Requirements for the Doctoral Program in ACO

Program Requirements

The Coordinating Committee for the Ph.D. program in Algorithms, Combinatorics, and Optimization has established the following core curriculum. This curriculum is designed to provide students with significant flexibility in choosing courses, while simultaneously ensuring a solid grounding in the fundamentals of ACO.

More information on specific courses can be found in the home departments:

The Computer Science Department (Algorithms and Complexity group)
The Department of Mathematical Sciences (Discrete Mathematics group)
The Tepper School of Business (Operations Research group)

Courses

All ACO students will be required to take 2 semester CS classes, 2 semester Math classes, and the equivalent of 2 semester Tepper classes (i.e 4 mini classes). Also required is 1 probability class.

The 2 CS classes will include Algorithms (15-750), plus one additional theoretical class chosen from the following courses.

15-850 Advanced Algorithms
15-855 Computational Complexity Theory
15-857 Analytical Performance Modeling of Computer Systems
15-859 Special Topics in Theory: Advances in Coding Theory
15-859 Special Topics in Theory: Algorithmic Superpower Randomization
15-859 Special Topics in Theory: Spectral Graph Theory and The Laplacian Paradigm
15-896 Algorithms, Games, and Networks

The 2 Math classes will include Discrete Math (21-701), plus one additional math class from the following courses:
- 21-610 Algebra
- 21-720 Measure and Integration
- 21-737 Probabilistic Combinatorics
- 21-738 Extremal Combinatorics
The 4 Tepper mini classes will include Linear Programming (47-834), Convex Optimization (47-851), Integer Programming (47-830) as required classes, plus one more mini from the following courses:

47-835 Graph Theory
47-836 Networks and Matchings
47-831 Advanced Integer Programming
47-862 Constraint Programming
47-xxx Combinatorial Optimization

Students who are based in the Tepper School are required to complete two additional mini classes from the Tepper school.

The 1 probability class will include one of: Probability (21-721), Probability Theory and Stoch Processes I (36-753), or Analytical Performance Modeling (15-857).

Students who are based in the Department of Mathematical Sciences with a start date on or after July 1, 2024 are required to complete the course requirements by the end of their 6th semester.

Qualifying Exam

Every ACO student will be required to take the same Qualifying Exam. This exam will be given in January after the student's 3rd semester. The exam will contain 1 question on Algorithms, 1 question on Discrete Math, 1 question on Linear Programming, 1 question on Convex Optimization, 1 question on Integer Programming.

Please see http://aco.math.cmu.edu/ACO_CSD_qual_reqs.html for specific exam requirements for Computer Science Department ACO students.

Research

Research is obviously a big component of the ACO program. Each department has different research expectations, as well as policies, for when students should find research advisors. You should talk with your department head to understand the research expectations for your department.

Weekly Research Seminar

During your participation in the Algorithms, Combinatorics, and Optimization program, you are expected to participate in the weekly ACO research seminar. You are also expected to take advanced courses in the area of your research in addition to the course requirements listed above.

Dissertation

Regardless of your home department, by the end of the third semester (if not earlier), you must choose a faculty member to supervise your research and dissertation. As an ACO student, you will be subject to an annual review by the ACO faculty who will judge whether the thesis work is proceeding satisfactorily. The procedures for forming a thesis committee, completing a thesis proposal, and defending the thesis are governed by the rules of the student's home department.

Teaching and Programming Skills

To graduate, you will need some teaching experience, and all students must demonstrate programming skills. (For every student, a faculty member, approved by the student's advisor, must attest that the student has adequately demonstrated programming skills.)

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