# Computational Applied Mathematics and Operations Research (CMOR)

**CMOR 220 - INTRODUCTION TO ENGINEERING COMPUTATION**

**Short Title: **INTRO TO ENG COMPUTATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Modeling, Simulation, and Visualization using Matlab and Python. This project-based course introduces students to engineering computation in Matlab and Python. Computational projects motivated by different science and engineering applications are used to introduce basic numerical methods, and develop computational solutions using Matlab and Python. No programming knowledge is required or expected; students learn how to implement their solutions in Matlab and Python. Lectures are held Mondays and Wednesdays. In a laboratory component held on Fridays, students work in small groups on computational projects led by a Rice Learning Assistant. Fall/Spring semester: meeting 3 times per week (50min each meeting). Summer semester: meeting 5 times per week (65min each meeting) OR refer to the current schedule. Recommended Prerequisite(s): MATH 101 or MATH 105

**CMOR 238 - SPECIAL TOPICS**

**Short Title: **SPECIAL TOPICS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Activity Course, Intensive Learning Experience, Independent Study, Internship/Practicum, Laboratory, Lecture, Lecture/Laboratory, Research, Seminar, Studio

**Credit Hours: **1-4

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Topics and credit hours vary each semester. Contact department for current semester's topic(s). Repeatable for Credit.

**CMOR 302 - MATRIX ANALYSIS**

**Short Title: **MATRIX ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Equilibria and the solution of linear systems and linear least squares problems. Eigenvalue problem and its application to solve dynamical systems. Singular value decomposition and its application. Recommended Prerequisite(s): (MATH 212 or MATH 222) and (CAAM 210 or CMOR 220 or COMP 140)

**CMOR 303 - MATRIX ANALYSIS FOR DATA SCIENCE**

**Short Title: **MATRIX ANALYSIS DATA SCIENCE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Solution of linear systems and linear least squares problems. Eigenvalue problem and singular value decomposition. Introduction to gradient based methods. Applications to data science. Recommended Prerequisite(s): (MATH 212 or MATH 222) and (CAAM 210 or CMOR 220 or COMP 140 or STAT 405)

**CMOR 304 - DIFFERENTIAL EQUATIONS IN SCIENCE AND ENGINEERING**

**Short Title: **DIFF EQUATIONS SCI & ENG

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 or CMOR 220)

**CMOR 350 - STOCHASTIC MODELS**

**Short Title: **STOCHASTIC MODELS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **ECON 307 or STAT 310 or STAT 311 or STAT 315

**Description: **Fundamentals of stochastic modeling in engineering and operations research. Topics include discrete-time Markov chains, Poisson processes, birth-and-death processes and other continuous-time Markov chains, renewal processes, with applications in applications in queueing, inventory, finance, healthcare, and epidemics. Recommended Prerequisite(s): MATH 212 and (CAAM 210 or CMOR 220 or COMP 140) and (CAAM 335 or CMOR 302 or MATH 355)

**CMOR 360 - INTRODUCTION TO OPERATIONS RESEARCH AND OPTIMIZATION**

**Short Title: **INTRO TO O.R. AND OPTIMIZATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Formulation of mathematical models of complex decisions arising in management, economics, and engineering. Models using linear, nonlinear, stochastic and integer programming, as well as networks. Linear programming duality and its modeling implications. Overview of basic solution methods for these optimization models. Recommended Prerequisite(s): MATH 212 and (CAAM 334 or CMOR 303 or CAAM 335 or CMOR 302 or MATH 211 or MATH 355) and (CAAM 210 or CMOR 220 or COMP 140)

**CMOR 404 - GRAPH THEORY**

**Short Title: **GRAPH THEORY

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Graduate/Undergraduate Equivalency: CMOR 504.

**CMOR 405 - PARTIAL DIFFERENTIAL EQUATIONS I**

**Short Title: **PARTIAL DIFFERENTIAL EQNS I

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Graduate/Undergraduate Equivalency: CMOR 505. Recommended Prerequisite(s): MATH 321 AND MATH 322 Mutually Exclusive: Cannot register for CMOR 405 if student has credit for CMOR 505.

