry, Hyperbolic Geometry, Symplectic Geometry, Complex Geometry, Complex Analysis, Riemannian Geometry, Topics in Complex Analysis, Algebraic Topology II, Differential Topology, Differential Manifolds II, Topics in Geometry, and Principle Bundles.

**Optimization, Numerical Analysis, and related subjects:**

Topics in Numerical Analysis, Nonlinear Optimization, Control Theory, Advanced Linear Optimization, Advanced Nonlinear Optimization, Introduction to Control Theory, Topics in Mathematical Modeling, Integer Programming, and Numerical Linear Algebra.

**Computer Science: **

Complexity Theory, Geometric Modeling and Design, Advanced Mathematical Software, Advanced Theory of Computation, Topics in Computer Science, Parallel Algorithms, Computational Geometry, Advanced Topics in Computer Science and Technology, Distributed Artificial Intelligence, Quantum Computations, Topics in Cryptology, Topics in Theory of Computation, Foundations of Theoretical Cryptography, Machine Learning Theory, Advanced Topics in Algorithms, Coding Theory.

**Logic: **

Model Theory, Computational Logic, Constructive Mathematics, Heyting Arithmetic, Advanced Logic, Topics in Logic, Models of Arithmetic and Set Theory, Formal Methods, Proof Theory, and Topics in Mathematical Logic.