Course Schedule and Catalog

Long Title: INTRODUCTION TO ENGINEERING COMPUTATION

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture/Laboratory

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Modeling, Simulation, and Visualization via MATLAB. Numerical methods: Newton's method in one and several dimensions. Gaussian elimination and optimization. Application to problems in science and engineering. Lectures are held Monday and Wednesdays. In a laboratory component held on Fridays, students work in small groups on computational projects led by a Rice Learning Assistant. Recommended Prerequisite(s): MATH 101.

Long Title: MATRIX ANALYSIS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3 TO 4

Description: Equilibria and the solution of linear systems and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration. Optional 1-credit laboratory motivates concepts from the course via physical experiments involving circuits, spring networks, and vibrating mechanical systems. Recommended Prerequisite(s): (MATH 212 or MATH 222) and (CAAM 140 or COMP 210)

Long Title: DIFFERENTIAL EQUATIONS IN SCIENCE AND ENGINEERING

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Classical and numerical solution techniques for ordinary and partial differential equations. Fourier series and the finite element method for initial and boundary value problems arising in diffusion and wave propagation phenomena. Recommended Prerequisite(s): (MATH 212 or MATH 222) AND CAAM 210.

Long Title: INTRODUCTION TO OPERATIONS RESEARCH AND OPTIMIZATION

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Formulation and solution of mathematical models in management, economics, engineering and science applications in which one seeks to minimize or maximize an objective function subject to constraints, including models in linear, nonlinear and integer programming; basic solution methods for these optimization models; problem solving using a modeling language and optimization software. Recommended Prerequisite(s): MATH 212 and (CAAM 335 OR MATH 211 OR MATH 355).

Long Title: THEORETICAL NEUROSCIENCE I: BIOPHYSICAL MODELING OF CELLS AND CIRCUITS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: This course introduces current theoretical methods used to model the properties of nerve cells and the processing of information by neuronal networks. Concrete examples that can be implemented using MATLAB will be emphasized. The starting point is the passive cable properties of single neurons and the Hodgkin-Huxley model of action potential generation. Subsequently, models of synaptic transmission and active properties of dendritic trees will be considered. This will be followed by stochastic properties of single neurons and information encoding using mean and instantaneous firing rates in visual neurons. Finally, methods to analyze phase-locking and activity in populations of cells as well as learning algorithms will be considered. Cross-list: ELEC 488, NEUR 415. Recommended Prerequisite(s): MATH 211 OR CAAM 335.

Long Title: THEORETICAL NEUROSCIENCE II: LEARNING, PERCEPTION, AND COGNITION

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: The course will introduce methods to modeling of: perception and cognition (using Bayesian models), sensory coding, and the neurobiological basis of learning and memory. Cross-list: ELEC 489, NEUR 416. Recommended Prerequisite(s): CAAM 415 or NEUR 415.

Long Title: COMPUTATIONAL SCIENCE I

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture/Laboratory

Credit Hours: 3

Description: Scientific programming using high level languages, including C, Fortran, and C++. Emphasis on use of numerical libraries. Basic techniques of project planning, source management, documentation, program construction, i/o, visualization. Object-oriented design for numerical computing. Recommended Prerequisite(s): CAAM 419

Long Title: PARTIAL DIFFERENTIAL EQUATIONS I

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: First order of partial differential equations. The method of characteristics. Analysis of the solutions of the wave equation, heat equation and Laplace's equation. Integral relations and Green's functions. Potential theory, Dirichlet and Neumann problems. Asymptotic methods: the method of stationary phase, geometrical optics, regular and singular perturbation methods. Cross-list: MATH 423. Recommended Prerequisite(s): MATH 321 AND MATH 322

Long Title: DYNAMICAL SYSTEMS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Existence and uniqueness for solutions of ordinary differential equations and difference equations, linear systems, nonlinear systems, stability, periodic solutions, bifurcation theory. Theory and theoretical examples are complemented by computational, model driven examples from biological and physical sciences. Cross-list: MATH 435. Recommended Prerequisite(s): CAAM 210 AND MATH 212 AND (CAAM 335 OR MATH 355) AND (MATH 302 OR MATH 321).