**CMOR 410 - MODELING MATHEMATICAL PHYSICS**

**Short Title: **MODELING MATHEMATICAL PHYSICS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Graduate/Undergraduate Equivalency: CMOR 510. Recommended Prerequisite(s): (CAAM 336 or CMOR 304)

**CMOR 415 - THEORETICAL NEUROSCIENCE: FROM CELLS TO LEARNING SYSTEMS**

**Short Title: **THEORETICAL NEUROSCIENCE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Undergraduate Upper-Level

**Description: **We present the theoretical foundations of cellular and systems neuroscience from distinctly quantitative point of view. We develop the mathematical and computational tools as they are needed to model, analyze, visualize and interpret a broad range of experimental data. Cross-list: ELEC 488, NEUR 415. Graduate/Undergraduate Equivalency: CMOR 615. Recommended Prerequisite(s): CAAM 210 or CMOR 220 or MATH 211 or CAAM 335 or CAAM 302 or MATH 355. Mutually Exclusive: Cannot register for CMOR 415 if student has credit for CMOR 615.

**CMOR 416 - NEURAL COMPUTATION**

**Short Title: **NEURAL COMPUTATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Undergraduate Upper-Level

**Description: **How does the brain work? Understanding the brain requires sophisticated theories to make sense of the collective actions of billions of neurons and trillions of synapses. Word theories are not enough; we need mathematical theories. The goal of this course is to provide an introduction to the mathematical theories of learning and computation by neural systems. These theories use concepts from dynamical systems (attractors, oscillations, chaos) and concepts from statistics (information, uncertainty, inference) to relate the dynamics and functions of neural networks. We will apply these theories to sensory computation, learning and memory, and motor control. Students will learn to formalize and mathematically answer questions about neural computations, including “what does a network compute?”, “how does it compute?”, and “why does it compute that way?” Prerequisites: knowledge of calculus, linear algebra, and probability and statistics. Cross-list: ELEC 489, NEUR 416.

**CMOR 420 - COMPUTATIONAL SCIENCE**

**Short Title: **COMPUTATIONAL SCIENCE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Grading and assignments would be different between the 400/500 level. Graduate/Undergraduate Equivalency: CMOR 520. Recommended Prerequisite(s): (CAAM 210 or CMOR 220 and CAAM 335 or CMOR 302) or (CAAM 453 or CMOR 422)

**CMOR 421 - HIGH PERFORMANCE COMPUTING**

**Short Title: **HIGH PERFORMANCE COMPUTING

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Grading and assignments would be different between the 400/500 level. Instructor Permission Required. Graduate/Undergraduate Equivalency: CMOR 521. Recommended Prerequisite(s): (CAAM 419 or CMOR 420)

**CMOR 422 - NUMERICAL ANALYSIS**

**Short Title: **NUMERICAL ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **CAAM 334 or CMOR 303 or CAAM 335 or CMOR 302

**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. Graduate/Undergraduate Equivalency: CMOR 522.

**CMOR 423 - NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS**

**Short Title: **NUMERICAL METHODS FOR PDES

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture/Laboratory

**Credit Hours: **3

**Course Level: **Undergraduate Upper-Level

**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. Graduate/Undergraduate Equivalency: CMOR 523. Recommended Prerequisite(s): CAAM 336 or CMOR 304 Mutually Exclusive: Cannot register for CMOR 423 if student has credit for CMOR 523.

**CMOR 430 - ITERATIVE METHODS FOR SYSTEMS OF EQUATIONS AND UNCONSTRAINED OPTIMIZATION**

**Short Title: **SYST OF EQNS & UNCONST OPTIM

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Iterative methods for linear systems of equations including Krylov subspace methods, including the conjugate gradient method and GMRES; gradient and Newton-like methods for unconstrained optimization and nonlinear least squares problems; Newton and Newton-like methods for nonlinear systems of equations; techniques for improving the global convergence of these algorithms; implementation of these methods in Matlab or Python; applications to example problems in science and engineering. Graduate/Undergraduate Equivalency: CMOR 530. Recommended Prerequisite(s): (CAAM 453 or CMOR 422)

**CMOR 435 - DYNAMICAL SYSTEMS**

**Short Title: **DYNAMICAL SYSTEMS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Undergraduate Upper-Level

**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): (MATH 212 or MATH 221) and (CAAM 335 or MATH 355 or MATH 354) and (MATH 302 or MATH 321 or MATH 331)

**Course URL: **math.rice.edu

**CMOR 441 - LINEAR AND INTEGER PROGRAMMING**

**Short Title: **LINEAR AND INTEGER PROGRAMMING

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 302 and (CAAM 335 or CMOR 302 or MATH 355 or MATH 354)

