**AMAT 530 Scientific and Numerical Computing I 3 Credits**

Prerequisite(s): MATH 335 or equivalent. Introduction to the mathematical and algorithmic foundations of numerical computing, and the practical implementation of solutions to scientific problems. Topics covered include error analysis, data fitting including interpolation, numerical solution of linear and nonlinear equations of one variable as well as systems of equations, numerical differentiation and integration, Monte Carlo simulation, and symbolic computing. Applications will include a variety of problems from the sciences, engineering, and economics. 3 hours lecture.

**AMAT 532 Applied Linear Algebra 3 Credits**

Prerequisite(s): MATH 335 or equivalent. Introduction to the theory and techniques of linear algebra. Topics covered include vector spaces and linear transformations, including inner product, matrix representations, binary and quadratic forms, eigenvectors, canonical forms, and functions of matrices. Applications include singular value decomposition, least squares approximation, and linear programming/optimization. 3 hours lecture.

**AMAT 534 Data-Driven Modeling and Computation 3 Credits**

Prerequisite(s): MATH 335 or equivalent. Introduction to the computational methods needed to perform data-driven modeling and analysis of scientific problems. Topics covered include an overview of statistical methods including hypothesis testing, time-frequency analysis using fast Fourier transform (FFT) and wavelets with application to filtering and averaging, image processing, model reduction using singular value decomposition (SVD), principal component analysis (PCA), and dynamic mode decomposition (DMD), and an introduction to machine learning and compressed sensing. 3 hours lecture.

**AMAT 536 Applied Probability and Stochastic Processes 3 Credits**

Prerequisite(s): MATH 340 or PHYS 320 or equivalent. Introduction to applied probability and stochastic processes. Topics covered include an overview of probability including random variables, expected values, random walks, probability densities, moment-generating functions, and normal variable theorems, Wiener process, Ornstein-Uhlenbeck processes, Langevin equations, Markov processes, Poisson process, and applications including survivability and reliability. 3 hours lecture.

**AMAT 540 Scientific and Numerical Computing II 3 Credits**

Prerequisite(s): AMAT 530 or equivalent. Introduction to the mathematical and algorithmic foundations of numerical computing, and the practical implementation of solutions to scientific problems involving numerical linear algebra and the solution of differential equations. Topics covered include direct methods for solving linear systems, iterative techniques, approximation of eigenvalues, and solution of ordinary differential equation initial-value problems using Runge-Kutta methods and multistep methods. Applications will include a variety of problems from the sciences, engineering, and economics. 3 hours lecture.

**AMAT 542 Methods of Applied Mathematics 3 Credits**

Prerequisite(s): MATH 420 or equivalent. Introduction to a selection of methods of applied mathematics. Topics covered include an overview of complex analysis including contour integration and residue calculus, calculus of variations, regular and singular perturbation theory including multiple-scales analysis and matched asymptotics. 3 hours lecture.

**AMAT 544 Applied Differential Equations 3 Credits**

Prerequisite(s): MATH 420 or equivalent. Introduction to the solution of ordinary and partial differential equations which arise as models in scientific applications. Topics covered include linear systems of ordinary differential equations including Floquet theory, Sturm-Liouville equations, Fourier solution of linear partial differential equations, method of characteristics, and hyperbolic conservation laws. 3 hours lecture.

**AMAT 546 Mathematical Biology 3 Credits**

Prerequisite(s): MATH 340 or PHYS 320; and MATH 420; or equivalent.
Introduction to mathematical modeling of biological and biomedical phenomena. Topics covered include population genetics, enzyme kinetics, protein networks, epidemiology, pharmacokinetics, and pattern formation. 3 hours lecture.

**AMAT 548 Nonlinear Dynamics 3 Credits**

Prerequisite(s): MATH 420 or equivalent. Introduction to nonlinear dynamics. Topics covered include an overview of discrete and continuous dynamics including bifurcation theory in one, two, and higher dimensions. 3 hours lecture.

**AMAT 649 Independent Study 3 Credits**

Prerequisite(s): Departmental approval. Independent study under the direction of a faculty member, offering the opportunity to pursue extensions of an existing course or courses. Approval must be obtained beforehand. May be repeated once for a maximum of six semester hours provided the topic is different.

**AMAT 650 Seminar 1 Credit**

Attendance at the Mathematical Sciences Colloquium. May be repeated for a maximum of 3 semester hours.

**AMAT 696 Internship 3 Credits**

Prerequisite(s): Permission of graduate program coordinator. Culminating project-based internship undertaken by students in their last year of study. The internship project focuses on a specific topic of interest to the student that incorporates and applies what they have learned throughout their time in the MS Applied Mathematics program.

**AMAT 697 Capstone 3 Credits**

Prerequisite(s): Permission of graduate program coordinator. Culminating project-based experience undertaken by students in their last year of study. The capstone project focuses on a specific topic of interest to the student that incorporates and applies what they have learned throughout their time in the MS Applied Mathematics program.

**AMAT 698 Master's Thesis 3 Credits**

Prerequisite(s): Departmental approval. Independent thesis research under faculty advisement. Students must follow the MSU Thesis Guidelines, which may be obtained from the Graduate School. Students should take AMAT 699 if they do not complete AMAT 698 within the semester.

**AMAT 699 Master's Thesis Extension 1 Credit**

Prerequisite(s): AMAT 698 and permission of GPC; Continuation of Master's Thesis Project. Thesis Extension will be graded as IP (in Progress) until thesis is completed, at which time a grade of Pass or Fail will be given. Independent thesis research under faculty advisement. Students must follow the MSU Thesis Gidelines, which may be obtained from the Graduate School. Students should take AMAT 699 again if they do not complete AMAT 699 within the semester.