Program Overview

Computational Applied Mathematics and Operations Research (CMOR) Program

The Computational Applied Mathematics and Operations Research (CMOR) program at Rice University offers a comprehensive curriculum that combines mathematical modeling, computational methods, and optimization techniques to solve complex problems in various fields.

Undergraduate Courses

• CMOR 220: Introduction to Engineering Computation: Modeling, simulation, and visualization using Matlab and Python.
• CMOR 238: Special Topics: Topics and credit hours vary each semester.
• CMOR 302: Matrix Analysis: Equilibria and the solution of linear systems and linear least squares problems.
• CMOR 303: Matrix Analysis for Data Science: Solution of linear systems and linear least squares problems, eigenvalue problem, and singular value decomposition.
• CMOR 304: Differential Equations in Science and Engineering: Classical and numerical solution techniques for ordinary and partial differential equations.
• CMOR 350: Stochastic Models: Fundamentals of stochastic modeling in engineering and operations research.
• CMOR 360: Introduction to Operations Research and Optimization: Formulation of mathematical models of complex decisions and optimization problems.
• CMOR 404: Graph Theory: Study of the structure and properties of graphs.
• CMOR 405: Partial Differential Equations I: First-order partial differential equations and analysis of solutions.
• CMOR 410: Modeling Mathematical Physics: Derivation and properties of solutions of partial differential equations governing motion of fluids and solids.
• CMOR 415: Theoretical Neuroscience: From Cells to Learning Systems: Theoretical foundations of cellular and systems neuroscience.
• CMOR 417: Scientific Machine Learning: Introduction to scientific machine learning and its application to physical problems.
• CMOR 420: Computational Science: Scientific programming using high-level languages.
• CMOR 421: High Performance Computing: Theory and application of message passing interface for programming scientific computing applications.
• CMOR 422: Numerical Analysis: Construction and application of numerical algorithms for root finding, interpolation, and approximation of functions.
• CMOR 423: Numerical Methods for Partial Differential Equations: Various numerical methods for solving partial differential equations.
• CMOR 428: Computational Differential Equations: Introduction to the implementation of computational methods for solving model partial differential equations.
• CMOR 430: Iterative Methods for Systems of Equations and Unconstrained Optimization: Iterative methods for linear systems and unconstrained optimization problems.
• CMOR 435: Dynamical Systems: Existence and uniqueness of solutions of ordinary differential equations and difference equations.
• CMOR 437: Optimization Foundations of Data Science: Optimization methods for machine learning.
• CMOR 438: Data Science and Machine Learning: Fundamentals of data science and machine learning.
• CMOR 441: Linear and Integer Programming: Linear optimization with continuous and integral variables.
• CMOR 442: Large-Scale Optimization: Decomposition of large-scale linear, nonlinear, and integer programs.
• CMOR 444: Discrete Optimization: Discrete optimization broadly involves finding the best solution from a finite set of possibilities.
• CMOR 446: Graph Algorithms: Graph algorithms in operations research.
• CMOR 451: Simulation Modeling and Analysis: Simulation techniques for studying complex stochastic systems.
• CMOR 452: Service Systems Analytics: Broad exploration of large-scale service systems using data analytics, stochastic models, optimization, and simulation techniques.
• CMOR 455: Stochastic Control and Applications: Stochastic control theory and applications.
• CMOR 461: Logistics and Supply Chain Management: Inventory management, scheduling, distribution, and location models.
• CMOR 462: Optimization Methods in Finance: Portfolio optimization and asset allocation models.
• CMOR 463: Operations Research in Healthcare: Operations research in healthcare systems and medical decision-making.
• CMOR 464: Manufacturing Processes and Systems: Fundamentals of manufacturing processes and systems.
• CMOR 465: Revenue Management & Pricing: Ever wondered why airfares change?
• CMOR 467: Optimization for Energy Systems: Optimization problems associated with electric power system modeling and optimization.
• CMOR 477: Special Topics: Topics and credit hours vary each semester.
• CMOR 490: Undergraduate Research Projects: Semester-long undergraduate-level research on a topic in computational and applied mathematics and/or operations research.
• CMOR 491: Undergraduate Research Projects: Semester-long undergraduate-level research on a topic in computational and applied mathematics and/or operations research.
• CMOR 492: Senior Design Project I: Team-oriented year-long design projects that utilize modeling, analysis, and scientific computing skills.
• CMOR 493: Senior Design Project II: Continuation of CMOR 492.
• CMOR 494: Pedagogy for CMOR 220 Rice Learning Assistants: Support for Rice Learning Assistants as they instruct their own lab sections of CMOR 220.
• CMOR 495: Losing the Precious Few: The class will read from Tapia's text and discuss issues associated with the underrepresentation of Blacks and Hispanics in academic and national science and engineering activities.
• CMOR 496: Computational and Applied Mathematics Seminar: Prepares a student for research in the mathematical sciences on a specific topic.