**Description: **This course provides a rigorous introduction to linear optimization with continuous and integral variables. We explore the theory and algorithms of linear and integer programming. Topics studied in the linear programming part include polyhedral theory, duality, and algorithms for solving linear programs. Building on linear programming, the second part of this course studies linear optimization with integral variables. Here, the topics covered are integral polyhedra and perfect formulations, including TU matrices and TDI systems. We culminate with exact methodologies for integer programming, including branch-and-bound and cutting-plane techniques. This course provides the foundations for further studies in convex optimization, combinatorial optimization, and stochastic programming. Graduate/Undergraduate Equivalency: CMOR 541. Recommended Prerequisite(s): CAAM 378 or CMOR 360

**CMOR 442 - LARGE-SCALE OPTIMIZATION**

**Short Title: **LARGE-SCALE OPTIMIZATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **(CAAM 378 or CMOR 360) and COMP 140 and (CMOR 302 or CMOR 303 or MATH 354 or MATH 355)

**Description: **Decomposition of large-scale linear, nonlinear and integer programs. Minkowski representation of polyhedra. Benders' and Dantzig-Wolfe decomposition. Relaxations, including Lagrangian relaxation. Examples include multicommodity flow and stochastic linear programs. Design and testing of computational strategies for difficult optimization problems. Students will implement projects in Python. Graduate/Undergraduate Equivalency: INDE 546. Recommended Prerequisite(s): CMOR 441 and MATH 302

**CMOR 446 - GRAPH ALGORITHMS**

**Short Title: **GRAPH ALGORITHMS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Graph Algorithms in Operations Research. Topics include: spanning trees, graph search algorithms, shortest path problems, worst case time complexity analysis, computational complexity, dominating set problems, vertex and edge cover problems, python implementations, and other problems in graph optimization. Instructor Permission Required. Recommended Prerequisite(s): CMOR 360

**CMOR 451 - SIMULATION MODELING AND ANALYSIS**

**Short Title: **SIM MODELING AND ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **CMOR 350

**Description: **This course introduces simulation techniques that uses statistical sampling, probability models and computational tools to study complex stochastic systems arising in service operations, healthcare, telecommunications, production, logistics, inventory and financial systems. Topics covered include generating random objects (random variables and stochastic processes, discrete-event systems), input and output analysis, steady-state simulation, variance-reduction methods, rare-event simulation, Markov chain Monte Carlo methods, and simulation-based optimization. The course lectures are supplemented with programming components in homework and projects. Graduate/Undergraduate Equivalency: CMOR 551. Recommended Prerequisite(s): MATH 212, (STAT 310 or STAT 311 or STAT 418), (CAAM 334 or 303 or CAAM 335 or CMOR 302), and MATH 302

**CMOR 452 - SERVICE SYSTEMS ANALYTICS**

**Short Title: **SERVICE SYS ANALYTICS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **CMOR 360

**Corequisite: **CMOR 350

**Description: **This course provides a broad exploration of large-scale service systems using data analytics, stochastic models, optimization and simulation techniques. In particular, through the data collection, preparation, visualization and analysis, students will understand the demand and service processes. Through the optimization and stochastic models and simulations, students will formulate decisions problems to determine optimal capacity (workforce and other resources) and resource allocations to meet the in the long-term and short-term horizons. Applying these modeling and analytical techniques and tools, students will conduct case studies in modern service systems such as healthcare, on-demand service systems, transportation and recreational services.

**CMOR 455 - STOCHASTIC CONTROL AND APPLICATIONS**

**Short Title: **STOCHASTIC CONTROL & APP

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **CAAM 382

**Description: **Stochastic control theory and applications in a variety of areas including dynamic resource allocation, finance, inventory, queueing and stochastic networks, and epidemiology. Topics include foundations of stochastic control for Markov processes and diffusions, maximum principle, dynamic programming and Hamilton-Jacobi-Bellman (HJB) equations, finite-horizon and infinite-horizon discounted and average problems, optimal stopping problem, impulse control, risk sensitive control, differential games, viscosity solutions, iteration and policy iteration and other numerical solution algorithms. Graduate/Undergraduate Equivalency: CMOR 555. Recommended Prerequisite(s): Equivalent of advanced course work in calculus (e.g., MATH 212), statistics and probability theory (e.g., STAT 310 or STAT 311, STAT 418), linear algebra (e.g., CAAM 334 or CAAM 345) and analysis (e.g., MATH 302), and differential equations.

**CMOR 461 - LOGISTICS AND SUPPLY CHAIN MANAGEMENT**

**Short Title: **LOG & SUPPLY CHAIN MANAGEMENT

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **(CAAM 378 or CMOR 360) and (CAAM 382 or CMOR 350)

**Description: **Inventory management: EOQ, newsvendor, reorder point order quantity, multi-echelon models. Scheduling, distribution & location models. Vehicle routing problems. Supply chain coordination. Sustainability in supply chains. Graduate/Undergraduate Equivalency: INDE 561.

