Computational and Applied Mathematics (CAM)

Supervised projects selected to suit the needs of the graduate student, including those wishing to perform an internship as part of the Curricular Practical Training Program. Projects to be chosen in consultation with the student’s advisor. Acceptable research outlines and project reports are required. Students may count credits received in only one offering of this course toward the number of credits required for their degree.

Prerequisite: a course in a high-level programming language. This course introduces students to a number of computing topics. Topics include LINUX operating system and its editors, C programming language, R programming language, LaTeX and Beamer, as well as William and Mary’s high performance computing network.

Prerequisite(s): Equivalent of MATH 351. Development and use of systematic procedures for assisting decision makers in evaluating alternative choices. Emphasis is on problem formulation, uncertainty and risk assessment, Bayes, minimax and other decision rules and applications. Problems will be solved using appropriate software tools.

Prerequisite: equivalent of MATH 351. Topics covered in this course include the theory, design, conduct, and statistical analysis of experiments. Special emphasis is placed upon factorials and fractional factorials to optimize experimental resources.

A study of realistic and diverse Operations Research problems with emphasis upon model formulation, interpretation of results and implementation of solutions. Topics include applications of linear programming, goal programming, decomposition of large-scale problems, and job scheduling algorithms. Problems will be solved using appropriate software tools.

Prerequisite: equivalent of MATH 351. Topics covered in this course include the theory, mechanics, and application of simple and multiple linear regression.

Prerequisite(s): equivalent of MATH 211. Theory and applications of linear programming. Topics include the simplex method, duality theory, sensitivity analysis and interior point methods. Problems will be solved using appropriate software tools.

Topics include unconstrained optimization, nonlinear least-squares, feasible-point methods, and penalty and barrier methods, with an emphasis on effective computational techniques.

Business analytics (BA) refer to the use of data by organizations, including businesses, non-profits, and government entities, to extract insights and enhance decision-making processes. It finds application in various areas such as operations, marketing, finance, and strategic planning, among others. This course underscores that BA is not a theoretical field; its methodologies only hold significance when they can translate into practical insights that enhance the speed, dependability, and quality of decisions.

This course emphasizes coding of Mixed Integer Programming (MIP) models, interpreting solver results, and deepening the understanding of solving techniques. Solver techniques include Lagrangian relaxation, Benders decomposition, column generation, as well as branch and bound, polyhedral theory and cutting planes.

Prerequisite(s): equivalent of courses MATH 451/551 and CAM 606. Introduction to probabilistic models and statistical methods used in analysis of reliability problems. Topics include models for the lifetime of a system of components and statistical analysis of survival times data. Problems will be solved using appropriate software tools.

Discrete optimization problems are those problems with decisions that are logical (yes/no) or countable. Both exact and heuristic methods for discrete optimization models will be presented in the course. Topics include relaxation techniques, constructive heuristics, improving search techniques (simplex method, simulated annealing, tabu search and genetic algorithms), branch and bound schemes, and valid inequalities for branch and cut methods.

Graded Pass/Fail. No credits earned in this course may be applied to the number of credits required to satisfy graduate degree requirements.  This course may be repeated. 

Prerequisite: CAM 628 and equivalent of MATH 451/551. This course provides a deeper understanding of the optimization principles that underpin modern machine learning and data science. Topics include regularized regression, support vector machines, and reinforcement learning models. Students will explore real-world applications and gain hands-on experience, formulate and solve data-driven optimization problems efficiently.

Prerequisite(s): equivalent of courses MATH 451/551 and CAM 606. This course introduces statistical techniques used in the analysis of simulation models. The first half of the course develops techniques for determining appropriate inputs to a simulation model, and the last half develops analysis techniques that are applied to the output of a simulation model.

Network location problems arise in many diverse applications. Examples include locating facilities, sensors, components, vehicles, people, services, and actuators. The course will include topics from classical location theory (covering, center and median problems) as well as more recent topics in the literature.

Graded Pass/Fail. Students must attend at least seven research talks. No credits earned in this course may be applied to the number of credits required for a degree. This course may be repeated.

This course provides a deeper understanding of the optimization principles that underpin modern machine learning and data science. Topics include regularized regression, support vector machines, and reinforcement learning models. Students will explore real-world applications and gain hands-on experience, formulate and solve data-driven optimization problems efficiently.

A treatment of Master’s level topics of interest not routinely covered by existing courses. Material may be chosen from various areas of computational operations research. May be repeated for different topics. This course may be repeated for credit.

Graded Pass/Fail. Permission of the instructor and the Graduate Director required. A description of the intended contents of the readings course must be approved by the Graduate Director before the student may register for the course. Only one offering of this course may count towards meeting the M.S. degree requirements.

Prerequisite(s): equivalent of courses MATH 451/551 and CAM 606. Simulation model building in a high-level simulation language. Topics include network, discrete-event, and continuous modeling approaches. Interfaces between the three modeling approaches are presented. Familiarity with univariate and multivariate probability distributions is required for input modeling and simulation output analysis. Course culminates in a semester project.

Graded Pass/Fail. Permission of Graduate Director required. Students will select a faculty advisor and committee in their area of specialization within computational and applied mathematics, prepare a research proposal abstract for approval by the Graduate Director, undertake a research project, and write a paper describing their research.