Long Title: PARTIAL DIFFERENTIAL EQUATIONS OF MATHEMATICAL PHYSICS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Derivation and properties of solutions of the partial differential equations of continuum physics. Basic concepts of continuum mechanics, ideal fluids, Navier-Stokes equations, linear elasticity, acoustics, basic principles of thermodynamics, Newtonian heat flow, porous flow, Maxwell's equations, electrical circuits. Recommended Prerequisite(s): CAAM 336.

Long Title: APPLIED MATRIX ANALYSIS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: A second course in matrix analysis that presents advanced theoretical results alongside motivating applications. Topics include: properties of Hermitian, positive definite, nonnegative and stochastic matrices; Perron-Frobenius Theorem; spectral perturbation theory; singular value inequalities; generalized eigenvalue problems; functions of matrices; Lyapunov, Sylvester, and Riccati matrix equations. Applications include dynamical systems, control theory, and Markov chains.

Long Title: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture/Laboratory

Credit Hours: 3

Description: This course covers various numerical methods for solving partial differential equations: aspects of finite difference methods, finite element methods, finite volume methods, mixed methods, discontinuous Galerkin methods, and meshless methods. Both theoretical convergence and practical implementation of the methods are studied for elliptic and parabolic problems. Cross-list: CEVE 455. Recommended Prerequisite(s): CAAM 336.

Long Title: NUMERICAL ANALYSIS I

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): CAAM 335 AND CAAM 336

Description: Construction and application of numerical algorithms for root finding, interpolation and approximation of functions, quadrature, and the solution of differential equations; fundamentals of computer arithmetic; solution of linear systems, linear least squares problems, and eigenvalue problems via matrix factorizations; Newton and Newton-like methods for nonlinear systems of equations. Computer programming in MATLAB is required.

Long Title: ADVANCED NUMERICAL ANALYSIS II

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Iterative methods for linear systems of equations including Krylov subspace methods; Newton and Newton-like methods for nonlinear systems of equations; Gradient and Newton-like methods for unconstrained optimization and nonlinear least squares problems; techniques for improving the global convergence of these algorithms; linear programming duality and primal-dual interior-point methods. Credit may not be received for both CAAM 454 and CAAM 554. Graduate/Undergraduate Equivalency: CAAM 554. Recommended Prerequisite(s): CAAM 453. Mutually Exclusive: Cannot register for CAAM 454 if student has credit for CAAM 554.

Long Title: DYNAMICAL SYSTEMS LAB

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Laboratory

Credit Hours: 1

Description: Modeling, simulation and visualization of dynamical systems in MATLAB.

Long Title: INTRODUCTION TO GRAPH THEORY

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Study of the structure and properties of graphs, together with a variety of applications. Includes paths, cycles, trees, connectivity, matchings, colorings, planarity, directed graphs, and algorithms. Some knowledge of linear algebra is recommended.

Long Title: LINEAR AND INTEGER PROGRAMMING

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Linear and integer programming involve formulating and solving fundamental optimization models widely used in practice. This course introduces the basic theory, algorithms, and software of linear and integer programming. Topics studied in the linear programming part include polyhedron concepts, simplex methods, duality, sensitivity analysis and decomposition techniques. Building on linear programming, the second part of this course introduces modeling with integer variables and solution methodologies in integer programming including branch-and-bound and cutting-plane techniques. This course will provide a basis for further studies in convex and combinatorial optimization. Credit may not be received for both CAAM 471 and CAAM 571. Graduate/Undergraduate Equivalency: CAAM 571. Recommended Prerequisite(s): CAAM 335 and CAAM 378 Mutually Exclusive: Cannot register for CAAM 471 if student has credit for CAAM 571.

Long Title: COMBINATORIAL OPTIMIZATION

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: General theory and approaches for solving combinatorial optimization problems are studied. Specific topics include basic polyhedral theory, minimum spanning trees, shortest paths, network flow, matching and matroids. The course also covers the traveling salesman problem. Recommended Prerequisite(s): CAAM 378 OR CAAM 471.

Long Title: PEDAGOGY FOR CAAM 210 RICE LEARNING ASSISTANTS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 2

Description: This course is designed to support Rice Learning Assistants (RLAs) as they instruct their own lab sections of CAAM 210. Topics include analysis of computational science and engineering concepts, issues of problem-based learning (PBL), theories of learning, and fundamental teaching skills. Required for CAAM 210 RLAs. Instructor Permission Required. Repeatable for Credit.