**CMOR 462 - OPTIMIZATION METHODS IN FINANCE**

**Short Title: **OPT METHODS IN FINANCE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **CAAM 378 or CMOR 360

**Description: **Portfolio optimization and asset allocation models. Risk management and option pricing. Deterministic and stochastic optimization approaches, as well as linear and nonlinear approaches will be used to model decisions arising in finance. Graduate/Undergraduate Equivalency: INDE 567.

**CMOR 463 - OPERATIONS RESEARCH IN HEALTHCARE**

**Short Title: **OPER RES IN HEALTHCARE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Operations research in healthcare systems and medical decision-making. Application areas will include hospital resource management, patient scheduling, treatment planning and organ transplantation. Modeling techniques will include mathematical programming, stochastic processes, Markov decision processes and simulation. Recommended Prerequisite(s): CMOR 350, CMOR 360

**CMOR 464 - MANUFACTURING PROCESSES AND SYSTEMS**

**Short Title: **MANUFACTURING PROC AND SYS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Fundamentals of manufacturing processes and systems. Topics include basic factory dynamics, benchmarking, design and control of single-stage production systems, queueuing network approximations for multi-stage production systems, analysis of flow lines and job shops, push & pull systems, impact of variability in manufacturing processes, lean manufacturing. Instructor Permission Required. Recommended Prerequisite(s): CMOR 350

**CMOR 477 - SPECIAL TOPICS**

**Short Title: **SPECIAL TOPICS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Activity Course, Intensive Learning Experience, Independent Study, Internship/Practicum, Laboratory, Lecture, Lecture/Laboratory, Research, Seminar, Studio

**Credit Hours: **1-4

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Topics and credit hours vary each semester. Contact department for current semester's topic(s). Repeatable for Credit.

**CMOR 490 - UNDERGRADUATE RESEARCH PROJECTS**

**Short Title: **UNDERGRAD RESEARCH PROJECTS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Satisfactory/Unsatisfactory

**Course Type: **Research

**Credit Hours: **1-6

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Semester-long undergraduate-level research on a topic in computational and applied mathematics and/or operations research. Instructor Permission Required. Repeatable for Credit.

**CMOR 491 - UNDERGRADUATE RESEARCH PROJECTS**

**Short Title: **UNDERGRAD RESEARCH PROJECTS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Satisfactory/Unsatisfactory

**Course Type: **Research

**Credit Hours: **1-6

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Semester-long undergraduate-level research on a topic in computational and applied mathematics and/or operations research. Instructor Permission Required. Repeatable for Credit.

**CMOR 492 - SENIOR DESIGN PROJECT I**

**Short Title: **SENIOR DESIGN PROJECT I

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture/Laboratory

**Credit Hours: **2

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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.

**CMOR 493 - SENIOR DESIGN PROJECT II**

**Short Title: **SENIOR DESIGN PROJECT II

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture/Laboratory

**Credit Hours: **2

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **CMOR 492

**Description: **Continuation of CMOR 492. Seminars focus on the presentation of results from design groups and provide guidance on the composition of a substantial project report.

**CMOR 494 - PEDAGOGY FOR CMOR 220 RICE LEARNING ASSISTANTS**

**Short Title: **PEDAGOGY FOR RLAS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hours: **2

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **This course is designed to support Rice Learning Assistants (RLAs) as they instruct their own lab sections of CMOR 220. Topics include analysis of computational science and engineering concepts, issues of problem-based learning (PBL), theories of learning, and fundamental teaching skills. Required for CMOR 220 RLAs. Instructor Permission Required. Repeatable for Credit.

**CMOR 495 - LOSING THE PRECIOUS FEW**

**Short Title: **LOSING THE PRECIOUS FEW

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **The class will read from Tapia's text: Losing the Precious Few: How America Fails to Educate Minorities in Science and Engineering and then discuss in class issues associated with the underrepresentation of Blacks and Hispanics in academic and national science and engineering activities. Topics will include racism, immigration, student admissions, faculty hiring, faculty promotion, the role of minority serving institutions, mistaking foreign minorities for the Precious Few, support issues and leadership.

**CMOR 496 - COMPUTATIONAL AND APPLIED MATHEMATICS SEMINAR**

**Short Title: **COMP & APPLIED MATH SEMINAR

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hours: **1-6

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Graduate/Undergraduate Equivalency: CMOR 696. Repeatable for Credit.

