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One of the most rapidly growing areas of research in applied mathematics, computer science, and operations research has been dealing with discrete structures. This has been most evident in the fields of combinatorics, discrete optimization, and the analysis of algorithms. Increasingly, work in each of these subjects has come to depend on knowledge of all of them. Indeed, many of the most significant advances have resulted from the efforts of researchers in more than one, if not all three, of these areas.
In response to these developments, Georgia Tech has introduced a doctoral degree program in Algorithms, Combinatorics, and Optimization (ACO). This multidisciplinary program is sponsored jointly by the School of Mathematics, the School of Industrial and Systems Engineering, and the College of Computing. Faculty for the program are drawn from these three sponsoring units, as well as from the School of Electrical and Computer Engineering and the College of Business.
The ACO program is arranged to bring together the study of discrete structures and the design and analysis of algorithms in areas such as graph theory, integer programming, combinatorial optimization, and polyhedral theory. It is intended for students possessing a strong background in one or more of the fields represented by the three sponsoring units. Each student in the program has a single home department chosen from the School of Mathematics, the School of Industrial and Systems Engineering, and the College of Computing. Courses for the program are drawn from all three of these units, and include study in such areas as combinatorial methods, algebraic structures, probability, the analysis of algorithms, computational complexity, linear programming, discrete optimization, and convex analysis.
The College of Computing is one of the sponsors of the multidisciplinary program in Algorithms, Combinatorics, and Optimization (ACO), an approved doctoral degree program at Georgia Tech. The other sponsoring units are the Stewart School of Industrial and Systems Engineering and the School of Mathematics. The degree program is administered by an oversight committee drawn primarily from the sponsoring units.
The study of discrete structures is a rapidly growing area in computer science, applied mathematics, and operations research, most obviously in the analysis of algorithms, combinatorics, and discrete optimization. Collaborative work among the three traditionally separate disciplines is already common. The doctorate in Algorithms, Combinatorics, and Optimization will prepare students for careers in this exciting and expanding field.
Students are expected to be well prepared in at least one of the three fields represented by the sponsoring units (computer science, mathematics, and operations research). Each student in the program is admitted through one of the three sponsoring units, which serves as the home department. Coursework is drawn from all three disciplines. The research advisor may be any member of the ACO program faculty, which is drawn from electrical and computer engineering, management, and other disciplines in addition to the three sponsoring units.
The ACO core curriculum consists of the following one-semester courses:
- CS 6505 - Computability and Algorithms or CS 6520 Complexity (CoC students must select the latter)
- CS 6550 - Design and Analysis of Algorithms
Industrial and Systems Engineering
- ISyE 7661 - Theory of Linear Inequalities
- ISyE 7686 - Advanced Combinatorial Optimization
- Math 6014 - Graph Theory
- Math 6121 - Algebra I (Students with home in ISyE may substitute Math 6112 Advanced Linear Algebra)
- Math 7018 - Probabilistic Methods in Combinatorics
Note on CS 6505 vs. CS 6520. The corresponding question on the comprehensive examination will be based on CS 6505. Math and ISyE students should take CS 6505, unless they know the material. CS students are expected to already know the material of CS 6505.
Additional Course Requirements
Each student must complete at least 15 semester hours of course work at the 6000 or higher level in addition to the courses that constitute the program core. The following courses are required, depending on the student's home department:
- Two theory courses at the level of 7000 or above
Industrial and Systems Engineering
- ISyE/Math 6761 - Stochastics I
- ISyE 6663 - Nonlinear Optimization
- Math 6337 - Real Analysis I
- Math 6338 - Real Analysis II is not required but is strongly encouraged
- Two of the following three:
Math 6112 - Advanced Linear Algebra
Math 6321 - Complex Analysis
A 6000 level or above topology/geometry course
Students apply to the ACO Program at Georgia Tech through any one of the three sponsoring units: the College of Computing, the H. Milton Stewart School of Industrial and Systems Engineering, or the School of Mathematics. To be considered for admission to ACO, a student must be admitted to the doctoral program in one of these units. Decisions concerning admissions to the ACO program are made by the Coordinating Committee for the program, and are based on those materials supplied in support of the application for graduate admission.
Each unit has its own deadline for applications. However, to receive full consideration for admission to the ACO Program starting in the Fall semester, applicants should complete their application before December 20 of the previous year. Review of applications begins shortly thereafter. Late applications may be considered at the discretion of the admissions committee. Admissions during a term other than Fall are rare.
Please note that applicants to the ACO program should take the GRE Mathematics Subject Test. If you are unable to take the test we will still consider your application; however, in that case the rest of your academic record should make up for the lack of the test score. We will be looking for other signs of excellence such as independent research, successful participation in the Putnam examination or other mathematics competitions, and/or superior academic performance. You may be asked to take the test at a later date.
The ACO program is an elite program and as such maintains stringent admission requirements. It is expected that incoming students either have a strong background in at least two of the areas represented by the three participating units, or have demonstrated excellence in one area (as described in the previous paragraph). In addition, ACO students are expected to be committed to their chosen field of study and to posses a strong work ethic.
To assess the qualities of an applicant the ACO Admissions Committee considers all materials submitted by the applicant, including Statement of Purpose, transcript(s), GRE scores (including the mathematics subject test) and letters of recommendation.
If you are not sure whether you qualify, or whether the ACO program is the right choice for you, and would like to receive advice from us, please fill out the pre-application form and one of our staff members will get back to you.