Academics
Ph.D. Program
For the prospective OR Ph.D. student, the School provides coursework and conducts research in support of several formal concentrations listed below. Through the respective links, you can find the recommended course listings for each of the options. Note also that Institute requirements for the Ph.D. include a minor program of study, satisfactory completion of a comprehensive examination, and a doctoral dissertation. Details involving these requirements can be found in the document ISyE Graduate Handbook.
Students should consult with their Academic Advisor regarding the suitability of their background as it relates to preparation for various courses comprising the student's program option. The Ph.D. is a research degree. In this context, students who are interested in doctoral study in ISyE can select from a host of academic concentrations. Equally important, the Ph.D. student in ISyE will also find that he/she can pursue work at virtually any of the points across the applied/theoretical spectrum. Indeed, many of our Ph.D. students are motivated by the challenge of tackling critical, real-world problems that exist in a host of settings arising in business and industry. Alternately, other students are simply more interested in theoretical work that extends the boundaries of what is known within the various contexts related to the mathematics of our problem-solving methodologies. At both of these extremes and at many points in between, ISyE Ph.D. students will find a rich set of educational and research opportunities as well as a supportive faculty of the first-rank whose specialty area(s) are consistent with these aims.
· Stochastic Systems
· Supply Chain Engineering
· Economic Decision Analysis
· Applied Statistics
· Algorithms, Combinatorics, and Optimization (aco)
Ph.D. with concentration in Optimization
The optimization program of study is directed primarily at students interested in advanced-level coursework and research that deals with the fundamental subject matter of operations research methodologies. Included is a strong core component covering the three basic areas in mathematical programming: linear, combinatorial, and nonlinear optimization. Also, a year long core sequence of study in stochastics is included as are courses in mathematical statistics and theoretical computer science. Students then tend to complement their specific programs of study with upper division courses that set the stage for their research pursuits.
Ph.D. with concentration in Optimization
REQUIRED
- ISyE 6661 - Linear Optimization
- ISyE 6662 - Discrete Optimization
- ISyE 6663 - Nonlinear Optimization
- Math 6xxx - (flexible but not statistics, stochastics, or probability)
- CS 6550 - Design and Analysis of Algorithms or
ISyE 6679 - Computational Methods in Operations Research or
a computational alternative* approved by an optimization faculty advisor and the Associate Chair.
Six courses total from the two groups below, constrained as indicated:
DEPTH REQUIREMENT (select at least two courses from the list below)
- ISyE 7872 - Convexity
- ISyE 7873 - Advanced Nonlinear Programming
- ISyE 7876 - Advanced Combinatorial Optimization
- ISyE 7877 - Advanced Integer Programming
BREADTH REQUIREMENT (select at least three courses from the list below)
- ISyE 6761 - Stochastic Processes I
- ISyE 6762- Stochastic Processes II
- ISyE 6664 - Stochastic Optimization
- ISyE 6412 - Theoretical Statistics
- ISyE 6831 - Advanced Simulation
- Math 6241 - Probability I
- Math 6242 - Probability II
All 11 courses in the Program of Study must be completed in order to attain doctoral candidacy.
*Relevant alternative computational courses include ones such as Math 6643, Math 6644, CSE 6xxx, and others.
Ph.D. with concentration in Stochastics
The stochastic systems track is aimed at students interested in the advanced study of those complex systems where the attribute of randomness predominates. A firm grounding in probability and stochastics processes influence the program of study. Topics that arise in coursework and research contexts that motivate this program include the theory of queues, telecommunication networks, reliability, portfolio selection, random graphs and networks, and the probabilistic analysis of algorithms among others.
CORE
- ISyE 6761 - Stochastic Processes I
- ISyE 6762 - Stochastic Processes II
- ISyE 6831 - Advanced Simulation
- Math 6241 - Probability I
DEPTH REQUIREMENT (at least two of the following courses)*
- ISyE 6656 - Queueing Theory
- ISyE 6664 - Stochastic Optimization
- Math 6242 - Probability II
- Math 7244 - Stochastic Processes and Stochastic Calculus I
BREADTH REQUIREMENT (at least three of the following courses)*
- ISyE 6412 - Theoretical Statistics
- ISyE 6661 - Linear Optimization
- ISyE 6662 - Discrete Optimization
- ISyE 6663 - Nonlinear Optimization
- ISyE 7872 - Convexity
- ISyE 7873 - Advanced Nonlinear Programming
- ISyE 7876 - Advanced Combinatorial Optimization
- ISyE 7877 - Advanced Integer Programming
APPLICATION/COMPUTATION REQUIREMENT (at least one from the following courses)*
- BIOL 7023 - Bioinformatics
- ISyE 6201 - Manufacturing Systems
- ISyE 6202 - Warehousing Systems
- ISyE 6203 - Transportation and Supply Chain Systems
- ISyE 6645 - Monte Carlo Methods
- ISyE 6679 - Computational Methods on Operations research
- ISyE 6759 - Stochastic Processes in Finance I
All ten courses in the Program of Study must be completed in order to attain doctoral candidacy. Also, any changes or substitutions to the above Program of Study must be approved by the student’s advisor and the Associate Chair for Graduate Studies.
