Requirements for the Doctoral Program in ACO
Course 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. (Students entering the program prior to Fall 1997 may choose
instead to follow the previous
requirements.)
More information on specific courses can be found in the home
departments: CS,
TSB, and
Math.
The course requirements for the ACO doctoral program consist of 10
course semesters (counting minis as 1/2 semester): 3 semesters in
Mathematics, 3 in Computer Science, and 3 in TSB, plus a semester of
Probability Theory.
Mathematics:
- CORE COURSE (required of all students):
- Discrete Math (21-701)
- 2 of the following, at least 1 of which must be a starred option:
- *Algebra (21-610)
- *Real Analysis and Lebesgue Integration (21-620 and 21-621)
- Numerical Analysis (21-660)
- Methods of Optimization (21-690)
Computer Science:
- CORE COURSE (required of all students):
- Algorithms (15-750)
- 2 of the following:
- Artificial Intelligence (15-780)
- Computer Systems (15-740)
- Programming Languages (15-711)
- Software Systems (15-712)
- Complexity Theory (15-855)
- Security and Cryptography (15-827)
- Theory of Performance Modeling (15-849)
- Algorithms in the Real World (15-853)
- Machine Learning Theory (15-859B)
- or any course in the 15-85x numbering (upper-level algorithms/theory)
TSB:
- CORE COURSES (required of all students):
- One mini: Theory and Algorithms for LP
- One mini: Graph theory
- One mini: Integer programming
- 3 minis to be taken from:
- Networks and Matchings
- Advanced Integer Programming
- Convex Polytopes
- Advanced Linear Programming
- Dynamic Programming
- Nonlinear programming
- Optimal Control Theory
- Approximation Algorithms
- Topics in Polyhedral Combinatorics
- Packing and Covering
- Computational Molecular Biology
- Network Design Algorithms
- Special Topics in OR
Students are also required to take one of the following courses in
Probability Theory:
- Probability and Combinatorics (15-8xx)
- Probability Theory (21-780)
- Probability Theory and Stochastic Processes I (36-753)
In addition, there is a qualifying examination covering the fundamentals
of the program; The exam syllabus will take account of the choices
of electives made by the particular set of students taking the exam. This
examination will be given at the beginning of the student's fourth
semester.
Students are expected to have satisfied all course
requirements by the end of the sixth semester.
In the event that a student has already mastered the material covered
by a required course when entering the program, another course may be
substituted with approval from the student's advisor in consultation
with the ACO Coordinating Committee.
Research Requirements
During their residence at Carnegie Mellon, students in the Ph.D.
program in Algorithms, Combinatorics and Optimization are expected to
participate in the weekly ACO research seminar.
Students are also
expected to take advanced courses in the area of their research in
addition to the course requirements listed above.
At the end of the third semester (if not earlier), students should
choose a faculty member to supervise their research and dissertation. Throughout
this period, they will be subject to an annual review by the ACO
faculty. The ACO faculty will judge whether the thesis work is proceeding
satisfactorily. Approximately a year before the expected graduation
date, students must make a thesis proposal before a thesis committee,
composed of the advisor and two or more faculty members of the
student's choosing. The final transition point is the thesis defense,
which is presented before the same committee.
To graduate, students will need some teaching experience, and all
students must demonstrate
programming skills. (For every student, a faculty member, approved by the student's advisor,
would attest that the student has adequately demonstrated programming skills.)
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