Graduate Courses

• CMOR 500: Analysis: Real numbers, completeness, sequences, and convergence.
• CMOR 501: Applied Functional Analysis: Hilbert spaces, Banach spaces, spectral theory, and weak topologies.
• CMOR 504: Graph Theory: Study of the structure and properties of graphs.
• CMOR 505: Partial Differential Equations I: First-order partial differential equations and analysis of solutions.
• CMOR 507: Applied and Computational Microlocal and Harmonic Analysis: Introduction to microlocal and harmonic analysis.
• CMOR 508: Nonlinear Systems: Analysis and Control: Mathematical background and fundamental properties of nonlinear systems.
• CMOR 510: Modeling Mathematical Physics: Derivation and properties of solutions of partial differential equations governing motion of fluids and solids.
• CMOR 514: Industrial and Applied Data Science Theory and Practice: Pragmatic introduction to the foundational theory of data science.
• CMOR 517: Scientific Machine Learning: Introduction to scientific machine learning and its application to physical problems.
• CMOR 518: Applications in Computational Mathematics: Introduction to fundamental tools in computational mathematics and their application to science and engineering problems.
• CMOR 520: Computational Science: Scientific programming using high-level languages.
• CMOR 521: High Performance Computing: Theory and application of message passing interface for programming scientific computing applications.
• CMOR 522: Numerical Analysis: Construction and application of numerical algorithms for root finding, interpolation, and approximation of functions.
• CMOR 523: Numerical Methods for Partial Differential Equations: Various numerical methods for solving partial differential equations.
• CMOR 524: Advanced Numerical Analysis: Construction and analysis of numerical algorithms for root finding and approximation of functions.
• CMOR 525: Numerical Linear Algebra: Iterative methods for solving linear systems and eigenvalue problems.
• CMOR 526: Foundations of Finite Element Methods: Theory and implementation of finite element methods.
• CMOR 527: Discontinuous Galerkin Methods for Solving Engineering Problems: Theory and implementation of discontinuous Galerkin methods.
• CMOR 528: Computational Differential Equations: Introduction to the implementation of computational methods for solving model partial differential equations.
• CMOR 530: Iterative Methods for Systems of Equations and Unconstrained Optimization: Iterative methods for linear systems and unconstrained optimization problems.
• CMOR 531: Convex Optimization: Convex optimization problems and algorithms.
• CMOR 532: Optimization Theory: Derivation and application of necessity conditions and sufficiency conditions for constrained optimization problems.
• CMOR 533: Numerical Optimization: Numerical algorithms for constrained optimization problems.
• CMOR 534: Intro to Partial Differential Equation Based Simulation and Optimization: Introduction to the theory and numerical methods for the solution of elliptic partial differential equations.
• CMOR 536: Optimization with Simulation Constraints: Optimization problems in which evaluations of objective or constraint functions require computationally complex simulations.
• CMOR 537: Computer-Assisted Algorithm Design for Optimization and Machine Learning: Transition from merely using and analyzing optimization algorithms to actively designing them.
• CMOR 541: Linear and Integer Programming: Linear optimization with continuous and integral variables.
• CMOR 543: Combinatorial Optimization: General theory and approaches for solving combinatorial optimization problems.
• CMOR 544: Stochastic Optimization: Stochastic optimization models and computational approaches.
• CMOR 551: Simulation Modeling and Analysis: Simulation techniques for studying complex stochastic systems.
• CMOR 552: Mathematical Probability I: Measure-theoretic foundations of probability.
• CMOR 553: Introduction to Random Processes and Applications: Review of basic probability and random processes.
• CMOR 554: Applied Stochastic Processes: Theory of stochastic processes and applications.
• CMOR 555: Stochastic Control and Applications: Stochastic control theory and applications.
• CMOR 556: Stochastic Networks and Queueing Systems: Stochastic networks and queueing systems in various applications.
• CMOR 567: Optimization for Energy Systems: Optimization problems associated with electric power system modeling and optimization.
• CMOR 590: Graduate Research Projects: Semester-long graduate-level research on a topic in computational and applied mathematics and/or operations research.
• CMOR 591: Graduate Research Projects: Semester-long graduate-level research on a topic in computational and applied mathematics and/or operations research.
• CMOR 595: Practicum in Computational Applied Mathematics and Operations Research: Practical internships for graduate students in degree programs administered by the Department of Computational Applied Mathematics and Operations Research.
• CMOR 600: Thesis Writing: Assists the student in preparation of the MA/PhD thesis and in other writing projects.
• CMOR 615: Theoretical Neuroscience I: Biophysical Modeling of Cells and Circuits: Theoretical foundations of cellular and systems neuroscience.
• CMOR 618: Topics in Seismic Imaging: Content varies from year to year.
• CMOR 619: Topics in Inverse Problems: Theoretical, computational, and practical issues for inverse problems.
• CMOR 620: Topics in Computational Science: Content varies from year to year.
• CMOR 623: Topics in Numerical Differential Equations: Content varies from year to year.
• CMOR 625: Topics in Numerical Linear Algebra: Selected topics will vary depending on instructor and student interests.
• CMOR 636: Topics in Nonlinear Programming: Content varies from year to year.
• CMOR 646: Topics in Optimization: Content varies from year to year.
• CMOR 677: Special Topics: Topics and credit hours vary each semester.
• CMOR 696: Computational and Applied Mathematics Seminar: Prepares a student for research in the mathematical sciences on a specific topic.
• CMOR 800: Research and Thesis: For MA or PhD students working on their thesis research.