It is recommended that students complete ISyE 6761-2 before they sit for the comprehensive examination.
*The stated lists are likely to be extended; some currently listed courses may also be modified.
Ph.D. with concentration in Supply Chain Engineering
This program focuses on the design and analysis of manufacturing, distribution, and transportation systems. Students take fundamental coursework in optimization, stochastics, and statistics in order to build a firm base from which to deal with the myriad issues that arise in settings involving modern supply chain systems modeling and analysis: production and inventory systems, vehicle routing and scheduling, warehousing, and logistics.
DOMAIN CORE
- ISyE 62xx - Supply Chain Engineering (ISyE 6202 substitutes in AY 2007-08)
- ISyE 7xxx - Logistics Systems Engineering (ISyE 8852 substitutes in AY 2007-08)
- ISyE 7xxx - Production Systems Engineering (ISyE 8851 substitutes in AY 2007-08)
METHODS CORE
- ISyE 6661 - Linear Optimization
- ISyE 6662 - Discrete Optimization
- ISyE 6761 - Stochastic Processes I
- ISyE 6230 - Economic Decision Analysis
- ISyE 6414 - Statistical Modeling and Regression Analysis
COMPUTATIONAL CORE (select one from the list below)
- CSE 6140 - Computational Science and Engineering Algorithms
- CS 6550 - Design and Analysis of Algorithms
- ISyE 6679 - Computational Methods in Operations Research
By completion of the Ph.D., students must have taken a minimum of two additional courses related to their major area chosen in consultation with their advisor.
It is recommended that students complete the domain courses before they sit for the comprehensive examination.
A student is not admitted to candidacy until all of the stated course requirements in the Program of Study have been completed.
Ph.D. with concentration in Economic Decision Analysis (EDA)
Engineering economic decision analysis is a broad-based area of study that concentrates on both theoretical approaches and the applied methodologies in various decision-making domains within an economic environment. Typical settings that attract students to this program include multicriteria decision-making, capital budgeting, auctions, portfolio analysis and selection, economic forecasting, utility theory, and quantitative finance.
CORE
- ISyE 6225 - Engineering Economy
- ISyE 6230 - Economic Decision Analysis
- ECON 6106 - Microeconomic Analysis
ADDITIONAL COURSE REQUIREMENTS (7 courses as indicated)
All of the following:- Math 4317 - Real Analysis
- ISyE 6661 - Optimization I
- ISyE 6663 - Optimization III or ISyE 6664 Stochastic Optimization
- ISyE 6671 - Stochastic Processes I
- ISyE 6413 - Design and Analysis of Experiments
- ISyE 6414 - Statistical Modeling and Regression Analysis
- ISyE 6201 - Manufacturing Systems
- ISyE 6203 - Transportation and Supply Chain Systems
- Approved finance area elective (e.g., ISyE 6759 Stochastic Processes of Finance I, ISyE 6227 Introduction to Financial Engineering, ISyE 6673 Financial Optimization, ISyE 6783 Statistical Techniques of Financial Data, ISyE 6785 The Practice of Quantitative Finance, or ISyE 6793 Advanced Topics in Quantitative Finance)
- Approved economics area elective (e.g., ECON 6160 Econometric Analysis, ISyE 6223 Understanding and Supporting Human Decision Making, ISyE 8803 Game Theory, or ISyE 8803 Sustainable Systems)
It is recommended that the first seven courses listed above be taken before sitting for the comprehensive examination.
All ten courses in the Program of Study must be completed in order to obtain doctoral candidacy.
Ph.D. with concentration in Statistics
The emphasis in this track is on the use of statistics as a science that is employed in a technological environment. Within this context, a student takes fundamental coursework in mathematics, probability and statistics suitable to conduct advanced work and research in a variety of application domains. Among these are quality systems, manufacturing, production, and simulation.
