## Courses

A number of mathematics online courses are offered at the graduate level. These may be taken as part of a certificate or degree program, or by non-degree-seeking students on a course-by-course basis. For those interested in taking individual courses without enrolling in a degree or certificate program, you must first apply to be a non-degree studies (NDS) student. To learn more about enrolling as an NDS student or registering for courses, visit our Apply page.

Our graduate-level mathematics online courses are designed to provide convenient access to the training that is often required for career advancement. The application process is very simple, and online courses can be taken individually for continuing education or for the online master's program. Find descriptions of our graduate-level mathematics online courses below.

The Graduate Certificate in Mathematics requires 12 credits of coursework from this list of approved classes. At least 9 credits must be from courses at the 500 level or above.

#### MA 402 - Mathematics of Scientific Computing

Units: 3

This course will provide an overview of methods to solve quantitative problems and analyze data. The tools to be introduced are mathematical in nature and have links to Algebra, Analysis, Geometry, Graph Theory, Probability and Topology. Students will acquire an appreciation of [I] the fundamental role played by mathematics in countless applications and [II] the exciting challenges in mathematical research that lie ahead in the analysis of large data and uncertainties. Students will work on a project for each unit. While this is not a programming class, the students will do some programming through their projects.

Offered in Fall and Spring

#### MA 405 - Introduction to Linear Algebra

Units: 3

This course offers a rigorous treatment of linear algebra, including systems of linear equations, matrices, determinants, abstract vector spaces, bases, linear independence, spanning sets, linear transformations, eigenvalues and eigenvectors, similarity, inner product spaces, orthogonality and orthogonal bases, factorization of matrices. Compared with MA 305 Introductory Linear Algebra, more emphasis is placed on theory and proofs. MA 225 is recommended as a prerequisite. Credit is not allowed for both MA 305 and MA 405

Offered in Fall Spring Summer

#### MA 493 - Special Topics in Mathematics

Units: 1 - 6

Directed individual study or experimental course offerings.

Offered in Fall and Spring

#### MA 501 - Advanced Mathematics for Engineers and Scientists I

Units: 3

Survey of mathematical methods for engineers and scientists. Ordinary differential equations and Green's functions; partial differential equations and separation of variables; special functions, Fourier series. Applications to engineering and science. May not be taken for graduate credit by Master's or Ph.D. students in Mathematics or Applied Mathematics. Credit for this course and MA 401 is not allowed.

Offered in Fall Spring Summer

#### MA 502 - Advanced Mathematics for Engineers and Scientists II

Units: 3

Determinants and matrices; line and surface integrals, integral theorems; complex integrals and residues; distribution functions of probability. Not for credit by mathematics majors. Any student receiving credit for MA 502 may receive credit for, atmost, one of the following: MA 405, MA 512, MA 513

Offered in Spring Only

#### MA 507 - Survey of Real Analysis

Units: 3

A broad overview of topics in analysis. Historical development, logical refinement and applications of concepts such as limits, continuity, differentiation and integration. May not be taken for graduate credit by Master's or Ph.D. students in Mathematics or Applied Mathematics.

Offered in Fall Spring Summer

YEAR: Offered Alternate Years

#### MA 508 - Survey of Geometry

Units: 3

A broad overview of topics in geometry. Various approaches to study of geometry, including vector geometry, transformational geometry and axiomatics. May not be taken for graduate credit by Master's or Ph.D. students in Mathematics or Applied Mathematics.

Offered in Fall Spring Summer

YEAR: Offered Alternate Years

#### MA 509 - Survey of Abstract Algebra

Units: 3

A broad overview of topics in abstract algebra. Theory of equations, polynomial rings, rational functions and elementary number theory. May not be taken for graduate credit by Master's or Ph.D. students in Mathematics or Applied Mathematics.

Offered in Fall Spring Summer

YEAR: Offered Alternate Years

#### MA 510 - Selected Topics In Mathematics For Secondary Teachers

Units: 1 - 6

Coverage of various topics in mathematics of concern to secondary teachers. Topics selected from areas such as mathematics of finance, probability, statistics, linear programming and theory of games, intuitive topology, recreational math, computers and applications of mathematics. Course may be taken for graduate credit for certification renewal by secondary school teachers. Credit towards a graduate degree may be allowed only for students in mathematics education.

Offered in Spring and Summer

YEAR: Offered Alternate Years

#### MA 511 - Advanced Calculus I

Units: 3

Fundamental theorems on continuous functions; convergence theory of sequences, series and integrals; the Riemann integral. Credit for both MA 425 and MA 511 is not allowed

Offered in Fall and Spring

#### MA 513 - Introduction To Complex Variables

Units: 3

Operations with complex numbers, derivatives, analytic functions, integrals, definitions and properties of elementary functions, multivalued functions, power series, residue theory and applications, conformal mapping.

Offered in Fall and Spring

#### MA 520 - Linear Algebra

Units: 3

Vector spaces. Bases and dimension. Changes of basis. Linear transformations and their matrices. Linear functionals. Simultaneous triangularization and diagonalization. Rational and Jordan canonical forms. Bilinear forms.

Offered in Fall and Spring

#### MA 523 - Linear Transformations and Matrix Theory

Units: 3

Vector spaces, linear transformations and matrices, orthogonality, orthogonal transformations with emphasis on rotations and reflections, matrix norms, projectors, least squares, generalized inverses, definite matrices, singular values.

Offered in Fall and Spring

#### MA 540 - Uncertainty Quantification for Physical and Biological Models

Units: 3

Introduction to uncertainty quantification for physical and biological models. Parameter selection techniques, Bayesian model calibration, propagation of uncertainties, surrogate model construction, local and global sensitivity analysis.

Offered in Fall and Spring

YEAR: Offered Alternate Even Years

#### MA 580 - Numerical Analysis I

Units: 3

Algorithm behavior and applicability. Effect of roundoff errors, systems of linear equations and direct methods, least squares via Givens and Householder transformations, stationary and Krylov iterative methods, the conjugate gradient and GMRES methods, convergence of method.

Offered in Fall and Spring

#### MA 591 - Special Topics

Units: 1 - 6

Offered in Fall and Spring