Long Title: INDEPENDENT STUDY

Department: *Computational & Applied Math*

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Independent Study

Credit Hours: 1 TO 6

Description:  Repeatable for Credit.

Long Title: INDEPENDENT STUDY

Department: *Computational & Applied Math*

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Independent Study

Credit Hours: 1 TO 6

Description:  Repeatable for Credit.

Long Title: SENIOR DESIGN PROJECT I

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture/Laboratory

Credit Hours: 2 TO 3

Description: Students engage in team-oriented year-long design projects that utilize modeling, analysis, and scientific computing skills to solve a problem motivated by an application in engineering or the physical, biological, or social sciences. Participants attend regular seminars addressing research techniques and effective written and verbal presentation of mathematics.

Long Title: SENIOR DESIGN PROJECT II

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture/Laboratory

Credit Hours: 2 TO 3

Prerequisite(s): CAAM 495

Description: Continuation of CAAM 495. Seminars focus on the presentation of results from design groups and provide guidance on the composition of a substantial project report.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: A seminar course that will cover a selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics. The course may be repeated multiple times for credit. Cross-list: MATH 498, STAT 498, Graduate/Undergraduate Equivalency: CAAM 698. Mutually Exclusive: Cannot register for CAAM 498 if student has credit for CAAM 698. Repeatable for Credit.

Long Title: COMPUTATIONAL AND APPLIED MATHEMATICS SEMINAR

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 6

Description: This course prepares a student for research in the mathematical sciences on a specific topic. Each section is dedicated to a different topic. Current topics include eigenvalues, model reduction, combinatorial optimization, optimization algorithms, scientific computing, and numerical analysis. The topics may vary each semester. FALL 2014: We will introduce and study the most common Matrix Groups, prove the fundamental results of Representation Theory for Finite Groups and apply these findings to basic questions in Quantum Mechanics and network design in Theoretical Mechanics and Theoretical Computer Science. In particular, we will 1) characterize the full electronic spectrum of the buckyball, 2) construct a large class of Buckminister Fuller's tensegrities, and 3) construct expanders (large graphs that remain well connected and yet have relatively few edges). Recommended Prerequisite: One course in Linear Algebra. Graduate/Undergraduate Equivalency: CAAM 699. Repeatable for Credit.

Long Title: ANALYSIS I

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Real numbers, completeness, sequences and convergence, compactness, continuity, the derivative, the Riemann integral, fundamental theorem of calculus. Vector spaces, dimension, linear maps, inner products and norms. Credit may not be received for both CAAM 401 and CAAM 501. Instructor Permission Required.Graduate/Undergraduate Equivalency: CAAM 401. Mutually Exclusive: Cannot register for CAAM 501 if student has credit for CAAM 401.

Long Title: ANALYSIS II

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Continuation of Analysis I. Vector spaces of functions, sequences and series, convergence. Continuity and differentiability of functions of several variables, the derivative as a linear map, the contraction mapping principle, inverse and implicit function theorems, fundamental theorems on differential equations, multivariable integration, Stoke's theorem and relatives. Credit may not be received for both CAAM 402 and CAAM 502. Instructor Permission Required.Graduate/Undergraduate Equivalency: CAAM 402. Recommended Prerequisite(s): CAAM 501. Mutually Exclusive: Cannot register for CAAM 502 if student has credit for CAAM 402.

Long Title: NONLINEAR SYSTEMS: ANALYSIS AND CONTROL

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Mathematical background and fundamental properties of nonlinear systems: Vector norms, matrix norms, matrix measures, existence and uniqueness of solutions of ordinary differential equations. Linearization, second order systems, periodic solutions, approximate methods. Lyapunov stability: Stability definitions, Lyapunov's direct method, invariance theory, stability of linear systems, Lyapunov's linearization method, converse theorems. Selected topics in nonlinear systems analysis and nonlinear control from: Input/Output stability: Small gain theorem, passivity theorem. Perturbation theory, averaging, and singular perturbations. Feedback linearization control. Other methods in the control of nonlinear systems such as backstepping, sliding mode and other Lyapunov-based design methods. Advanced nonlinear and adaptive robot control. Cross-list: ELEC 508, MECH 508.

