# ccdm_phd

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### Handbook of the Combinatorial Computing and Discrete Mathematics (CCDM) PhD Program for Students with Mathematics Home Department

**0. Overview:**

The CCDM program is an option within the Mathematics Ph.D. program. Students are expected to meet the normal pre-requisites for admission to the Ph.D. program and to satisfy certain pre-requisites for the CCDM program as well. Students admitted to the CCDM program with regular Ph.D. status in the Mathematics graduate program are required to take 33 credit hours of regular course work beyond the M.S. degree, exclusive of research and seminar requirements. Entrance exam requirements, and course work distribution requirements, are slightly different for mathematics Ph.D. students in the CCDM program. For the entrance exam, the CCDM breadth exam replaces one of the mathematics subject area exams (Algebra, Analysis, Topology, Differential Equations). Course work requirements in the major/minor areas (representing a total of 24 hours) depend on the home department(s) of the student’s thesis adviser (chair or co-chair of the the student’s PhD committee), as outlined below.

**1. Admission:**

Only students who have gained admission status in the Mathematics PhD program will be considered for admission to the CCDM program. Prerequisite courses must include:

CS 320 or 601 or 602(Algorithms/Data Structures and Software Engineering),

Math 341 or 343 or 441(Linear/Abstract Algebra),

Stat 461(Probability)

Students are expected to have taken Math 451-452 with a B average or above. Depending on their mathematics background, students from M.S. programs outside mathematics may be admitted provisionally without these courses, but must take them during their first year and achieve at least a B average. Students without a sufficient mathematics background may be admitted to the M.S. program in Mathematics until sufficient prerequisites are taken.

**2. Course and Dissertation Requirements:**

**(2.1)** A total of at least 33 hours of approved graduate coursework credit at the 500-level or above in Mathematics, Statistics, and Computer Science (or approved electives) must be completed beyond an MS degree. These do not include any seminar or research hours normally taken within the program. Courses which do not count towards graduate degrees in one of these areas will not count towards these hours.

**(2.2)** A student in the CCDM program must take all of these courses:

CS 520(Advanced Analysis of Algorithms), Math 571(Combinatorics),

Math 573(Graph Theory), Stat 561(Probability)

A student with credit for one of more of these courses with taken in connection with a previous degree program will not need to retake the courses, but the overall credit requirements in the program will not be reduced.

**(2.3)** At least 24 hours must be taken in doctoral-level courses. This is to include at least 12 credit hours in a major area and at least 6 hours in each of the two minor areas.

The major and minor areas must be chosen from at least three of the groups listed below.

A. Analysis, Differential Equations, Numerical Analysis and Computational Science, Topology.

B. Algebra, Combinatorics, Combinatorial Optimization and Matroid Theory, Graph Theory, Number Theory, Set Theory.

C. CS courses:

Algorithms, Automata Theory, Formal Languages, Advanced graphics and image processing, Data Mining, Pattern Recognition, Artificial Intelligence

D. STAT courses

Data Mining, Advanced Statistical Theory, Stochastic Processes, Bioinformatics

With the approval of the Graduate Programs Committee, at most one course in a minor area may be below the 700 (doctoral) level.

**(2.4)** For CCDM students with mathematics chairs, the major area and one of the minor areas must be taken within the Department of Mathematics. For CCDM students with mathematics and computer science/statistics co-chairs, either the major area or both of the minor areas must be taken within the Department of Mathematics.

**(2.5)** A student must complete a PhD dissertation worth at least 24 hours of doctoral research credits.

**3. Advisory Committees**

**(3.1)** Before the forming of the PhD Committee of a student, an Advisory Committee will be appointed by the Graduate Director to the student, following the same guideline defined in the Graduate HandBook of the Mathematics Department.

**(3.2)** The student must file a request with the Graduate Director to appoint a dissertation committee (the PhD Committee).

**(3.3)** The PhD Committee shall consist of five members with the dissertation adviser as chair (or cochair). If the dissertation adviser’s home department is not from mathematics, then a co-chair from mathematics will be appointed. At least one member of the committee must represent a department other than the student’s home department and at least one member should be a faculty member from outside the CCDM. At least three committee members should be recognized CCDM

faculty. The dissertation adviser and at least one other member will represent the major area. This committee will be appointed by the Graduate Director after consultation with the student, the proposed dissertation adviser, the department chairpersons, and the other faculty members involved.

**4. Examinations**

**(4.1)** A student must pass the CCDM Entrance Exam consisting of the CCDM breadth exam (algorithms, combinatorics, probability, and graph theory) and one written exam from the following: Algebra, Real Analysis, Differential Equations, and Topology. This must be done within two years of entering the Ph.D. program. Any delays must be approved by the Graduate Programs Committee.

**(4.2)** Retaking exams:

Each student can take the CCDM breadth exam and any of the Mathematics subject area exams up to two times.

The funding of a Graduate teaching Assistant in the Department of Mathematics is subject to termination if the student fails to pass the (Regular or CCDM) PhD entrance exam within two years.

**(4.3)** A CCDM PhD applicant must pass the Qualifying Exam within two years after the passing of the Entrance Exam. The Qualifying Exam consists of three parts:

PART 1: One three-hour written examination over the major area, followed by an oral exam.

PART 2: Presentation of a dissertation prospectus.

PART 3: This part is needed only when the student fails to meet the GPA requirement (3.5 or better) on one or both of the minor areas. One three-hour written examination over each minor area in which the student fails to meet the GPA requirement must be taken.

**(4.4)** The grading and appeal procedures of these exams will follow the same procedures as defined in the Graduate HandBook of the Mathematics Department.

**5. Switching Programs**

**(5.1)** Upon the approval of the Advisory Committee of the student, a student may switch between the CCDM program and the regular PhD program after their first year, with the corresponding examination requirements applying. The Entrance Exam of the new program must be passed within one additional year. A CCDM student that has failed the CCDM breadth exam twice will not be allowed to switch to the regular PhD program. A student in the regular Ph.D. program that fails any subject area exam twice will not be allowed to switch to the CCDM program.

**(5.2)** Students who fail to pass their program’s Entrance Exam within the required period will be terminated. Any delays or exceptions must be approved by the Graduate Programs Committee.

**6. Other Requirements and Possible Conflict Between Programs**

**(6.1)** A student in the CCDM program must also fulfill other requirements which are not stated or revised above and which are stated as PhD requirements in the Graduate Handbook of the Mathematics Department.

**(6.2)** Except for the revisions stated in Section 2: Course and Dissertation Requirements and Section 4: Examinations, the Graduate Handbook of the Mathematics Department will take precedence should there be a conflict between the CCDM document and the Graduate Handbook of the Mathematics Department.