Graduate Courses

Featured Courses [Spring 2021]

Basic equations governing compressible and incompressible fluid mechanics. Finite difference and finite volume schemes for hyperbolic, elliptic, and parabolic partial differential equations. Practical applications in low Reynolds number flow, high-speed gas dynamics, and porous media flow. Software design and use of public-domain codes. Students with credit for MATH 930 may not complete this course for further credit.

MATH 740 - Galois Theory (cross-listed with MATH 440) 

Galois theory studies roots of polynomial equations, combining field theory and group theory to study symmetries of these equations. Famously, these ideas led to a proof that (unlike the quadratic formula for degree-2 polynomials) no formula exists to solve polynomial equations of degree 5 or more. Proving this theorem is one goal of this class.

How do we represent formulas on a computer? How fast can we multiply integers and polynomials? Can we factor polynomials in polynomial time? This course is about computing with mathematical objects symbolically. This includes numbers, polynomials, and elementary functions.

Featured Courses [Fall 2020]

APMA 920 - Numerical Linear Algebra

The course is aimed at students interested in scientific computing and modeling. We will cover a variety of topics in numerical linear algebra and its applications with an emphasis on understanding stability (robustness) and speed. We will develop, analyze and implement a range of algorithms and see how they work in practice and theory. We program and test our methods in Matlab – almost no prior knowledge is assumed.

MATH 747 - Coding Theory (cross-listed with MATH 447)

How did the Mariner 9 space probe transmit high-resolution photos of Mars to Earth 50 years ago? How can a compact disc play back music perfectly even after the disc surface is damaged? How do cellphones maintain call quality despite signal reflections from buildings and noise from other calls? Explore the hidden mathematics behind modern communications.

MATH 708 - Discrete Optimization (cross-listed with MATH 408)

Discrete optimization is a field that has grown almost from scratch in the past 70 years. This development is driven in part from its applicability to a wide range of practical problems, such as scheduling and network design, and its close ties to computer science. However, it is also a beautiful mathematical topic that connects to diverse areas of mathematics, including classical problems in combinatorics, algebra and geometry.

Mathematics 600-Level Courses

MATH 603-4: Foundations of Mathematics *
MATH 604-4: Geometry *

* These courses cannot be taken toward Mathematics MSc or PhD program requirements

Mathematics 700-Level Courses

MATH 701-3: Computer Algebra
MATH 708-3: Discrete Optimization
MATH 709-3: Numerical Linear Algebra and Optimization 
MATH 716-3: Numerical Analysis II
MATH 718-3: Partial Differential Equations
MATH 719-3: Linear Analysis
MATH 724-3: Applications of Complex Analysis   
MATH 725-3: Real Analysis
MATH 739-3: Algebraic Systems
MATH 740-3: Galois Theory
MATH 741-3: Commutative Algebra and Algebraic Geometry
MATH 742-3: Cryptography
MATH 743-3: Combinatorial Theory
MATH 745-3: Graph Theory
MATH 747-3: Coding Theory
MATH 748-3: Network Flows
MATH 761-3: Continuous Mathematical Models   
MATH 762-3: Fluid Dynamics
MATH 767-3: Dynamical Systems
MATH 770-3: Variational Calculus
MATH 795-3: Selected Topics in Applied Mathematics
MATH 796-3: Selected Topics in Mathematics

Mathematics 800-Level Courses

MATH 800-4: Mathematics: Selected Topics
MATH 801-4: Computer Algebra
MATH 808-4: Advanced Linear Programming
MATH 817-4: Groups and Rings
MATH 818-4: Algebra and Geometry
MATH 819-4: Algebra: Selected Topics
MATH 820-4: Graph Theory
MATH 821-4: Combinatorics
MATH 827-4: Discrete Mathematics: Selected Topics
MATH 831-4: Real Analysis I
MATH 833-4: Analysis: Selected Topics
MATH 841-4: Topology: Selected Topics
MATH 842-4: Algebraic Number Theory
MATH 843-4: Analytic and Diophantine Number Theory
MATH 845-4: Number Theory: Selected Topics
MATH 846-4: Cryptography
MATH 875-0: PhD Preliminary Examination
  > Resources
MATH 876-0: PhD Comprehensive Examination
  > Resources
MATH 877-1: Supplementary Reading
MATH 879-0: PhD Thesis Proposal
MATH 880-6: MSc Project
MATH 888-0: Ph.D. Comprehensive Examination: Operations Research
MATH 890-0: Practicum I
MATH 891-0: Practicum II
MATH 894-2: Reading
MATH 895-4: Reading
MATH 898-6: MSc Thesis
MATH 899-12: PhD Thesis

Mathematics 900-Level Courses: Applied and Computational Mathematics

APMA 900-4: Asymptotic Analysis of Differential Equations
APMA 901-4: Partial Differential Equations
APMA 905-4: Applied Functional Analysis
APMA 912-4: Advanced Partial Differential Equations
APMA 920-4: Numerical Linear Analysis
APMA 922-4: Numerical Solution of Partial Differential Equations
APMA 923-4: Numerical Methods in Continuous Optimization
APMA 929-4: Selected Topics in Numerical Methods
APMA 930-4: Computational Fluid Dynamics
APMA 934-4: Selected Topics in Fluid Dynamics
APMA 935-4: Analysis and Computation of Models
APMA 939-4: Selected Topics in Mathematical Image Processing
APMA 940-4: Mathematics of Data Science
APMA 981-4: Selected Topics in Continuum Mechanics
APMA 982-4: Selected Topics in Mathematical Physics
APMA 990-4: Selected Topics in Applied Mathematics
APMA 995-0: PhD Oral Candidacy Exam