(*disclaimer:* I completed by degree requirements in December 2004. It's possible that the current requirements have changed.)

While I was working on my Ph.D., I used this web page to keep track of the various program requirements I had and had not completed.

The official documentation explaining the degree requirements for a Ph.D. in Combinatorics & Optimization can be found in the graduate calendar. Passages highlighted in blue below are quoted directly from this source.

Here are the main requirements:

- course work (completed)
- research skills seminar (completed)
- first stage comprehensive exam (completed)
- second stage comprehensive exam (completed)
- lecturing requirement (completed)
- thesis (completed!)

Eight courses, including: 2 of C&O 630, C&O 634, C&O 642, C&O 644 1 of C&O 650, C&O 652 1 of C&O 663, C&O 666 1 additional course from C&O 630, C&O 634, C&O 642, C&O 644, C&O 650, C&O 652, C&O 663, C&O 666, C&O 685 At least 5 of the 8 courses taken for credit toward the degree must be C&O courses. |

**Status:** completed, Spring 2002

Here are the course I've taken to meet this requirement:

- C&O 739X Sequence Analysis
- C&O 644 Algebraic Graph Theory
- C&O 751 Matroid Theory
- C&O 650 Combinatorial Optimization
- C&O 685 The Mathematics of Public-Key Cryptography
- E&CE 720 Special Topics in Computers and Digital
- C&O 634 Combinatorial Designs
- C&O 666 Continuous Optimization

In the department, this seminar is usually called "the grad student seminar". Masters and PhD students new to the department participate in the seminar. Each student gives a short talk and their presentation is evaluated by the other participants.

Required for the PhD students in C&O unless the student satisfied this requirement as a MMath student at the C&O department. |

**Status:** completed during MMath degree

The first stage is a written examination covering the fundamentals of
combinatorics and optimization. These are usually offered once a
year, in the spring term. The student must write one exam from two of
the following three categories: Combinatorial Enumeration, Graph Theory Continuous Optimization, Discrete Optimization Cryptography, Quantum Computing (The choice of exams is made by the student, in consultation with their supervisor.) The first stage of the comprehensives must be taken within four terms of the student's first registration in the PhD program. The [first stage] Comprehensive Examination Requirement is satisfied by passing both examinations. |

There are several different choices a student can make in satisfying this requirement. Once a category is chosen there is a further choice of which exam to write in that category. For example, a student who choses the Optimization category then decides to write either the continuous optimization exam or the discrete optimization exam (but not both).

**Status:** completed, Spring 2002

Here are the exams I chose to write:

- Cryptography (9am-12pm, 27 June 2002)
- Discrete Optimization (9am-12pm, 3 July 2002)

The second stage comprehensive is an oral exam at which the student is expected to give a brief description of the questions they propose to work on for the PhD and a summary of the main results in this area. A handout giving more details is available from the Graduate Secretary. This exam should normally be taken within one year of completing the first-stage of the comprehensives. It must be taken at least one full term before the PhD defence is scheduled. |

Before you can do your second stage comprehensive exam you must form an advisory committee:

Each student has an Advisory Committee, which normally consists of the student's supervisor and two other department members with expertise in the area of the student's research interests. The Advisory Committee acts as the examining committee at the student's second stage comprehensive examination, and is usually formed at this time. The members of the advisory committee will also usually act as examiners at the student's PhD defence. The Advisory Committee is selected by the Graduate Officer, who will consult the student and their supervisor. |

**Status:** completed, Spring 2003

My advisory committee consists of:

- Doug Stinson (supervisor, School of Computer Science)
- Alfred Menezes (Department of C&O)
- Guang Gong (Department of E&CE)

Every PhD student will be required to lecture under supervision
during the program of studies. If a PhD student gives a scheduled
course on a regular basis, the same two faculty members will attend
three of the lectures and make a confidential, constructive critique
of the student's performance to the student. The candidate may not put the thesis on display until at least the term following that in which the Lecturing Requirement was successfully completed. |

**Status:** completed, Spring 2004

Here are the lectures I gave:

*A Left-to-Right Algorithm for Minimal Weight Integer Representations*

CACR Cryptography Seminar

29 July 2004, 3:30pm, DC 1304*Bernstein's security argument for standard Rabin-Williams signatures*

C&O Cryptography Study Group

6 July 2004, 2:30pm, MC 5158A*Spanning Trees*

MATH 239 Lecture

18 June 2004, 9:30am, MC 4065

The candidate must prepare a thesis, embodying the results of original research, of a standard that would warrant publication in a research journal of the field. The thesis must be acceptable to the student's supervisor, to two professors in the Department and one professor outside the Department, and to an external examiner familiar with the student's research field. The student is required to defend the thesis at an oral examination. This requirement is met when the thesis has been successfully defended and accepted. |

**Status:** completed, December 2004.

Here are some important dates:

*thesis due at the math undergraduate office*-- 27 October 2004*oral examination*-- 8 December 2004, 11:00am, DC 1302

My examiners were:- Doug Stinson (supervisor, School of Computer Science)
- Alfred Menezes (Department of C&O)
- Edlyn Teske (Department of C&O)
- Guang Gong (Department of E&CE)
- Jerome Solinas (US National Security Agency, [external examiner])

The result of my oral examination was that my thesis was accepted. After incorporating the changes suggested by my examiners, I submitted my revised thesis for binding on 22 December 2004. You can view the final version of my thesis here.

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