University Catalog 2007-2008

University Catalog >IT&E > Systems Engineering and Operations Research

Systems Engineering and Operations Research

Phone: 703-993-1670

Web: seor.gmu.edu

Faculty

Professors: Adelman, Chang, Donohue, Hoffman, Nash, Polyak, Sage, Schum, Sofer (chair)

Associate professors: Brouse, Chen, Laskey, Loerch, Shortle, White

Assistant professors: Ganesan, Liu

Affiliated faculty members: Gulledge, Houck, VanTrees

Research and term professors: Gross, Sherry, Wagenhals, Wagner, Wolman

Adjunct professors: Alexander, Barry, Camp, Carley, Durbin, Fischer, Humphrey, Killam, McDevitt, Nguyen, Patel, Rothwell, Taft, Wieland, Yost

The Systems Engineering and Operations Research (SEOR) Department offers a bachelor's degree in systems engineering, a certificate for undergraduates (the equivalent of a minor) in operations research and engineering, and master's degrees in systems engineering and operations research. In addition, the department offers five certificate programs at the master's level: architecture-based systems engineering; command, control, communications, computing, and intelligence (C4I); military operations research; computational modeling; and systems engineering for computer, information, and software-intensive systems. Students interested in pursuing doctoral education in operations research or systems engineering are encouraged to read the sections on the interdisciplinary PhD in information technology and the PhD study in systems engineering and operations research.

Systems engineers determine the most effective ways for an organization to use all of a given system's components: people, machines, materials, information, and energy. The engineers plan, design, implement, and manage integrated systems, working to ensure performance, safety, reliability, and maintainability. They also work to ensure that systems are delivered on time at reasonable cost. Examples of systems are computer networks, automobiles, intelligent robots, stereos, the Metro, and Mason. Whereas other engineering disciplines concentrate on individual aspects of a system, such as electronics, ergonomics, or software, systems engineers focus on the system as a whole. Systems engineering, perhaps more than any other engineering discipline, is involved with the human and organizational aspects of developing the desired system. Systems engineering is the people-oriented engineering profession.

Operations research is the professional field that deals with using scientific methods in engineering and management decision making, often focusing on how best to allocate limited resources. Operations researchers do for organizations what physicists do for the physical world: they try to find order in apparent chaos by identifying the structure in complex situations and understanding how the components of organizations interact. The goal is to explain and predict the effects of actions taken on these systems. Much of this work is developing and manipulating mathematical and computer models of organizational systems composed of people, machines, information, and procedures. The overall purpose is to provide a rational basis for decision making.

Mason's operations research faculty are principally involved in the theoretical and empirical study of managerial and operational processes, and the use of mathematical and computer models to optimize these systems. Models are needed for a variety of decision-making purposes in business, industry, scientific research, and government to describe different environments and relate alternative plans of action. Thus, the courses in operations research focus on quantitative modeling and the analysis of complex systems. Courses stress the use of contemporary computer hardware and software in modeling and analysis. The Bureau of Labor Statistics predicts that the field of operations research will be one of the fastest-growing professions of the next decade.

Obviously, there is much overlap between systems engineering and operations research. The department encourages students of either discipline to elect courses in the other. For more information, go to seor.gmu.edu.

Course Work

The department offers all courses designated SYST and OR in the Course Descriptions chapter of this catalog.

Undergraduate Program

The mission of the undergraduate program is to equip students with the ability to participate productively in the many professional activities associated with the engineering of a trustworthy system that satisfies client needs. The term "system" is interpreted broadly to include information, telecommunication, defense, health delivery, transportation and manufacturing systems, and corporate processes.

Specifically, the objectives of the systems engineering program are that graduates of the program will be able to

Systems Engineering, BS

The program leading to the BS in systems engineering prepares students for a professional career in systems engineering. The educational program reflects the systems engineer's unique perspective, which considers all aspects of a system throughout its lifetime. Mason's systems engineering program is interdisciplinary, drawing from engineering, computer science, operations research, psychology, and economics. The core systems engineering courses tie these diverse threads to provide a global understanding of how individual engineering disciplines fit into the development of complex, large-scale systems. Students gain depth in a technical area by selecting a sequence of technical electives that constitute an emphasis. Students construct their own emphasis with the help of their advisor. A yearlong senior design project provides hands-on experience in applying various systems engineering methods and tools.