**CMOR 500 - ANALYSIS**

**Short Title: **ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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, derivatives in R^d, inverse function theorem, implicit function theorem, multiple integration, change of variable theorem. Instructor Permission Required.

**CMOR 501 - APPLIED FUNCTIONAL ANALYSIS**

**Short Title: **APPLIED FUNCTIONAL ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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): MATH 322

**CMOR 504 - GRAPH THEORY**

**Short Title: **GRAPH THEORY

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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. This course covers the same lecture material as CMOR 404, but fosters greater theoretical sophistication through more challenging problem sets and exams on the graduate side. Graduate/Undergraduate Equivalency: CMOR 404.

**CMOR 505 - PARTIAL DIFFERENTIAL EQUATIONS I**

**Short Title: **PARTIAL DIFFERENTIAL EQNS I

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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. Additional course work is required beyond the undergraduate course requirements. Cross-list: MATH 513. Graduate/Undergraduate Equivalency: CMOR 405. Recommended Prerequisite(s): MATH 321 AND MATH 322 Mutually Exclusive: Cannot register for CMOR 505 if student has credit for CMOR 405.

**CMOR 507 - APPLIED AND COMPUTATIONAL MICROLOCAL AND HARMONIC ANALYSIS**

**Short Title: **MICROLOCAL & HARMONIC ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **CAAM 423 or CMOR 405

**Description: **Introduction to microlocal and harmonic analysis. Oscillatory integrals, Wavefront set, Pseudodifferential and Fourier Integral Operators and their calculus, and basic symplectic geometry. Egorov’s theorem and propagation of singularities. Wavepackets, matrix classes and discretization; USFFT and fast curvelet transform. Parametrix construction for wave equations and applications in imaging. Recommended Prerequisite(s): MATH 302, (CAAM 334 or CMOR 303 or CAAM 335 or CMOR 302), MATH 401, (CAAM 453 or CMOR 422), MATH 522.

**CMOR 508 - NONLINEAR SYSTEMS: ANALYSIS AND CONTROL**

**Short Title: **NONLINEAR SYSTEMS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Graduate

**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.

**CMOR 510 - MODELING MATHEMATICAL PHYSICS**

**Short Title: **MODELING MATHEMATICAL PHYSICS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **This course combines basic physical principles with vector calculus to derive many important partial differential equations governing motion of fluids and solids. Topics include stress, strain, idealized fluids, linear elasticity, acoustics, basics of thermodynamics, Navier-Stokes. Graduate/Undergraduate Equivalency: CMOR 410. Recommended Prerequisite(s): (CAAM 336 or CMOR 304).

**CMOR 514 - INDUSTRIAL AND APPLIED DATA SCIENCE – THEORY AND PRACTICE**

**Short Title: **INDUSTRIAL & APPLIED DATA SCI

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **2

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **This graduate-level course presents a pragmatic introduction to the foundational theory of data science along with a series of practical skills for working data scientists. It includes modern aspects of data science driven by massively more data and computer power such as deep neural networks, reinforcement learning and the principles of generative AI. The course is supplemented by practical programming exercises to be completed every week by all students. Industrial-strength applications of data science in the energy sector, from image and text processing to physics-based simulations are discussed in appropriate detail, along with how the enterprise value gets delivered in practice. How does data science relate to MLOps, how do data science teams work, how quickly will skillsets need updating? Recommended Prerequisite(s): Equivalent of advanced course work in computer programming (e.g. COMP 321), calculus (e.g. MATH 212), statistics or probability theory, linear algebra (e.g. CAAM 334 or CMOR 303 or CAAM 335 or CMOR 302). Proficiency in MATLAB (course programming language) or Python (alternative to MATLAB available to course participants).

**CMOR 518 - APPLICATIONS IN COMPUTATIONAL MATHEMATICS**

**Short Title: **APPLICATIONS IN COMP MATH

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students. Enrollment limited to students in a Master of Comp & Appl Math, Master of Comp Sci & Eng, Master of Computer Science, Master of Data Science, Master of Electrical Comp Eng, Master of Eng Mgmt & Leadershp, Master of Industrial Eng, Master of Mechanical Eng or Master of Statistics degrees.

**Course Level: **Graduate

**Description: **Introduction to fundamental tools in computational mathematics and their application to science and engineering problems using Python. Topics include tools from linear algebra for data compression, least squares, and dynamical systems; modeling and simulation using ordinary differential equations; approximation and interpolation of functions; gradient-based methods for parameter estimation.

