Stevens Institute of Technology

 

Arthur E. Imperatore

School of Sciences and Arts

 

Master of Science

Stochastic Systems Analysis & Optimization

 

 

The students will learn cutting edge tools for optimization under uncertainty and risk

 

The Department of Mathematics at Stevens offers an interdisciplinary graduate program in Stochastic Systems to educate students in the area of analysis and optimal decisions for complex systems involving uncertain data.This unique program combines analysis of uncertainty with operations research methods and modern decision tools as stochastic programming and stochastic optimal control.

Our Goals are:

- to provide excellent education in the mathematical fundamentals of analysis and optimization of stochastic systems

- to focus on rigorous quantitative methods for decisions in the presence of uncertainty and risk including relevant areas such as stochastic and statistical analysis and forecasting, optimization and optimal control methods, and risk measures.

 

We work with interested faculty in the engineering and management schools to include examples of practical applications which will provide you with a broader professional perspective.

 

Our program integrates courses in statistics, stochastic processes, stochastic optimization and optimal control theory with applications in financial systems, networks design and routing, supply-chain management, actuarial science, telecommunication systems, statistical pattern recognition analysis associated with electronic commerce, medical diagnosis and others.You will be encouraged to apply the tools and techniques you learn to problems derived from your own professional work and interests.

 

Stevens Provides Two Program Options

The Master of Science in Stochastic Systems

Analysis and Optimization is a traditional ten course, 30 credit program.

 

The Graduate Certificate Program is a four course, 12 credit program for those who either do not require a rigorous educational foundation in this area, or for those who may not wish to commit to the full Masterís program at this time.All course credits obtained in the certificate program may be counted towards the Masterís degree in Stochastic Systems Analysis and Optimization.

 

Master of Science Program Courses

For the Masterís degree, six core courses and four electives are required.The electives must be chosen with the consent of the studentís advisor.

 

Core Courses (6)

Ma 547 Advanced Calculus I

Ma 611 Probability

Ma 612 Mathematical Statistics

Ma 623 Stochastic Process

Ma 629 Convex Analysis and Nonlinear Optimization *

Ma 661Dynamic Programming and Stochastic Optimal Control *

 

Typical Electives (4)

Ma 615 Numerical Analysis I

Ma 641 Time Series Analysis

Ma 662 Stochastic Programming *

Ma 655 Optimal Control *

Ma 627 Combinatorial Optimization

CS 652 Reliability Theory

Ma 632 Game Theory

Ma 720 Multivariate Statistics

CS 535 Financial Computing

 

Mgt 782 Simulation of Stochastic Systems

Mgt 730 Design and analysis of Experiments

En 780 Nonlinear Correlation and System Identification

 

A student may wish to complete the program with a concentration in Analysis of Uncertain Systems.In this case the courses Time Series Analysis, Multivariate Statistics, Design and Analysis of Experiments, Reliability Theory or Simulation of Stochastic Systems are recommended.A student may wish to complete the program with concentration on Optimal Decisions Under Uncertainty and in this case, the courses Stochastic Programming, Optimal Control, Combinatorial Optimization, Game Theory, or Simulation of Stochastic Systems are recommended. It is not necessary to complete the program with a concentration and every student may choose electives suitable for their needs and interests.

 

Graduate Certificate in Stochastic Systems

 

The Graduate Certificate program consists of the three core courses selected from those below plus one elective chosen with the consent of the studentís advisor.

Ma 612 Mathematical Statistics

Ma 623 Stochastic Process

Ma 629 Convex Analysis and Nonlinear Optimization

Ma 661Dynamic Programming and Stochastic Optimal Control

 

Who Should Enroll

Everyone involved with making optimal business decisions in the presence of uncertainty about important parameters.Situations of this type are common.

 

 

For example:

-         energy production that will cover uncertain demand

-         design or expansion of network systems that are able to deal with uncertain traffic; the networks may be roads, or computer networks for internet, telecommunication or other services

-         building and construction which can withstand earthquakes, wind, etc.

-         insurance and investment that will survive the turbulence of the market with a high probability

-         medical diagnostics where one negative test may not imply the absence of the disease

-         airline crew scheduling and ticket pricing

-         university admissions or admission in other institutions froma large uncertainpool of applicants.

 

Admission Requirements

 

Entering graduate students must know calculus, linear algebra, and have some basic knowledge in probability.

 

 

Related Programs

 

Other related graduate programs offered by the Department of Mathematical Sciences are:

Graduate Certificate in Applied Statistics

Master of Science, Applied Mathematics

Master of Science, Applied Statistics

Master of Science, Mathematics

Ph.D., Mathematics

 

Program director

Professor Darinka Dentcheva received her Ph.D. degree in Mathematics from Humboldt Univeristy in Berlin, Germany, in 1989.Her research interests are in the areas of optimization theory, statistics and decision making under uncertainty and risk.She is the author of many theoretical papers in these fields and has significant experience in applied projects.

 

Professor Dentcheva is a member of the Stochastic Programming Committee of the Mathematical Programming Society, and an Associate Editor of SIAM Journal on Optimization.

 

 

For more information on this graduate program, please contact:

Dr. Darinka Dentcheva

Department of Mathematical Sciences

Stevens Institute of Technology

Hoboken, NJ 07030

201-216-8640

ddentche@stevens-tech.edu

 

 

* The courses are newly introduced graduate courses designed specially for the program.