This program is accredited by the Engineering Accreditation Commission of the Accreditation Board for Engineering and Technology, 111 Market Place, Suite 1050, Baltimore, MD 21202-4012; 410-347-7700. The requirements for the degree may be satisfied on a part-time basis. Cooperative education provides students with the opportunity to integrate paid, career-related work experience with classroom learning.

Degree Requirements

In addition to Mason's general education requirements, students must meet specific requirements for this degree. In the first two years, students obtain a basic foundation in mathematics, the natural sciences, computing, writing, humanities, fine arts, and social sciences. The systems engineering program builds on this foundation, teaching theoretical knowledge, practical skills, and the ability to apply systems thinking to problems. Teamwork, collaborative learning, analytical skills, practical problem solving, and oral and written communication are strongly stressed.

Course requirements for the systems engineering major are as follows:

Writing-Intensive Requirement

Mason's writing-intensive requirement for systems engineering majors is satisfied by successful completion of SYST 489.

Synthesis Requirement

Mason's synthesis requirement for systems engineering majors is satisfied by successful completion of SYST 495.

General Education Electives

General education electives should be selected from the department's list of approved courses.

Sample Schedule

The following sample schedule shows the required and elective courses in the program. Students are strongly encouraged to follow this sample schedule to ensure that prerequisites are satisfied. For students who do not place into MATH 113 by taking the math placement exam, an alternate schedule is available.

First Semester
COMM 100 Oral Communication 3
ECON 103 Contemporary Microeconomic Principles 3
ENGL 101 Composition 3
ENGR 107 Introduction to Engineering 2
MATH 113 Analytic Geometry and Calculus I 4
Total 15


Second Semester
CS 112 Computer Science I 4
MATH 114 Analytic Geometry and Calculus II 4
PHYS 160 University Physics I 3
PHYS 161 University Physics I Laboratory 1
SYST 101 Understanding Systems Engineering 3
Total 15


Third Semester
CS 211 Computer Science II 3
MATH 213 Analytic Geometry and Calculus III 3
PHYS 260 University Physics II 3
PHYS 261 University Physics II Lab 1
SYST 210 Systems Design 3
Literature 3
Total 16


Fourth Semester
CHEM 251General Chemistry for Engineers or CHEM 211 General Chemistry 4

CMATH 203 Matrix Algebra 3
MATH 214 Elementary Differential Equations 3
SYST 220 Dynamical Systems I 3
SYST 221 Systems Modeling Laboratory 1
Total 14


Fifth Semester
ENGL 302 Advanced Composition (for natural sciences and technology) 3
OR 441 Deterministic Operations Research 3
STAT 346 Probability for Engineers 3
SYST 320 Dynamical Systems II 3
Technical elective 3
Total 15


Sixth Semester
STAT 354 Engineering Statistics 3
SYST 330 Systems Methods 3
SYST 335/OR 335 Discrete Systems Modeling and Simulation 3
SYST 371 Systems Engineering Management 3
SYST 473 Decision and Risk Analysis 3
Total 15


Seventh Semester
SYST 470 Human Factors Engineering 3
SYST 489 Senior Seminar 3
SYST 490 Senior Design Project I 3
Arts 3
Technical elective 3
Total 15


Eighth Semester
HIST 100 Western Civilization 3
OR 442 Stochastic Operations Research 3
SYST 495 Senior Design Project II 3
Technical elective 3
Global understanding 3
Total 15


All systems engineering students are assigned a faculty advisor. With the help and approval of the advisor, each student is required to complete a plan of study. This plan of study, contained in the detailed pamphlet available from the SEOR office, constitutes a learning plan for the degree program. The advisor must approve changes to the plan of study. All students in systems engineering are required to see their advisor at least once each semester to plan for the next semester's registration.

The systems engineering program requires 9 credits of technical electives. Students must select one of the following technical specializations, each containing three courses.

Operations Research

Control Systems

Computer Network Systems

Software-Intensive Systems

Engineering Systems

In addition to receiving a BS degree, students may wish to select a sequence that contributes toward a minor program.

Change of Major

Students who want to change their major to systems engineering must have a GPA of at least 2.75 in all math, physics, engineering, and computer science courses taken to fulfill requirements for the systems engineering degree and should have completed MATH 114 with a grade of B or better.

Certificate in Operations Research and Engineering

This certificate program is open to students enrolled in the computer science, decision sciences, and mathematics undergraduate degree programs. The certificate augments the standard curricula with material on the computational aspects of operations research. Because the demand for people trained in this area is great, this program expands the career options available to students.