**CMOR 520 - COMPUTATIONAL SCIENCE**

**Short Title: **COMPUTATIONAL SCIENCE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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. Grading and assignments would be different between the 400/500 level. Graduate/Undergraduate Equivalency: CMOR 420. Recommended Prerequisite(s): (CAAM 210 or CMOR 220 and CAAM 335 or CMOR 302) or (CAAM 453 or CMOR 422)

**CMOR 521 - HIGH PERFORMANCE COMPUTING**

**Short Title: **HIGH PERFORMANCE COMPUTING

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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. Grading and assignments would be different between the 400/500 level. Instructor Permission Required. Graduate/Undergraduate Equivalency: CMOR 421. Recommended Prerequisite(s): (CAAM 519 or CMOR 520)

**CMOR 522 - NUMERICAL ANALYSIS**

**Short Title: **NUMERICAL ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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. Graduate/Undergraduate Equivalency: CMOR 422.

**CMOR 523 - NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS**

**Short Title: **NUMERICAL METHODS FOR PDES

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Graduate

**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. May receive credit for only one of the following courses: CAAM 452/CEVE 455/CAAM 536/CEVE 555. Cross-list: CEVE 555. Graduate/Undergraduate Equivalency: CMOR 423. Recommended Prerequisite(s): CAAM 336 or CMOR 304 Mutually Exclusive: Cannot register for CMOR 523 if student has credit for CMOR 423.

**CMOR 524 - ADVANCED NUMERICAL ANALYSIS**

**Short Title: **ADV NUMERICAL ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Corequisite: **CMOR 500

**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. Instructor Permission Required.

**CMOR 525 - NUMERICAL LINEAR ALGEBRA**

**Short Title: **NUMERICAL LINEAR ALGEBRA

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Iterative methods for solving linear systems: Jacobi, Gauss-Seidel, geometric multigrids, p-multigrids, algebraic multigrids. Connection between multigrid methods and some special architectures of neural networks. Randomized methods for matrix computations: randomized matrix matrix multiplications, randomized SVD, randomized least squares and QR. Recommended Prerequisite(s): (CAAM 453 or CMOR 422 or CAAM 550 or CMOR 522 or CAAM 553 or CMOR 524)

**CMOR 526 - FOUNDATIONS OF FINITE ELEMENT METHODS**

**Short Title: **FINITE ELEMENT METHODS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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.

**CMOR 527 - DISCONTINUOUS GALERKIN METHODS FOR SOLVING ENGINEERING PROBLEMS**

**Short Title: **DISCONTINUOUS GALERKIN METHODS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **The course will present the theory and implementation of discontinuous Galerkin methods for partial differential equations common in engineering applications. Two main classes of problems are covered: steady-state and time-dependent elliptic/parabolic and hyperbolic equations. These include (but are not limited to) the Poisson and heat equations, linear wave equations, and nonlinear conservation laws. Recommended Prerequisite(s): (CAAM 336 or CMOR 304 or CAAM 453 or CMOR 422 or CAAM 553 or CMOR 524)

**CMOR 530 - ITERATIVE METHODS FOR SYSTEMS OF EQUATIONS AND UNCONSTRAINED OPTIMIZATION**

**Short Title: **SYST OF EQNS & UNCONST OPTIM

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **This course covers the same lecture material as CMOR 430, but fosters greater theoretical sophistication through more challenging problem sets and exams. Graduate/Undergraduate Equivalency: CMOR 430. Recommended Prerequisite(s): (CAAM 550 or CMOR 522) or (CAAM 553 or CMOR 524).

**CMOR 531 - CONVEX OPTIMIZATION**

**Short Title: **CONVEX OPTIMIZATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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 or CMOR 302 and MATH 321)

**CMOR 532 - OPTIMIZATION THEORY**

**Short Title: **OPTIMIZATION THEORY

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**CMOR 533 - NUMERICAL OPTIMIZATION**

**Short Title: **NUMERICAL OPTIMIZATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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 or CMOR 532 (may be taken concurrently) and CAAM 454 or CMOR 430).

