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# PhD Candidacy Progress

Most PhD programs in North America have some form of comprehensive exams one way or another. Anyone who fails to hit the necessary milestone (i.e. passing the necessary comprehensive exams) is deemed not to have made a satisfactory progress toward their doctorate, which is a basis for academic dismissal.In the case of Dalhousie, one needs to pass two non-specialist written comprehensive exams, and at least one of these two must be in abstract algebra or analysis, both of which are course-based.† There are other non-course-based‡ exams in a variety of subjects, including: number theory, combinatorics and graph theory, general relativity, probability, differential geometry, general and algebraic topology, numerical analysis, and statistics. This phase must be completed within 16 months of registration in the program.

After a student passes the two non-specialist written comprehensive exams, the student needs to write a written report which serves as the thesis proposal. This thesis proposal and the syllabus on the student's research subject prepared in advance by the student's PhD supervisory committee (which includes the student's PhD advisor) will be the subject of the oral specialist comprehensive examination. This exam must be passed within 24 months of registration in the program.

For more information about Dal's comprehensive exams (or anything about Dalhousie's graduate program in mathematics), refer to the Graduate Handbook (most recently updated June 2019).

I passed both comprehensive exams on 25 August 2020. So there will be no more updates apart from uploading the solutions to the past comprehensive exams (should they become available in the past comprehensive exams binder, which is available in the department office).

## Phase I: Non-specialist written comprehensive exams (complete)

- Advanced Algebra I: Written on 2019-04-15;
**Passed on 2019-04-18** - Advanced Algebra II: Written on 2018-12-10;
**Passed on 2018-12-17** - Combinatorics and graph theory: Written on 2019-05-15;
**Passed on 2019-05-24**

## Materials for non-specialist comprehensive exam preparations

### Solutions to selected non-specialist comprehensive exams

*The past comprehensive exam solutions can only be accessed via Dalhousie's secure network. Connect through Dalhousie VPN if you have access to it. You need to do this only when you are trying to access the page from home. Otherwise, you will get the "403 Forbidden" error.*

### Course notes

- (Winter 2019) MATH 5045C: Advanced Algebra I (module theory; for the algebra comprehensive exam)§
- (
*Winter 2019*) MATH RI: Rings and Ideals (for the algebra comprehensive exam) - (Fall 2018) MATH 5055: Advanced Algebra II (Galois theory; for the algebra non-specialist comprehensive exam)
- (
*Fall 2018*) MATH GRT: Group Theory (for the algebra comprehensive exam) - (Fall 2018) MATH 5370C: Combinatorics (Comprehensive Exam Edition) (for the combinatorics non-specialist comprehensive exam)‡
- (
*Summer 2019*) MATH CGT: Catalan Numbers and Graph Theory (for the combinatorics comprehensive exam; not covered in MATH 5370)

## Phase II: Number theory specialist oral comprehensive examination (PhD thesis proposal defence)

- Oral Specialist Examination: Conducted and passed on 2020-08-25;
**officially advanced to PhD candidacy**

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Last modified on 23 August 2023