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Online Master of Science in Applied & Computational Mathematics

Course Descriptions

Core Courses

All courses are worth five credits.

AMATH 501: Vector Calculus & Complex Variables

Quarter: Autumn

This course emphasizes acquisition of solution techniques. It illustrates ideas with specific example problems arising in science and engineering. The curriculum includes applications of vector differential calculus, complex variables, line and surface integrals, integral theorems, Taylor and Laurent series, and contour integration.

AMATH 502: Introduction to Dynamical Systems & Chaos

Quarter: Winter

This course provides an overview of methods that describe the qualitative behavior of solutions on nonlinear differential equations. The curriculum includes phase space analysis of fixed pointed and periodic orbits, bifurcation methods, a description of strange attractors and chaos, and an introduction to maps. It highlights applications to engineering, physics, chemistry and biology.

AMATH 503: Methods for Partial Differential Equations

Quarter: Spring

This course covers separation of variables, Fourier series and Fourier transforms, Sturm-Liouville theory and special functions, eigenfunction expansions and Green’s functions.

Prerequisite: AMATH 501

AMATH 581: Scientific Computing

Quarter: Autumn

This course uses a project-oriented computational approach to solving problems arising in the physical and engineering sciences; finance and economics; and the medical, social and biological sciences. The problems studied require the use of advanced MATLAB routines and toolboxes. The course also covers graphical techniques for data presentation and communication of scientific results.

AMATH 584: Applied Linear Algebra & Introductory Numerical Analysis

Quarter: Autumn

This course studies the use of numerical methods for solving linear systems of equations. The curriculum includes linear least squares problems, matrix eigenvalue problems, nonlinear systems of equations, interpolation, quadrature and initial-value ordinary differential equations.

Other Applied Math Courses

All courses are worth five credits.

AMATH 515: Fundamentals in Optimization

Quarter: Winter (offered odd years)

The course covers fundamental concepts in optimization, with a focus on applications. We’ll start with basic convex analysis, conjugacy and Fenchel duality. We’ll move on to a range of applications, discussing modeling, algorithms and problem structure. In particular, you’ll explore sparse and robust regression, nonlinear inverse problems, time series applications and topics in machine learning (including neural nets).

AMATH 575: Dynamical Systems

Quarter: Spring (offered odd years)

This course offers an overview of the ways in which complex dynamics arise in nonlinear dynamical systems. Topics include bifurcation theory, universality, Poincare maps, routes to chaos, horseshoe maps, Hamiltonian chaos, fractal dimensions, Lyapunov exponents and the analysis of time series. We'll study examples from biology, mechanics and other relevant fields.

Prerequisite: AMATH 502

AMATH 582: Computational Methods for Data Analysis

Quarter: Winter

The course includes exploratory and objective data analysis methods applied to the physical, engineering and biological sciences. It includes a brief review of statistical methods and their computational implementation for studying time series analysis, image processing and compression, spectral analysis, filtering methods, principal component analysis and orthogonal mode decomposition.

AMATH 583: High-Performance Scientific Computing

Quarter: Spring

This course features an introduction to hardware, software and programming for large-scale scientific computing. It includes an overview of multicore, cluster and supercomputer architectures; procedure and object oriented languages; parallel computing paradigms and languages; graphics and visualization of large data sets; validation and verification; and scientific software development.

Prerequisite: AMATH 581

AMATH 585: Numerical Analysis of Boundary Value Problems

Quarter: Winter (offered even years)

This course covers numerical methods for steady-state differential equations, two-point boundary value problems and elliptic equations, iterative methods for sparse symmetric and non-symmetric linear systems, conjugate gradients and preconditioners.

Prerequisite: AMATH 581 or AMATH 584

AMATH 586: Numerical Analysis of Time-Dependent Problems

Quarter: Spring (offered even years)

This course focuses on numerical methods for time-dependent differential equations, including explicit and implicit methods for hyperbolic and parabolic equations. It also covers stability, accuracy, and convergence theory; and spectral and pseudospectral methods.

Prerequisite: AMATH 581, AMATH 584 or AMATH 585

AMATH 600: Independent Research or Study

Quarter: Varies

Students will independently seek faculty to supervise their work in this course and develop a mutual understanding of how the independent study requirement can be satisfied. Some examples include reading book chapters or research papers beyond standard course material, or conducting original research under the guidance of the faculty member. To earn credit as an elective, students must take four credits, which are typically taken over two quarters. Students who are interested should review the full Independent Study Policy.