Required Courses

Plus two of the following courses:

Interdisciplinary Minor Programs

By taking appropriate sequences of technical electives and, in some cases, a few courses in addition to the 120 credits required for graduation, students in the systems engineering program can obtain a minor in an interdisciplinary program. Available minors include data analysis and computer science. Students should see their advisor and the departments offering the minors for specific requirements.

BS/Accelerated MS in Systems Engineering

Qualified undergraduate students may apply for this five-year program, which leads to a BS in an engineering discipline and an MS in systems engineering. The program can be completed in 144 credits. Applicants must be Mason undergraduate students majoring in systems engineering, computer science, computer engineering, electrical engineering, or civil and infrastructure engineering. Students may apply after they have completed at least 90 credits applicable to the BS degree. Students must have an overall GPA of at least 3.30 on courses applicable to the BS degree and must have successfully completed all MATH and PHYS requirements.

Students must complete all requirements for the BS in their chosen major. Students in the accelerated program may apply to have the BS degree from the appropriate Volgenau School program conferred during the semester during which they expect to complete BS requirements. The MS degree is granted on completion of remaining courses.

Up to two courses (6 credits) of master's level courses taken as part of the undergraduate degree may be applied to the graduate degree. These two courses may be chosen from the list of graduate courses in the following table. For BS candidates, these graduate courses replace the corresponding undergraduate courses listed in the table. The undergraduate version of these courses may not be applied toward the MS degree.

Under-graduate Graduate

Any other 500-level SYST course may be applied to both the undergraduate and graduate degrees with approval of the advisor and department chair.

BS/Accelerated MS Program in Operations Research

Qualified undergraduate students may apply for this five-year program leading to a BS in an engineering discipline and an MS degree in operations research. The program can be completed in 144 credits. Applicants must be Mason undergraduate students majoring in systems engineering, computer science, computer engineering, electrical engineering, or civil and infrastructure engineering. Students may apply for the program after they have completed at least 90 credits applicable to the BS degree. Students must have an overall GPA of at least 3.30 on courses applicable to the BS degree and must have completed all MATH and PHYS requirements. Criteria for admission are identical to criteria for admission into the MS program, with the exception that students do not need to have completed an undergraduate degree before admission.

Students must complete all requirements for the BS in their chosen major. Students may apply to have the BS degree from the appropriate Volgenau School program conferred during the semester during which they expect to complete BS requirements. The MS degree is granted on completion of remaining courses.

Up to two courses (6 credits) of master's level courses taken as part of the undergraduate degree may be applied to the graduate degree. For BS candidates, these graduate courses replace the corresponding undergraduate courses. The undergraduate version of these courses may not be applied to the MS degree. Systems engineering majors in the accelerated program are required to take OR 541 and 542 in place of OR 441 and 442.

Graduate Programs

Operations Research, MS

This program prepares students for research and professional practice associated with the formulation and analysis of mathematical models for decision making and their computer implementation. Major components include optimization, queuing and network modeling, computer simulation and modeling, applied and computational probability, and application of these components to realistic and relevant operational analysis problems. Students are expected to become proficient in these areas, as well as in supporting areas of information technology necessary to implement operations research methods.

The program includes core courses and electives selected by the student with the aid of a faculty advisor. To obtain the MS degree, students complete an approved plan of study that contains a minimum of 30 graduate credits. Students may take courses through the Commonwealth Graduate Engineering Program. Appropriate courses may be transferred, with advisor approval, into this Mason degree program.

Admission Requirements

To be admitted to the program, students must hold a baccalaureate degree from an accredited institution in engineering, mathematics, computer science, physical sciences, economics, or a related field. They also must have completed courses in calculus (MATH 113, 114, and 213), matrix algebra (MATH 203), differential equations (MATH 214), applied probability and statistics (STAT 346), and a scientific programming language (CS 112). Other requirements are as follows:

The department offers SYST 500 as an intensive review of undergraduate engineering mathematics, including matrix algebra, transforms, differential equations, probability, and statistics. On acceptance, students will be required to take a foundation qualification test a week or two before school starts, unless waived by the department chair or graduate coordinator. Students who fail the test will be required to take SYST 500. A sample test is available from the department.