Long Title: COMPUTATIONAL SCIENCE II

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Theory and application of the message passing interface for programming scientific computing applications. Introduction to the architecture and programming of multicore and massively parallel processors, including general purpose graphics processing units, Insight for designing efficient numerical algorithms to improve parallelization of memory access and utilization of non-uniform memory architectures. Application interfaces include OpenMP, MPI, CUDA, OpenCL, and parallel numerical algorithm libraries. Instructor Permission Required. Recommended Prerequisite(s): CAAM 519.

Long Title: PARTIAL DIFFERENTIAL EQUATIONS II

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): CAAM 423 OR MATH 423

Description: Mathematical analysis of wave propagation. Hyperbolic systems, energy estimates, existence of weak solutions, domains of dependence and influence, Green's functions, geometric optics, boundary value problems, numerical methods. Recommended Prerequisite(s): CAAM 552.

Long Title: APPLIED FUNCTIONAL ANALYSIS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Hilbert spaces, Banach spaces, spectral theory, and weak topologies with applications to signal processing, control, and partial differential equations. Biennial; Offered in Odd Years. Recommended Prerequisite(s): CAAM 402 and MATH 322.

Long Title: NUMERICAL LINEAR ALGEBRA

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): CAAM 453 OR CAAM 553

Description: Direct methods for large, sparse linear systems; regularization of ill-conditioned least squares problems; backward error analysis of basic algorithms for linear equations and least squares, sensitivity and conditioning of linear systems and least square problems; condition estimation. Preconditioned iterative methods for linear systems (CG, GMRES, BiCGstab, QMR); multigrid methods. Matrix theory including spectral decompositions, Schur form, eigenvalue perturbation theory, and the geometry of subspaces. Eigenvalue algorithms, Sylvester and Lyapunov equations, the implicitly shifted QR algorithm, computation of the SVD, generalized eigenvalue problems. Introduction to large scale eigenvalue algorithms. Proficiency in MATLAB and acquaintance with one or more of C, F77, C++, F90 is required. Recommended Prerequisite(s) CAAM 453 or CAAM 553 or CAAM 550

Long Title: FOUNDATIONS OF FINITE ELEMENT METHODS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: This course addresses the theory and implementation of finite element methods. Topics include weak solutions of partial differential equations, Sobolev spaces, approximation theory, convergence and reliability of the numerical methods. Continuous and discontinuous finite element methods are considered.

Long Title: ADVANCED NUMERICAL ANALYSIS I

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): CAAM 401 OR CAAM 501

Description: Construction and analysis of numerical algorithms for root finding, interpolation and approximation of functions, quadrature, and the solution of differential equations; fundamentals of computer arithmetic; solution of linear systems, least squares problems, and eigenvalue problems via matrix factorizations; the singular value decomposition (SVD) and basic sensitivity analysis. Computer programming in MATLAB is required. This course covers fewer topics than CAAM 453 with greater theoretical depth. Prerequisite CAAM 501 may be taken concurrently with CAAM 553.

Long Title: ADVANCED NUMERICAL ANALYSIS II

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: This course covers the same lecture material as CAAM 454, but fosters greater theoretical sophistication through more challenging problem sets and exams. Credit may not be received for both CAAM 454 and CAAM 554. Graduate/Undergraduate Equivalency: CAAM 454. Recommended Prerequisite(s): CAAM 550 . Mutually Exclusive: Cannot register for CAAM 554 if student has credit for CAAM 454.

Long Title: OPTIMIZATION THEORY

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Derivation and application of necessity conditions and sufficiency conditions for constrained optimization problems.

Long Title: NUMERICAL OPTIMIZATION

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Numerical algorithms for constrained optimization problems in engineering and sciences, including simplex and interior-point methods for linear programming, penalty, barrier, augmented Lagrangian and SQP methods for nonlinear programming. Recommended Prerequisite(s): CAAM 560 (may be taken concurrently) and CAAM 454.

Long Title: CONVEX OPTIMIZATION

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Convex optimization problems arise in communication, system theory, VLSI, CAD, finance, inventory, network optimization, computer vision, learning, statistics, etc., even though oftentimes convexity may be hidden and unrecognized. Recent advances in interior-point methodology have made it much easier to solve these problems and various solvers are now available. This course will introduce the basic theory and algorithms for convex optimization, as well as its many applications to computer science, engineering, management science and statistics. Biennial; Offered in Odd Years. Recommended Prerequisite(s): CAAM 335 and MATH 321.