CORE
- ISyE 6412 - Theoretical Statistics
- ISyE 6413 - Design and Analysis of Experiments
- ISyE 6416 - Computational Statistics
- ISyE 6650 - Probabilistic Models and Their Applications or Math 6241: Probability I
- ISyE 7401 - Advanced Statistical Modeling
THEORY (select two or more):
- ISyE 6420 - Bayesian Statistics
- ISyE 6761 - Stochastic Process I
- ISyE 6762 - Stochastic Process II
- ISyE 6781 - Reliability Theory
- ISyE 7405 - Multivariate Data Analysis
- Math 6242 - Probability II
- Math 6262 - Statistical Estimation
- Math 6263 - Testing Statistical Hypotheses
METHODS (select three or more):
- ISyE 6402 - Time Series
- ISyE 6404 - Nonparametric Statistics
- ISyE 6405 - Statistical Methods for Manufacturing Design and Improvement
- ISyE 6414 - Statistical Modeling and Regression Analysis
- ISyE 6805 - Reliability Engineering
- ISyE 7400 - Advanced Design of Experiments
- ISyE 7406 - Data Mining and Statistical Learning
ELECTIVES (select one or more):
- BIOL 7023 - Bioinformatics
- CS 7645 - Numerical Machine Learning
- ECE 6254 - Statistical Digital Signal Processing
- ISyE 6201 - Manufacturing Systems
- ISyE 6202 - Warehousing Systems
- ISyE 6203 - Transportation and Supply Chain Systems
- ISyE 6230 - Economic Decision Analysis
- ISyE 6644 - Simulation
- ISyE 6664 - Stochastic Optimization
- ISyE 6669 - Deterministic Optimization or ISyE 6661: Linear Optimization
- ISyE 6783 - Statistical Techniques of Financial Data Analysis
- ISyE 6831 - Advanced Simulation
All 11 courses satisfying the above requirements in the Program of Study must be completed in order to obtain doctoral candidacy.
PH.D. IN ALGORITHMS, COMBINATORICS, AND OPTIMIZATION (ACO)
The ACO program is a multidisciplinary effort, sponsored jointly with the School of Mathematics and the College of Computing. The intent of this program is to provide a formal vehicle for graduate education and research that builds on the close relationships between combinatorial mathematics, the analysis of algorithms, and fundamentals of optimization and that takes advantage of the resources at Georgia Tech in these areas. The Program is directed by an ACO Coordinating Committee drawn from the participating faculty and representing all of the participating units. Each student in the Program has a single home department and although students apply for admission to ACO independently, through the Coordinating Committee, they must first be admitted as Ph.D. students in their home unit which ultimately recommends the student's degree.
Students must satisfy the Institute requirements as described in the General Catalog. However, specific requirements of the ACO Program may vary significantly from those of other programs in the home department.
The requirements for each ACO student will include the satisfactory completion of a set of core courses shown below.
PROGRAM CORE
- CS 6550 Analysis of Algorithms
- ISyE 6661 Optimization I
- ISyE 6662 Optimization II
- Math 6014 Graph Theory
- Math 6021 Algebra
- Math 6221 Topics in Probability
ADDITIONAL COURSE REQUIREMENTS
Each ACO student must also complete at least 18 hours of course work at the 6000 level or higher in addition to the courses that constitute the core. Additional departmental requirements may be imposed and apply only to students who have the indicated department as their home unit. For ACO students from ISyE, the following additional course requirements must be satisfied:
- ISyE/Math 6761 Stochastics I
- Math 6021 Topology of Euclidean Spaces
- CS 6520 Complexity
- One additional courses from Statistics, Simulation, or an Operations Research "applications" area.
MINOR REQUIREMENT
Each ACO student must satisfy the Institute requirement of a minor program of study consisting of at least 9 hours of course work chosen to the satisfaction of the Coordinating Committee and the student's home department. Courses in the program core may not be used as part of a minor program.
COMPREHENSIVE EXAMINATION
Typically, by the end of the third semester in residence, each ACO student will be required to take a written Comprehensive Examination. This examination will be based primarily on the contents of the courses in the program core and one additional course selected from CS 7520, CS 7530, CS 6520, or CS 7510. Based on the results of this test and other measures of the student's performance, the Coordinating Committee may pass the candidate, fail the candidate with the recommendation that the test be readministered in part or in whole after allowing at most one year for remediation of the student's deficiencies, or fail the student unconditionally. Upon passing the examination, students will be advised that they will be admitted to candidacy for the Ph.D. upon satisfactory completion of all requirements and filing a statement naming the dissertation advisor and research topic.
THE DISSERTATION AND FINAL DOCTORAL EXAMINATION
The dissertation and final doctoral examination must meet the usual criteria of the Institute. Dissertation advisory committees and doctoral examination committees must represent the home department and at least one other participating unit in the Program. The dissertation advisor may reside in any of the participating units.