Culminating Experience

Goals of the Culminating Experience

1. Draw upon experiences and ideas from courses in the program.

2. Demonstrate a deep understanding of a particular topic or topics.

3. View a deep collection of mathematical ideas in the broader context of mathematics.

Students will declare which of the following two options they choose when they apply to advance to candidacy.

Thesis Option

• We envision this option to remain very similar to the thesis requirement of the current program.
• We propose a requirement of a minimum 3.25 GPA in order to be eligible to choose this option.
  • Because graduate students would not be allowed to receive grades below a B- and could receive at most one B-, this GPA requirement is not exceptionally demanding.
• Students would work in depth in an area of mathematics under the guidance of a faculty advisor and would choose two other faculty to be on their committee.
• The thesis itself should demonstrate in-depth knowledge of the topic and should be an example of precise and polished mathematical writing.
• There will also be a thesis defense, which will consist of a 45-minute talk by the candidate similar to a mathematics conference presentation. The candidate should be able to communicate orally the important ideas of their work to a broad mathematics audience.
• The student will enroll in Thesis I and subsequently Thesis II to complete this option, see course description for proposal and committee requirements.

Comprehensive Exam Option

• There will be three comprehensive exams required. Exams 1 and 2 will be offered at the end of every semester and can be taken any time. Exam 3 must be taken during the final semester in the program (see below for more info on Exam 3):
  • Exam 1: Written Algebra Exam
  • Exam 2: Written Analysis Exam
  • Exam 3: Oral Electives Exam
• Students may retake any exam at most once (two total attempts at any one exam), and only failed exams must be retaken.

Exam 1: Algebra

This is a written exam that will be created by the faculty who has most recently taught the graduate level algebra course. Many of the problems (but not all) will be selected from a large bank of algebra problems (at least 50 questions) that will have been created in time for the semester conversion. This bank of problems will be made available to the students who elect to take comprehensive exams.

Exam 2: Analysis

This is a written exam that will be created by the faculty who has most recently taught the graduate level analysis course. Many of the problems (but not all) will be selected from a large bank of analysis problems (at least 50 questions) that will have been created in time for the semester conversion. This bank of problems will be made available to the students who elect to take comprehensive exams.

Exam 3: Electives

This is an oral exam administered by a committee consisting of three faculty members, who are chosen by the student. Two of the faculty must have taught 3 or 4 unit elective courses (at least one of which must have been at the 600 level) that the student has taken. This exam is taken any time during the student's final semester, and the student must write an application to take this comprehensive exam (which signifies that it will be their final semester, oand utlines the scope of this exam, which includes content of the courses taught by those two faculty members). Any committee member can ask any question of the student within the agreed upon scope. During the student's final semester, the student will take a comprehensive exam preparation course that will be taught by the three committee members, who will each be available to meet with the student for at least one hour per week.