Long Title: LINEAR AND INTEGER PROGRAMMING

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: This course covers the same lecture material as CAAM 471, but fosters greater theoretical sophistication through more challenging problem sets and exams. Credit may not be received for both CAAM 471 and CAAM 571. Graduate/Undergraduate Equivalency: CAAM 471. Mutually Exclusive: Cannot register for CAAM 571 if student has credit for CAAM 471.

Long Title: MATHEMATICAL PROBABILITY I

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Measure-theoretic foundations of probability. Open to qualified undergraduates. Required for PhD students in statistics. Cross-list: STAT 581.

Long Title: INTRODUCTION TO RANDOM PROCESSES AND APPLICATIONS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Review of basic probability; Sequences of random variables; Random vectors and estimation; Basic concepts of random processes; Random processes in linear systems, expansions of random processes; Wiener filtering; Spectral representation of random processes, and white-noise integrals. Cross-list: ELEC 533, STAT 583.

Long Title: INDEPENDENT STUDY

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 15

Description:  Repeatable for Credit.

Long Title: INDEPENDENT STUDY

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 15

Description:  Repeatable for Credit.

Long Title: THESIS WRITING

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 3

Description: Assists the student in preparation of the CAAM MA/PhD thesis and in other writing projects. Structure of a scientific paper, effective approaches to technical writing, building literature review, results, and discussion sections, how to write a good abstract, oral presentation skills. Prerequisite: Advisor approval of topic and consent of the instructor(s). Instructor Permission Required. Repeatable for Credit.

Long Title: TOPICS IN COMPUTATIONAL SCIENCE

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: Content varies from year to year. Instructor Permission Required. Repeatable for Credit.

Long Title: OPTIMIZATION WITH SIMULATION CONSTRAINTS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 3

Description: Content varies from year to year. Recommended Prerequisite(s): CAAM 564. Repeatable for Credit.

Long Title: TOPICS IN INVERSE PROBLEMS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 3

Description: Theoretical, computational and practical issues for inverse problems in science and engineering. Selected topics will vary depending on instructor and student interests. Instructor Permission Required. Repeatable for Credit.

Long Title: TOPICS IN NUMERICAL LINEAR ALGEBRA

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: Selected topics will vary depending on instructor and student interests. Derivation and analysis of Krylov and subspace iteration methods for large eigenvalue problems (Lanczos, Arnoldi, Jacobi-Davidson algorithms); preconditioning for linear systems and eigenvalue problems (incomplete LU, domain decomposition, multigrid); convergence analysis including potential theory and pseudospectra. Applications: regularization of discrete inverse problems; dimension reduction for large dynamical control systems; effects on non-normality on behavior of dynamical systems and iterative processes. Recommended Prerequisite(s): CAAM 551. Repeatable for Credit.

Long Title: TOPICS IN NUMERICAL DIFFERENTIAL EQUATIONS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: Content varies from year to year. Instructor Permission Required. Repeatable for Credit.

Long Title: TOPICS IN OPTIMIZATION

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: Content varies from year to year. Instructor Permission Required. Repeatable for Credit.

Long Title: TOPICS IN NONLINEAR PROGRAMMING

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 3

Description: Content varies from year to year.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: A seminar course that will cover a selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics. The course may be repeated multiple times for credit. Cross-list: MATH 698, STAT 698, Graduate/Undergraduate Equivalency: CAAM 498. Mutually Exclusive: Cannot register for CAAM 698 if student has credit for CAAM 498. Repeatable for Credit.

Long Title: COMPUTATIONAL AND APPLIED MATHEMATICS SEMINAR

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 9

Description: This course prepares a student for research in the mathematical sciences on a specific topic. Each section is dedicated to a different topic. Current topics include bioinformatics, biomathematics, computational finance, simulation driven optimization, data simulation, and spectral optimization in rational mechanics. The topics may vary each semester. Instructor Permission Required.Graduate/Undergraduate Equivalency: CAAM 499. Repeatable for Credit.

Long Title: VISITING RESEARCH TRAINEE

Department: *Computational & Applied Math*

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Research

Credit Hours: 0

Long Title: THESIS

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 15

Description:  Repeatable for Credit.