The certificate Program in Optimization and Quantitative Decision Science (OQDS), formerly the certificate Program in Engineering and Management Systems (EMS), is focused on developing quantitative skills for optimal decision making in complex and uncertain environments. These skills are increasingly relevant to problems and decisions that face the leaders, managers, engineers, and scientists of our generation. Through this certificate program, students will learn to quantify risk and uncertainty, and to view any complex decision through the lens of mathematical optimization. This outlook will give them a more structured understanding of the decision itself, as they learn to rigorously formulate their constraints, objective functions(s), and the uncertainties involved. It will also lead them to the proper algorithmic tools that are needed to arrive at an optimal decision.

The certificate program can be of interest to students in engineering, the sciences, and the liberal arts who are interested in analytical thinking and quantitative reasoning for the purpose of decision making under uncertainty. Emphasis is placed on rigorous modeling and analysis, taking advantage of the vast flow of data and ubiquitous computing power available today.

The OQDS program complements the certificate program in Applied and Computational Mathematics, and the minors or certificate programs in Statistics and Machine Learning, Finance, and Computer Science.

## Admission to the Program

The OQDS certificate program is open to both B.S.E. and A.B. students. B.S.E. students are required to take math through Math 201 and 202, which will satisfy the math prerequisites of any of the core courses. However, there is flexibility in the choice of core courses, and the math prerequisites depend on the electives that a student chooses. For A.B. students, it is their responsibility to take the necessary prerequisites for their program of study; students are encouraged to take Math 202 (and preferably Math 201) prior to the certificate program's core course requirements.

To be admitted, interested students should email the Director of the program,[email protected]. The email should state the student's request to participate in the program, and should include the following information: the student's class year, area of concentration, and whether the student has placed out of any course requirements.

## Program of Study

The program for each student is worked out by the student and the departmental adviser. The OQDS certificate program does not have a GPA requirement and students may elect to take one requirement on a pass/fail grading basis. Courses taken during Spring 2020 and the 2020-2021 academic year on a pass/fail grading basis are not counted towards the one pass/fail course rule. **Certificate program students may double-count no more than two courses for both their concentration and the OQDS certificate.** We allow double counting with other certificate or minor programs, but it is the student’s responsibility to check the double-counting requirements of the other certificate or minor program(s) of interest.

The OQDS certificate program requirements are as follows:

## Course Requirements

All students must take five courses from the following three areas:

- One core course in optimization
- One core course in uncertainty analysis
- Three elective courses on applications to quantitative decision making

Students may choose to take more than one course from category (1) or (2) and count the additional course(s) towards category (3) as long as at least one course from category (3) is taken.

1) **One core course in optimization**

- ORF 307 - Optimization
- ORF 311 – Stochastic Optimization and Machine Learning in Finance
- ORF363/COS 323 - Computing and Optimization for the Physical and Social Sciences

In special circumstances, the Director of the program may approve alternative graduate courses for qualified students. Examples include ORF 522 (Linear and Nonlinear Optimization), ORF 523 (Convex and Conic Optimization), and ECE 522 (Large-Scale Optimization for Data Science).

2) **One core course in uncertainty analysis**

- CEE 460 - Risk Assessment and Management
- ECE 382 – Probabilistic Systems and Information Processing
- ECO 202 - Statistics and Data Analysis for Economics
- GEO 422 – Data, Models and Uncertainty in the Natural Sciences
- MAT 385 – Probability Theory
- MAT 486 – Random Processes
- ORF 245 - Fundamentals of Statistics
- ORF 309 – Probability and Stochastic Systems
- ORF 409 – Introduction to Monte Carlo Simulation
- PHI 371 – Philosophical Foundations of Probability and Decision Theory
- POL 345/SOC 305 - Introduction to Quantitative Social Science
- PSY 251 - Quantitative Methods
- SOC 301 – Statistical Methods in Sociology
- SPI 200 - Statistics for Social Science

In special circumstances, the director of the program may approve alternative graduate courses for qualified students. An example is ORF 526 (Probability Theory).