Students with minor deficiencies in preparation may be accepted conditionally pending removal of the deficiencies. Courses taken to remove admission deficiencies (including SYST 500) extend minimum requirements for the degree. Students whose undergraduate training was in the quantitative social sciences or quantitatively oriented business administration may be allowed to complete a portion of the mathematics prerequisite by taking SYST 500.

Degree Requirements

The program consists of 30 credits. Students must complete four core courses and the project (15 credits).

Core Courses, Project

* Students who have performed well in their undergraduate calculus-based probability class may take OR 645 Stochastic Processes instead.

In addition, at least three 600-level or higher OR courses must be taken. These include at least one deterministic methods and one stochastic methods course.

Deterministic methods courses:

Stochastic methods courses:

Electives

Up to two additional elective courses may be chosen with written concurrence of the advisor. These courses should be taken in an area appropriate to the student's interests, such as operations research statistics, computer science, information systems, systems engineering, electrical and computer engineering, economics, and mathematics. At least one of these electives must be taken from SEOR's course offerings.

With the advisor's permission, a qualified student may elect to write a thesis in place of 3 credits of course work from the methodological or applications area.

Students may construct concentration areas by choosing electives from among special groupings. The four concentrations available are optimization, stochastic modeling, decision analysis, and military operations research.

Students whose primary interest is in optimization may complete a concentration by choosing three courses from OR 640, 641, 642, 643, 644, 682, and 741. The remaining two courses are chosen with written concurrence of the advisor. They should be tailored to the student's interest and must include at least one stochastic methods course. The other course may be chosen from the department's offerings, appropriate offerings in other departments within the Volgenau School and appropriate courses from other university departments. A sample of possible courses outside SEOR is available from the department office.

Students concentrating in stochastic modeling must complete one 600-level statistics course (numbered 634 or above) and two courses from OR 645, 647, 648, and 677. The remaining two courses are chosen with written concurrence of the student's advisor and must include at least one deterministic methods course.

Students concentrating in decision analysis must complete OR 671 and 681, and SYST/STAT 664. The remaining two electives are chosen with written concurrence of the student's advisor and must include one deterministic methods course and one stochastic methods course.

Finally, students concentrating in military operations research must complete OR 651 and 652, and SYST 683. The remaining two courses are chosen with written concurrence of the student's advisor and must include one deterministic methods course and one stochastic methods course.

Particularly important to students planning a PhD program in information technology are the core courses that satisfy the breadth requirement.

Systems Engineering, MS

This program prepares students for a professional career in systems design, development, and management, associated with problem formulation, issue analysis, and evaluation of alternative courses of action. The program emphasizes both analytical and practical aspects of engineering complex systems. Students are expected to demonstrate proficiency in several quantitative modeling disciplines. Students are also expected to master issues relevant to practical aspects of systems design, engineering, and management. The program prepares students for careers in research and development, and pursuing advanced graduate study leading to the PhD in information technology.

Each student is assigned a faculty advisor with whom to work to complete an approved plan of study. This plan of study must include three core courses, two methods courses, three to four electives in a concentration, and a thesis or systems engineering project. The plan of study must include 30 graduate credits. Either a thesis (6 credits) or research project (3 credits) is required for the degree. Matriculation requirements for candidates needing additional work in mathematics or engineering also may be included in the plan of study.

Foundation and Admission Requirements

Applicants should have a baccalaureate degree from an accredited institution in engineering, mathematics, computer science, physical sciences, economics, or a related field. They also should have completed courses in calculus (MATH 113, 114, and 213), matrix algebra (MATH 203), differential equations (MATH 214), applied probability and statistics (STAT 346), and a scientific programming language (CS 112). Other requirements are as follows:

Students who have not completed a basic engineering undergraduate mathematics sequence will be required to complete courses in engineering calculus and matrix algebra prior to acceptance. On acceptance, students will be required to take a foundation qualification test a week or two before school starts, unless waived by the department chair or graduate coordinator. Students who fail the test will be required to take SYST 500 or other foundation courses. A sample test is available from the department.

Familiarity with analytical modeling software, such as spreadsheets or math packages, is also expected. Students should acquaint themselves with these software packages before beginning classes.

