The Department of Mathematics offers graduate courses on various levels, all of which are oriented toward research. There are numerous seminars that encourage research even more directly. The content of courses varies considerably from year to year, and the course descriptions below should be read only as a rough guide. Students usually acquire the standard beginning graduate material primarily through independent study and consultations with the faculty.
To earn the Doctor of Philosophy (Ph.D.), the student must pass a language requirement and both portions of the general examinations, submit an acceptable dissertation and sustain a final public oral examination.
"Incidental" M.A. Requirements
To qualify for the "Incidental" Master of Arts (M.A.), the student must pass the language requirement and the first part of the general examination, and be recommended by the faculty. (Note: It is expected that ALL students will pursue their Ph.D..)
One-Year in Residence
The student must be in residence for at least one academic year before standing for the general examination. If, however, a student wishes to take his/her general examination during either the October or January generals period during their first year, it must be approved by the DGSs and the Graduate School. Otherwise, the more acceptable time is during the April/May exam period.
The student must satisfy the language requirement by demonstrating to a member of the mathematics faculty a reasonable ability to read ordinary mathematical texts in at least one of the following three languages: French, German, and Russian. The language test must be passed before the end of the first year and before standing for the general examination.
In the first two years, students acquire a background in mathematics. Depending upon individual preparation, a student may take the general examination in the first or the second year of study.
The student must stand for an oral exam administered by a committee of three professors, including the advisor who serves as chair of the committee. A typical exam can last 2 to 3 hours. Areas covered are algebra, and real and complex variables.
The student must also choose two (2) special or advanced topics. These two additional topics are expected to come from distinct major areas of mathematics, and the student's choice is subject to the approval of the Department. Usually, in the second year, and sometimes even in the first, the student begins investigations of his/her own that lead to the doctoral dissertation.
The department collaborates with the Department of Physics in offering work in mathematical physics and leading to an advanced degree. For a student interested in mathematical physics, the general examination is adjusted to include mathematical physics as one of the two special topics.
A plan of study also may be coordinated with the Program in Applied and Computational Mathematics (PACM). See their program description for more information.
There are three general examination periods each academic year--October, January, and April/May. It has been a tradition of the students to post their exams as a resource and study guide for other students, see Graduate Students' Guide to Generals.
Dissertation and Final Public Oral Exam (FPOE)
The student must prepare an acceptable doctoral dissertation (thesis), which must demonstrate that the student has achieved a high level of understanding of his/her topic/field and is capable of doing independent research, and which must expand upon what was previously known or present a significant new interpretation of known materials. The Final Public Oral Exam is the successful presentation of the oral defense of the dissertation.
Preparation and Procedures for Ph.D. Defense:
Thesis LaTex template
Graduate students wishing to use LaTeX to write their doctoral thesis can use a premade LaTeX style file puthesis. Puthesis style has appropriate preset margins, title page and other settings that should help format the thesis.
Puthesis style files consist of
- puthesis.cls - the actual style file
- puthesis.sample.tex - first sample LaTeX file that shows how to use puthesis.cls
- thesis.tex - second sample LaTeX file
You should begin by copying at least the puthesis.cls file into the directory where you will be writing your thesis. You can do that by either clicking on puthesis.cls in the above list and downloading the file to appropriate directory, or else copy the file on the Linux/Unix systems from /usr/finehall/tex/puthesis/latest, for example:
cp /usr/finehall/tex/puthesis/latest/puthesis.cls my_thesis_directory/
Please take a look at the two sample files to get an idea on how to use puthesis style, or even better, begin by adapting one of sample files to your needs.