## MS&E 20: Discrete Probability Concepts And Models

Fundamental concepts and tools for the analysis of problems under uncertainty, focusing on structuring, model building, and analysis. Examples from legal, social, medical, and physical problems. Topics include axioms of probability, probability trees, belief networks, random variables, conditioning, and expectation. The course is fast-paced, but it has no prerequisites.

Terms: Sum
| Units: 4
| UG Reqs: WAY-FR

Instructors:
Shachter, R. (PI)

## MS&E 52: Introduction to Decision Making

How to ensure focus, discipline, and passion when making important decisions. Comprehensive examples illustrate Decision Analysis fundamentals. Consulting case studies highlight practical solutions for real decisions. Topics: declaring when and how to make a decision, framing and structuring the decision basis, defining values and preferences, creating alternative strategies, assessing unbiased probabilistic judgments, developing appropriate risk/reward and portfolio models, evaluating doable strategies across the range of uncertain future scenarios, analyzing relevant sensitivities, determining the value of additional information, and addressing the qualitative aspects of communication and commitment to implementation. Required for all students are three problem sets, three in-class exams, and a take-home final exam. Students taking the course for 4 units of credit must also complete and present a team project that analyzes a decision currently being made by an organization of their choice. Not intended for MS&E majors.

Terms: Sum
| Units: 3-4

Instructors:
Robinson, B. (PI)

## MS&E 92: Introduction to Health Policy Modeling

The application of mathematical models to problems in health policy. Estimating the benefits, harms, costs, and uncertainties of a health policy or intervention. Understanding concepts of cost-effectiveness analysis. Developing decision models that capture the tradeoffs between policy alternatives. Examples include disease screening, prevention, and treatment, combating the opioid epidemic, and protecting the blood supply. As a course project, students will develop a simple decision model to evaluate a current health policy problem.

Terms: Sum
| Units: 3

## MS&E 92Q: International Environmental Policy

Preference to sophomores. Science, economics, and politics of international environmental policy. Current negotiations on global climate change, including actors and potential solutions. Sources include briefing materials used in international negotiations and the U.S. Congress.

Terms: Win
| Units: 3

Instructors:
Weyant, J. (PI)

## MS&E 93Q: Nuclear Weapons, Energy, Proliferation, and Terrorism

Preference to sophomores. At least 20 countries have built or considered building nuclear weapons. However, the paths these countries took in realizing their nuclear ambitions vary immensely. Why is this the case? How do the histories, cultures, national identities, and leadership of these countries affect the trajectory and success of their nuclear programs? This seminar will address these and other questions about nuclear weapons and their proliferation. Students will learn the fundamentals of nuclear technology, including nuclear weapons and nuclear energy, and be expected to use this knowledge in individual research projects on the nuclear weapons programs of individual countries. Case studies will include France, UK, China, India, Israel, Pakistan, North Korea, South Africa, Libya, Iraq, and Iran, among others. Please note any language skills in your application. Recommended: 193 or 293.

Terms: Spr
| Units: 3
| UG Reqs: GER:DB-EngrAppSci

Instructors:
Hecker, S. (PI)

## MS&E 108: Senior Project

Restricted to MS&E majors in their senior year. Students carry out a major project in groups of four, applying techniques and concepts learned in the major. Project work includes problem identification and definition, data collection and synthesis, modeling, development of feasible solutions, and presentation of results. Service Learning Course (certified by Haas Center). Satisfies the WIM requirement for MS&E majors.

Terms: Win
| Units: 5

Instructors:
Ashlagi, I. (PI)
;
Chiu, S. (PI)
;
Goel, A. (PI)
;
Katila, R. (PI)
;
Pelger, M. (PI)
;
Tse, E. (PI)
;
Valentine, M. (PI)
;
Pontius, W. (TA)

## MS&E 111: Introduction to Optimization (ENGR 62, MS&E 211)

Formulation and computational analysis of linear, quadratic, and other convex optimization problems. Applications in machine learning, operations, marketing, finance, and economics. Prerequisite:
CME 100 or
MATH 51.

Terms: Spr
| Units: 3-4
| UG Reqs: GER:DB-EngrAppSci

Instructors:
Goel, A. (PI)
;
Aboumrad, G. (TA)
;
Kessel, K. (TA)
...
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## MS&E 111X: Introduction to Optimization (Accelerated) (ENGR 62X, MS&E 211X)

Optimization theory and modeling. The role of prices, duality, optimality conditions, and algorithms in finding and recognizing solutions. Perspectives: problem formulation, analytical theory, computational methods, and recent applications in engineering, finance, and economics. Theories: finite dimensional derivatives, convexity, optimality, duality, and sensitivity. Methods: simplex and interior-point, gradient, Newton, and barrier. Prerequisite:
CME 100 or
MATH 51 or equivalent.

Terms: Aut, Win
| Units: 3-4

Instructors:
Van Roy, B. (PI)
;
Ye, Y. (PI)
;
Dong, S. (TA)
;
Dwaracherla, V. (TA)
;
Kang, C. (TA)
;
Liu, C. (TA)
;
Mehdian, S. (TA)
;
Vallon, J. (TA)
;
Zou, J. (TA)

## MS&E 112: Mathematical Programming and Combinatorial Optimization (MS&E 212)

Combinatorial and mathematical programming (integer and non-linear) techniques for optimization. Topics: linear program duality and LP solvers; integer programming; combinatorial optimization problems on networks including minimum spanning trees, shortest paths, and network flows; matching and assignment problems; dynamic programming; linear approximations to convex programs; NP-completeness. Hands-on exercises. Prerequisites: basic concepts in linear algebra and probability theory,
CS 106A or X.

Last offered: Winter 2019

## MS&E 120: Probabilistic Analysis

Concepts and tools for the analysis of problems under uncertainty, focusing on focusing on structuring, model building, and analysis. Examples from legal, social, medical, and physical problems. Topics include axioms of probability, probability trees, random variables, distributions, conditioning, expectation, change of variables, and limit theorems. Prerequisite:
CME 100 or
MATH 51.

Terms: Aut
| Units: 5
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

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