Project or Thesis

Each student must complete a project (3 credits) or thesis (6 credits). Under the project option, students complete 3 credits of SYST 798 or OR 680, in which students propose and conduct an approved team project. A project report is submitted at the end of the semester, and a final presentation is made to the Systems Engineering and Operations Research Department faculty. Under the thesis option, students complete 6 credits of SYST 799. The master's thesis should reflect a significant independent research effort. The work is conducted under the guidance of a faculty thesis advisor from the Systems Engineering and Operations Research Department, and the final written thesis and oral defense are approved by a three-member faculty committee and submitted to the Volgenau School. The thesis work is expected to be completed while taking 6 credits of SYST 799. Although students may register for more than 6 credits, only 6 credits may be applied toward the degree.

Core Courses

Students must complete the following three core courses (9 credits):

Methods Courses

Students must complete two basic methods courses, including SYST 611 System Methodology and Modeling. The other basic methods course may depend on the emphasis chosen by the student and must be selected from the following list:

Emphasis Courses

Students must complete a set of elective courses that, together with the basic methods courses, constitute a clearly defined emphasis within systems engineering. Students pursuing the thesis option complete three electives in an emphasis; students pursuing the project option complete four electives in an emphasis.

Students may create their own emphasis with the approval of their advisor, or they may choose one of the following six emphases: systems engineering methods, systems management, architecture-based systems integration, C4I, systems engineering of computer-based systems, and advanced transportation systems. Approved basic methods courses and electives for the major emphases are as follows.

Systems Engineering Methods

Systems engineers must address a broad range of issues relevant to the design, implementation, analysis, and management of systems. This emphasis provides methodological tools that can be applied to the systems engineering process. Areas of focus include decision support systems, distributed intelligent systems, knowledge-based planning systems, network systems, probabilistic reasoning systems, sensor fusion systems, and optimization methods. The graduate program in systems engineering recognizes the importance of balancing an education in quantitative models and engineering tools with a proper understanding of the systems perspective.

Basic methods courses:

Elective courses:

Courses designated as basic methods courses may also be used as elective courses once the requirement of two basic methods courses has been met. The set of elective courses must constitute a well-defined focus and must be approved by the student's advisor.

Systems Management

The defining reality of the 20th century is evolution into a society of organizations and the emergence of management as a discipline. The technical disciplines of systems engineering are necessary but not sufficient for the development of successful systems. The management aspect of systems engineering involves tracking and controlling system development through the major phases of the system life cycle; identifying and resolving problems to minimize their effects on cost, schedule, and performance, and iteratively improving both product and process. The emphasis in systems management focuses on theory and practice and prepares students for careers in managing the development of complex systems.

Basic methods courses:

Elective courses:

The set of elective courses must constitute a well-defined focus. Basic methods courses beyond the two required methods courses may also be counted as elective courses. Approved electives include the following:

Architecture-Based Systems Integration

There is much interest today in the engineering of systems that comprise other component systems, where each of the component systems serves organizational and human purposes. These systems families are often categorized as systems of systems, federations of systems, or coalitions of systems. The design of architectures is a major ingredient in the design of systems families. Furthermore, it provides the conceptual basis for achieving system integration. This emphasis covers the formulation of the system integration problem, definition of architecture frameworks, use of structured analysis and object-oriented methodologies for the design of architectures, modeling and simulation for the evaluation of architectures, and approaches to integration. Both defense and industrial applications are considered.

Basic methods courses:

Elective courses:

The set of elective courses must constitute a well-defined concentration area. This emphasis area consists of three required courses and one elective course from an approved list. The three required courses are

The list of approved electives includes basic methods courses and the following:

Command, Control, Communications, Computing, and Intelligence (C4I)

C4I systems are pervasive throughout the civilian and military world, allowing responsible authorities, such as commanders or chief executive officers, to control resources such as personnel, equipment, and money. Civilian government examples include air-traffic control, drug enforcement, law enforcement agencies, and various emergency preparedness systems. Military systems include national-level crisis management systems, global command and control system, NATO command and control systems, and various tactical C4I systems of the military services. Private industry examples include the corporate management systems of large national and multinational firms.

These systems include the equipment, people, and procedures necessary to accomplish the mission. The equipment may include a variety of sensors, communications systems, and information-processing and decision-support systems. This area stresses the multidisciplinary approach necessary to understand the field.

The specialization focuses on the theory and practice of C4I and prepares students for careers in research, design, and development in the use and management of C4I systems. Courses emphasize analytical and behavioral aspects of engineering complex C4I systems.

Basic methods courses:

Elective courses:

The set of elective courses must constitute a well-defined concentration area. Examples of concentration areas include C3 architectures, C2 software, communications, decision support, modeling and simulation, or sensing and fusion.