**CMOR 534 - INTRO TO PARTIAL DIFFERENTIAL EQUATION BASED SIMULATION AND OPTIMIZATION**

**Short Title: **PDE SIMULATION AND OPTIM

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **(CAAM 501 or CMOR 500) and (CAAM 553 or CMOR 524)

**Description: **Introduction to the theory and numerical methods for the solution of elliptic partial differential equations (PDEs) and optimization problems governed by these PDEs. Topics include functional analysis, well-posedness of elliptic problems, optimality conditions for PDE constrained optimization problems and finite element discretizations. Recommended Prerequisite(s): (CAAM 554 or CMOR 530)

**CMOR 536 - OPTIMIZATION WITH SIMULATION CONSTRAINTS**

**Short Title: **OPTIMIZATION W/SIM CONSTRAINTS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Optimization problems in which evaluations of objective or constraint functions require computationally complex simulations arise in many engineering and science applications in the form of optimal design, optimal control, or parameter identification problems. This course introduces optimization approaches to solve these complex problems, and their application to engineering and science problems. Topics include derivative based optimization methods for problems with inexact function and derivative information, derivative approximations for functions involving computationally complex simulations, generation and use of surrogate models in optimization, derivative free optimization methods. Recommended Prerequisite(s): (CAAM 554 or CMOR 530 or CAAM 564 or CMOR 533)

**CMOR 541 - LINEAR AND INTEGER PROGRAMMING**

**Short Title: **LINEAR AND INTEGER PROGRAMMING

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **This course covers the same lecture material as CMOR 441, but fosters greater theoretical sophistication through more challenging problem sets and exams. Graduate/Undergraduate Equivalency: CMOR 441.

**CMOR 543 - COMBINATORIAL OPTIMIZATION**

**Short Title: **COMBINATORIAL OPTIMIZATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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.

**CMOR 544 - STOCHASTIC OPTIMIZATION**

**Short Title: **STOCHASTIC OPTIMIZATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **CAAM 571 or CMOR 541

**Description: **Stochastic optimization models arise in many contexts. This course focuses on stochastic programs, including stochastic integer programs and multi-stage stochastic programs. It will emphasize the interplay between theory and computational approaches.

**CMOR 551 - SIMULATION MODELING AND ANALYSIS**

**Short Title: **SIM MODELING AND ANALYSIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **This course introduces simulation techniques that uses statistical sampling, probability models and computational tools to study complex stochastic systems arising in service operations, healthcare, telecommunications, production, logistics, inventory and financial systems. Topics covered include generating random objects (random variables and stochastic processes, discrete-event systems), input and output analysis, steady-state simulation, variance-reduction methods, rare-event simulation, Markov chain Monte Carlo methods, and simulation-based optimization. The course lectures are supplemented with programming components in homework and projects. Graduate/Undergraduate Equivalency: CMOR 451.

**CMOR 552 - MATHEMATICAL PROBABILITY I**

**Short Title: **MATHEMATICAL PROBABILITY I

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Graduate

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

**CMOR 553 - INTRODUCTION TO RANDOM PROCESSES AND APPLICATIONS**

**Short Title: **INTRO RANDOM PROCESSES & APPL

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Graduate

**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.

**CMOR 554 - APPLIED STOCHASTIC PROCESSES**

**Short Title: **APPLIED STOCHASTIC PROCESSES

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **STAT 518 or CMOR 500

**Description: **This course covers the theory of some of the most frequently used stochastic processes in application: Poisson and renewal processes, discrete-time and continuous-time Markov chains, martingales, Brownian motion and diffusion processes. Cross-list: STAT 552.

**CMOR 555 - STOCHASTIC CONTROL AND APPLICATIONS**

**Short Title: **STOCHASTIC CONTROL & APP

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Stochastic control theory and applications in a variety of areas including dynamic resource allocation, finance, inventory, queueing and stochastic networks, and epidemiology. Topics include foundations of stochastic control for Markov processes and diffusions, maximum principle, dynamic programming and Hamilton-Jacobi-Bellman (HJB) equations, finite-horizon and infinite-horizon discounted and average problems, optimal stopping problem, impulse control, risk sensitive control, differential games, viscosity solutions, iteration and policy iteration and other numerical solution algorithms. Graduate/Undergraduate Equivalency: CMOR 455. Recommended Prerequisite(s): Equivalent of advanced course work in calculus (e.g., MATH 212), statistics and probability theory (e.g., STAT 310 or STAT 311, STAT418), linear algebra (e.g., CAAM 334 or CAAM 345) and analysis (e.g., MATH302), and differential equations.

**CMOR 590 - GRADUATE RESEARCH PROJECTS**

**Short Title: **GRADUATE RESEARCH PROJECTS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Research

**Credit Hours: **1-15

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Semester-long graduate-level research on a topic in computational and applied mathematics and/or operations research. Instructor Permission Required. Repeatable for Credit.

