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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, highspeed gas dynamics, and porous media flow. Software design and use of publicdomain codes. Students with credit for MATH 930 may not complete this course for further credit.
MATH 740  Galois Theory (crosslisted 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 degree2 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 (crosslisted with MATH 447)
How did the Mariner 9 space probe transmit highresolution 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 (crosslisted 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 600Level Courses
MATH 6034: Foundations of Mathematics *
MATH 6044: Geometry *
* These courses cannot be taken toward Mathematics MSc or PhD program requirements
Mathematics 700Level Courses
MATH 7013: Computer Algebra
MATH 7083: Discrete Optimization
MATH 7093: Numerical Linear Algebra and Optimization
MATH 7163: Numerical Analysis II
MATH 7183: Partial Differential Equations
MATH 7193: Linear Analysis
MATH 7243: Applications of Complex Analysis
MATH 7253: Real Analysis
MATH 7393: Algebraic Systems
MATH 7403: Galois Theory
MATH 7413: Commutative Algebra and Algebraic Geometry
MATH 7423: Cryptography
MATH 7433: Combinatorial Theory
MATH 7453: Graph Theory
MATH 7473: Coding Theory
MATH 7483: Network Flows
MATH 7613: Continuous Mathematical Models
MATH 7623: Fluid Dynamics
MATH 7673: Dynamical Systems
MATH 7703: Variational Calculus
MATH 7953: Selected Topics in Applied Mathematics
MATH 7963: Selected Topics in Mathematics
Mathematics 800Level Courses
MATH 8004: Mathematics: Selected Topics
MATH 8014: Computer Algebra
MATH 8084: Advanced Linear Programming
MATH 8174: Groups and Rings
MATH 8184: Algebra and Geometry
MATH 8194: Algebra: Selected Topics
MATH 8204: Graph Theory
MATH 8214: Combinatorics
MATH 8274: Discrete Mathematics: Selected Topics
MATH 8314: Real Analysis I
MATH 8334: Analysis: Selected Topics
MATH 8414: Topology: Selected Topics
MATH 8424: Algebraic Number Theory
MATH 8434: Analytic and Diophantine Number Theory
MATH 8454: Number Theory: Selected Topics
MATH 8464: Cryptography
MATH 8750: PhD Preliminary Examination
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MATH 8760: PhD Comprehensive Examination
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MATH 8771: Supplementary Reading
MATH 8790: PhD Thesis Proposal
MATH 8806: MSc Project
MATH 8880: Ph.D. Comprehensive Examination: Operations Research
MATH 8900: Practicum I
MATH 8910: Practicum II
MATH 8942: Reading
MATH 8954: Reading
MATH 8986: MSc Thesis
MATH 89912: PhD Thesis
Mathematics 900Level Courses: Applied and Computational Mathematics
APMA 9004: Asymptotic Analysis of Differential Equations
APMA 9014: Partial Differential Equations
APMA 9054: Applied Functional Analysis
APMA 9124: Advanced Partial Differential Equations
APMA 9204: Numerical Linear Analysis
APMA 9224: Numerical Solution of Partial Differential Equations
APMA 9234: Numerical Methods in Continuous Optimization
APMA 9294: Selected Topics in Numerical Methods
APMA 9304: Computational Fluid Dynamics
APMA 9344: Selected Topics in Fluid Dynamics
APMA 9354: Analysis and Computation of Models
APMA 9394: Selected Topics in Mathematical Image Processing
APMA 9404: Mathematics of Data Science
APMA 9814: Selected Topics in Continuum Mechanics
APMA 9824: Selected Topics in Mathematical Physics
APMA 9904: Selected Topics in Applied Mathematics
APMA 9950: PhD Oral Candidacy Exam
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