Students in the C4I specialization area must complete SYST 680/ECE 670/OR 683 Principles of C4I.

They may select their remaining electives from the list of basic methods courses or the following:

Systems Engineering of Computer-Based Systems

The computer-based systems emphasis provides specialized knowledge and experience in developing and modifying large complex software systems. It emphasizes technical and management aspects of the software engineering process. Computer-based systems engineers are concerned with the theoretical and practical aspects of technology, cost, and the social effect of computer systems that are both effective and efficient.

Basic methods courses:

Students must complete one of the following:

Elective courses:

The set of elective courses must constitute a well-defined focus. Basic methods courses beyond the two required methods courses may also be counted as elective courses. The set includes the following:

One of the following:

Advanced Transportation Systems (ATS)

Transportation is one of the most important and increasingly complex infrastructure networks of modern society. This emphasis looks at transportation operations, monitoring, and control from a systems engineering perspective. It uses both analytical and complex simulations to create awareness of how future transportation systems will evolve.

Basic methods courses:

Elective courses:

Two from the following list:

The remaining elective courses can be taken from the list above, the list of basic methods courses, and the following:

CEIE 660 Urban Transportation Planning

Dual-Degree MS in Operations Research and Statistical Science

This program allows students to earn an MS degree in operations research and an MS degree in statistical science by completing 48 credits of course work in both areas instead of the 60 that would be required if the degrees were sought independently.

Admission Requirements

Applicants must satisfy admission requirements for the MS in operations research program and the MS in statistical science program. A joint faculty committee from the Statistics and Systems Engineering and Operations Research Departments make final admission decisions into the dual-degree program.

Degrees Requirements

The dual-degree program requires a total of 48 credits as specified below:

A maximum of 6 credits across the two disciplines may be in independent research (thesis). The requirements for independent research are the same as detailed for the associated MS program.

Students in either the BS/Accelerated MS in Operations Research Program or the BS/Accelerated MS Statistics Program cannot get a reduction of 6 credits toward this dual degree. Students who want to proceed to a PhD degree will only be able to waive the number of credits specified in the associated PhD degree requirements, even though they have 48 credits at the MS level.

If a student decides not to complete the required 48 credits, a single MS degree will not be granted unless the student fulfills the requirements for the MS in operations research or the MS in statistical science.

Certificate in Architecture-Based Systems Integration (ABSI)

This program is available to students who hold bachelor's degrees in engineering and scientific disciplines or are in graduate status in such programs. Admission requirements are identical to those for the master's degree in systems engineering. To be eligible for a certificate, students must complete SYST 520, SYST 611 or ECE 521; SYST 619, 620, 621, and 622 with an average grade of B or better. The following is a suggested program of study for obtaining the certificate while studying for the MS in systems engineering degree (certificate-required courses indicated in italics):

Core courses:

Methods courses:

Elective courses:

Project:

Certificate in Command, Control, Communications, Computing, and Intelligence (C4I )

This certificate program is available to students who hold bachelor's degrees in engineering and scientific disciplines or are in graduate status in such programs. Admission requirements are identical to those for the master's degree in systems engineering. To be eligible for a certificate, students must complete with an average grade of B or better SYST 680; ECE 528 or OR 542; and three electives from the list of electives for the C4I emphasis of the MS in systems engineering. The following is a suggested program of study for obtaining the certificate while studying for the MS in systems engineering degree (certificate required courses indicated in italics:

Core courses:

Methods courses:

Elective courses:

Project:

Certificate in Systems Engineering for Computer, Information, and Software-Intensive Systems

This certificate is available to any student who holds a bachelor's degree in an engineering or scientific discipline or has graduate status in such a program. Admission requirements are identical to those for the master's degree in systems, except that the math requirements include only MATH 113, MATH 114, and a probability and statistics course. Note: Some certificate elective courses may require stronger math requirements.