**CMOR 591 - GRADUATE RESEARCH PROJECTS**

**Short Title: **GRADUATE RESEARCH PROJECTS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Research

**Credit Hours: **1-15

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Semester-long graduate-level research on a topic in computational and applied mathematics and/or operations research. Instructor Permission Required. Repeatable for Credit.

**CMOR 595 - PRACTICUM IN COMPUTATIONAL APPLIED MATHEMATICS AND OPERATIONS RESEARCH**

**Short Title: **PRACTICUM IN CMOR

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Satisfactory/Unsatisfactory

**Course Type: **Internship/Practicum

**Credit Hours: **1,2

**Restrictions: ** Enrollment is limited to Graduate level students. Enrollment limited to students in a Master of Comp & Appl Math, Master of Comp Sci & Eng or Master of Industrial Eng degrees.

**Course Level: **Graduate

**Description: **This course is restricted to graduate students in degree programs administered by the Department of Computational Applied Mathematics and Operations Research (CMOR). This course introduces current theoretical and applied problems in the practice of Computational Applied Mathematics and Operations Research through practical internships. Students will be required to complete a paid or unpaid off-campus internship. Students will be required to submit a written, 5-10 page report summarizing the experience developed during the internship, as well documenting how the internship was instrumental to the student’s course of study. This course is repeatable for credit, but the total number of CAAM 595 credits that can be applied to a specific degree program, may be limited by that degree program. Instructor Permission Required. Repeatable for Credit.

**CMOR 600 - THESIS WRITING**

**Short Title: **THESIS WRITING

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Assists the student in preparation of the 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.

**CMOR 615 - THEORETICAL NEUROSCIENCE I: BIOPHYSICAL MODELING OF CELLS AND CIRCUITS**

**Short Title: **THEORETICAL NEUROSCIENCE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Course Level: **Graduate

**Description: **We present the theoretical foundations of cellular and systems neuroscience from distinctly quantitative point of view. We develop the mathematical and computational tools as they are needed to model, analyze, visualize and interpret a broad range of experimental data. Additional course work required beyond the undergraduate course requirements. Cross-list: ELEC 588, NEUR 615. Graduate/Undergraduate Equivalency: CMOR 415. Mutually Exclusive: Cannot register for CMOR 615 if student has credit for CMOR 415.

**CMOR 618 - TOPICS IN SEISMIC IMAGING**

**Short Title: **TOPICS IN SEISMIC IMAGING

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**CMOR 619 - TOPICS IN INVERSE PROBLEMS**

**Short Title: **TOPICS IN INVERSE PROBLEMS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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.

**CMOR 620 - TOPICS IN COMPUTATIONAL SCIENCE**

**Short Title: **TOPICS COMPUTATIONAL SCIENCE

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**CMOR 623 - TOPICS IN NUMERICAL DIFFERENTIAL EQUATIONS**

**Short Title: **TOPICS IN NUM DIFF EQNS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**CMOR 625 - TOPICS IN NUMERICAL LINEAR ALGEBRA**

**Short Title: **TOPICS IN NUM LINEAR ALGEBRA

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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. Instructor Permission Required. Recommended Prerequisite(s): CAAM 551 or CMOR 525 Repeatable for Credit.

**CMOR 636 - TOPICS IN NONLINEAR PROGRAMMING**

**Short Title: **TOPICS NONLINEAR PROGRAMMING

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**CMOR 646 - TOPICS IN OPTIMIZATION**

**Short Title: **TOPICS IN OPTIMIZATION

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**CMOR 677 - SPECIAL TOPICS**

**Short Title: **SPECIAL TOPICS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Activity Course, Intensive Learning Experience, Independent Study, Internship/Practicum, Laboratory, Lecture, Lecture/Laboratory, Research, Seminar, Studio

**Credit Hours: **1-4

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topics and credit hours vary each semester. Contact department for current semester's topic(s). Repeatable for Credit.

**CMOR 696 - COMPUTATIONAL AND APPLIED MATHEMATICS SEMINAR**

**Short Title: **COMP & APPLIED MATH SEMINAR

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hours: **1-9

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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: CMOR 496. Repeatable for Credit.

**CMOR 800 - RESEARCH AND THESIS**

**Short Title: **RESEARCH AND THESIS

**Department: **Comp Appl Math Operations Rsch

**Grade Mode: **Standard Letter

**Course Type: **Research

**Credit Hours: **1-15

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **This course is for MA or PhD students working on their thesis research. Repeatable for Credit.