3) **Three elective courses on applications to quantitative decision making**

- ARC 311 – Building Science and Technology: Building Systems
- ARC 404 – Advanced Design Studio
- CBE 442 - Design, Synthesis and Optimization of Chemical Processes
- COS 324 - Introduction to Machine Learning
- COS 484 - Natural Language Processing
- COS 510 - Programming Languages
- COS 598D – Optimization for Machine Learning
- ECE 364 - Machine Learning for Predictive Data Analytics
- ECE 435 – Machine Learning and Pattern Recognition
- ECO 312 - Econometrics: A Mathematical Approach
- ECO 418 - Strategy and Information
- ECO 462 - Portfolio Theory and Asset Management
- ECO 466 - Fixed Income, Options and Derivatives: Models and Applications
- EGR 395 - Venture Capital & Finance of Innovation
- EGR 494 – Leadership Development for Business
- EGR 497 - Entrepreneurial Leadership
- EGR/ECE 491 - High-Tech Entrepreneurship
- MAE 331 – Aircraft Flight Dynamics
- MAE 345 – Introduction to Robotics
- MAE 410/ENE 410/CBE 410 – Optimization for the Design and Analysis of Energy Systems
- MAE 433 - Automatic Control Systems
- MAE 434 – Modern Control
- MAT 378 – Theory of Games
- MAT 490 – Mathematical Introduction to Machine Learning
- MOL/QCB 485 – Mathematical Models in Biology
- MUS/COS 314 – Computer and Electronic Music through Programming, Performance, and Composition
- MUS 316 – Computer and Electronic Music Composition
- ORF 350 – Analysis of Big Data
- ORF 387 - Networks
- ORF 401 – Electronic Commerce
- ORF 405 – Regression and Applied Time Series
- ORF 407 – Fundamentals of Queueing Theory
- ORF 435 – Financial Risk Management
- ORF 467 – Transportation Systems Analysis
- ORF 542 – Stochastic Optimal Control
- POL 250 – Introduction to Game Theory
- POL 341 – Experimental Methods in Politics
- POL 346 – Applied Quantitative Analysis
- POL 347/ECO 347 – Mathematical Models in the Study of Politics
- POL 352 – Comparative Political Economy
- PSY 255/CGS 255 – Cognitive Psychology
- SPI 340/PSY 321 - The Psychology of Decision Making and Judgment

In special circumstances, the Director of the program may approve alternative graduate courses for qualified students. Examples include ECE 524 (Foundations of Reinforcement Learning), ORF/APC 550 (Probability in High Dimension).

The program is willing to occasionally add courses which clearly satisfy the objective(s) of each area. Students wishing to propose a course should send the syllabus to the OQDS Director,[email protected], with an explanation of which area the course satisfies, and why.

## Independent Work

A senior thesis or project must be completed and submitted to the program Director,[email protected], that demonstrates a command of some portion of the core disciplines of uncertainty analysis and/or optimization. Students in engineering departments that require a one-semester project can typically use a suitably designed project to satisfy the requirement.

Acceptable theses can be on a wide range of topics, but they must demonstrate a command of the core disciplines of the OQDS certificate program, including stochastics and/or optimization. The thesis must demonstrate, in appropriate mathematics, the ability to model a problem and perform analysis that leads to some conclusion or scientific result. A thesis with minimal or no mathematical modeling is not acceptable.

Theses that are not allowed include "soft" topics such as the history of a nation’s economy, and hard-science theses (laboratory-based theses) that do not have a significant modeling or data-analysis component (for example, collecting observations and computing basic statistics is not sufficient).

## Certificate of Proficiency

Students who fulfill the requirements of the program receive a certificate of proficiency in "Optimization and Quantitative Decision Science" upon graduation.

**Committee:**

Director: Amir Ali Ahmadi, Operations Research and Financial Engineering

Interdepartmental Committee

- Matias Cattaneo, Operations Research and Financial Engineering (2019-2024)
- Elad Hazan, Computer Science (2015-2024)
- Alain Kornhauser, Operations Research and Financial Engineering (2005-2024)
- Peter Ramadge, Electrical Engineering (2019-2024
- Clancy Rowley, Mechanical and Aerospace Engineering (2019-2024)
- Robert Vanderbei, Operations Research and Financial Engineering (2019-2024)