To be eligible for a certificate, students must complete with an average grade of B or better SYST 510, 513, 530, and 619, and one of these elective courses: ECE 542; CS 656; INFS 612; SYST 542, 563, 620, and 621; SWE 620; and INFS 622. The following is a suggested program of study for obtaining the certificate while studying for the MS in systems engineering (required courses for the certificate are indicated in italics):

Core courses:

Methods courses:

Elective courses:

Project:

Certificate in Military Operations Research

This program provides knowledge, tools, and techniques to those who are working or plan to work in the field of military operations research. It is appropriate for students who cannot complete requirements for a master's degree in operations research, but who want a concentrated study of military modeling. Admissions requirements are identical to those for the master's degree in operations research. Certificate candidates must complete six courses, with an average grade of B or better, for a total of 18 graduate credits. To obtain the certificate, a student needs to complete the following: OR 541, 542, 635, 651, and 652, and SYST 683. Students who already have 3 credits of deterministic operations research can receive the certificate with 15 graduate credits. Those who already have taken a course equivalent to OR 542 should substitute OR 681.

Certificate in Computational Modeling

This certificate program provides knowledge, tools, and techniques to those who are working or plan to work in the field of computational modeling. Courses taken for this certificate program can count toward a master's degree in operations research or statistics or a PhD in computational sciences and informatics. One must be concurrently enrolled in the program for courses to count toward the certificate and the other degree. For admission into the certificate program, applicants must meet minimum entrance requirements for the MS in operations research, the MS in statistical science, or the PhD in computational sciences and informatics. Certificate candidates must complete the following courses: CSI 700/OR 682; OR 541 and 635; and STAT 634. In addition, candidates must choose any two of the following electives: CSI 744, 773; OR 542, 680; and SYST 683. Students who have already taken the equivalent of any of the required courses may, with permission of the department chair, complete the certificate program by taking only 15 credits of course work.

Certificate in Discovery, Design, and Innovation

This program responds to the growing need for professional knowledge in innovation. It provides a balanced understanding of the entire process: discovery of knowledge, use in inventive problem solving, development of inventions, and familiarity with using various inventive design methods and tools. The program is available to students who hold master's degrees in engineering and scientific disciplines or who are in such graduate programs. Students may pursue the certificate concurrently with any of the graduate programs in the Volgenau School; however, the certificate is not awarded until all requirements have been completed. Certificate candidates must complete at least 15 credits with an average grade of B or better. To obtain the certificate, students must take SYST 520 and IT 894 and 944, and two of the following: CEIE 601 or 670; SYST 512 or 573 (recommended if going on for MS in civil and infrastructure engineering); STAT 664/SYST664; SYST 781/STAT 781; STAT 652, 700, and 701; OR 671/SYST 672; or IT 819.

PhD Study in Systems Engineering and Operations Research

Doctoral study in both systems engineering and operations research is available through the PhD in Information Technology Program, which offers advanced courses in this discipline. The doctoral program allows students to take a broad range of courses and research options. Students may designate a specialization in systems engineering or operations research in their doctoral degree title. In that case, the degree conferred on a graduating student is a PhD in information technology with concentration in operations research or a PhD in information technology with concentration in systems engineering. Students may also pursue such doctoral studies without designating a specialization in their degree title.

Requirements

Students seeking one of these specializations must satisfy all requirements for the PhD in information technology. In addition, the following requirements must be met.

Admissions

Students are usually admitted with an MS degree in systems engineering, operations research, or some related engineering or information technology area. The admissions materials are similar to those of the PhD in information technology; however, submittal of GRE scores is mandatory.

Plan of Study

All decisions concerning the student's course requirements and plan of study must be approved by the advisor or director, with consent of the department's doctoral coordinator.

Doctoral Supervisory Committee

The committee chair should be selected from the list of approved chairs of SEOR. The dissertation director must be a member of SEOR. The doctoral supervisory committee must include at least three members from SEOR. The composition of the doctoral supervisory committee is to be approved by the doctoral coordinator. Permission for the comprehensive exam and dissertation defense are requested from the Volgenau School associate dean on the basis of a written request and plan that has been approved by the supervisory committee and the department's doctoral coordinator.

Qualifying Exams

Each student must take a set of four exams from three different degree programs from the following:

Advanced Emphasis Requirement

For students specializing in operations research, at least 18 of the 24 credits in the advanced emphasis requirement must be in OR courses numbered 600 or higher or in IT courses with an OR designation. For students specializing in systems engineering, at least 18 of the 24 credits must be in SYST courses numbered 600 or higher, or in IT courses with a SYST designation. All exceptions to this rule must be approved by the student's doctoral supervisor committee and the department's doctoral coordinator. The doctoral supervisory committee and the associate dean for graduate studies and research of the Volgenau School must approve the overall plan of study. A list of IT courses with an OR or SYST designation is available from the SEOR office.