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College of Arts & Sciences

Degree & Graduation Requirements for Mathematics Ph.D.

  1. University requirements listed in this graduate catalog for doctoral programs such as the minimum number of credits and the dissertation. There is no scholarly discipline component.
  2. The comprehensive examinations are structured as follows:
    1. Written examinations: Students are required to pass written examinations in two of the following subjects: Algebra, Analysis, Differential Equations, Statistics, and Topology. Their choices of subjects should be made in consultation with potential Ph.D. advisers. An examination in each subject will be offered twice each year, in late summer and in winter. A student may make no more than 5 total attempts at examinations, with a maximum of 3 attempts in any given subject area.
    2. Breadth requirement: Students must earn a grade of B or better in 4 MATH courses above 5999, excluding the core courses in the subjects of their two written examinations. At least one course must be a core course in an examination subject in which the student did not take a written examination. Project, seminar, and independent study courses may not be used for this requirement.
  3. Adequate progress: Students must progress through the requirements to meet the following deadlines:

Degree Milestones

Student Has M.S. from Elsewhere

  • Clock Starts: Enters department's doctoral program
  • Pass 1 written examination: winter of year 2
  • Pass 2 written examinations: winter of year 3
  • Find advisor and form advisory committee: 2 years
  • Breadth course requirement: 3 years
  • Advance to Candidacy: 3 years
  • Successfully defend dissertation: 7 years from entering doctoral program

Student Enters Through Department’s Master’s Program

  • Clock Starts: Entered department’s Master’s program.
  • Pass 1 written examination: winter of year 3
  • Pass 2 written examinations: winter of year 4
  • Find advisor and form advisory committee: 3 years
  • Breadth course requirement: 4 years
  • Advance to Candidacy: 4 years
  • Successfully defend dissertation: 7 years from entering doctoral program

Policies on Deadline Extensions

Students who miss a deadline to pass a written examination will be dismissed at the end of Spring semester. If they believe that some exceptional circumstances justify an extension to this deadline, they may request an extension from the Graduate Committee, in writing, including any supporting documentation, by March 1.

Students who miss the deadline to advance to candidacy will be dismissed at the end of Spring semester. If they believe that some exceptional circumstances justify an extension to this deadline, they may request an extension from the Graduate Committee, in writing, including letters of support from their advisor and advisory committee member and any other supporting documentation, by May 1. The renewal of any departmental financial support will be contingent upon advancing to candidacy by the end of Spring semester.

Culminating Experience 

A dissertation is required for completion of the Ph.D. program in mathematics.

Comprehensive Examination

The comprehensive examination consists of two written examinations and a breadth course requirement. Students may not register for MATH 8950 Dissertation until they have completed the comprehensive examination.

Written Examinations

Students are required to pass written examinations in two of the following subjects. Their choices of subjects should be made in consultation with potential Ph.D. advisers. An examination in each subject will be offered twice each year, in late summer and in winter. A student may make no more than five total attempts at examinations, with a maximum of three attempts in any given subject area.

Subjects & Core Courses

Algebra

Examination Syllabus

Core Courses

  • MATH 6221 Algebra I
  • MATH 6222 Algebra II

Prerequisites

  • MATH 5221 Modern Algebra I
  • MATH 5222 Modern Algebra II
Analysis

Examination Syllabus

Core Courses

  • MATH 6301 Analysis I
  • MATH 6302 Analysis II

Prerequisites

  • MATH 5301 Advanced Calculus I
  • MATH 5302 Advanced Calculus II
Differential Equations

Examination Syllabus

Core Courses

  • MATH 6411 Partial Differential Equations I
  • MATH 6412 Partial Differential Equations II

Prerequisites

  • MATH 5400 Advanced Differential Equations
  • MATH 5410 Fourier Analysis and Partial Differential Equations
  • One of:
    • MATH 5330 Hilbert Spaces and Applications
    • MATH 5301 Advanced Calculus I
    • MATH 5302 Advanced Calculus II
Topology

Examination Syllabus

Core Courses

  • MATH 6700 Point Set Topology
  • MATH 6710 Algebraic Topology

Prerequisites

  • MATH 5301 Advanced Calculus I
  • One of:
    • MATH 5302 Advanced Calculus II
    • MATH 5700 Introduction to Topology
Statistics

Examination Syllabus

Core Courses

  • MATH 6500 Mathematical Statistics
  • MATH 6510 Linear Models

Prerequisites

  • MATH 5301 Advanced Calculus I
  • MATH 5302 Advanced Calculus II
  • MATH 5500 Theory of Statistics
  • MATH 5510 Applied Statistics

Breadth Requirement

Students must earn a grade of B or better in 4 MATH courses above 5999, excluding the core courses in the subjects of their two written examinations. At least one course must be a core course in an examination subject in which the student did not take a written examination. Project, seminar, and independent study courses may not be used for this requirement.

Adviser and Advisory Committee

The student must choose (and be accepted by) a dissertation adviser. The adviser will form an Advisory Committee, consisting of the adviser and at least one other faculty member. The Advisory Committee is in charge of the student's study plan, and with determining if/when the student is prepared to undertake the independent research necessary for a dissertation. If the Advisory Committee judges that the student is not making satisfactory progress, they may recommend to the Graduate Committee that the student be withdrawn from the Ph.D. program.

Advancement to Candidacy

The student must form a Dissertation Committee, submit and orally defend a dissertation proposal, and have it approved by the committee. The committee consists of at least the adviser, the College Faculty Representative, and two other members. The proposal must demonstrate that the student has developed sufficient background expertise in a specialty to conduct research in it, and present a problem or conjecture, which, if solved, would be sufficient for a dissertation. Upon completion of the comprehensive examination and approval of the dissertation proposal, the student is admitted to candidacy.

Dissertation Proposal Structure

  1. First page: Title, Student’s name, adviser’s name, department, date.
  2. Second page: Abstract (1/4-1/2 of a page).
  3. Introduction (approximately 7 pages):
    1. Motivation and goals.
    2. Introduction to the general area of the research project, including a thorough literature review on the topic of study. This section will help the committee assess if student has sufficient background in the math and the subject-specific topics.
  4. List of specific problems (1/2-2 pages).
  5. Preliminary results and general research plan (2-5 pages).
  6. References (1-3 pages).

The proposal should be prepared in TeX/LaTeX, length between 12 and 20 pages.

Dissertation Proposal Timeline

  1. A preliminary versions of the proposal (no less than 8 pages) must be submitted to the dissertation committee no later than March 1 of the required semester. The goal of the preliminary proposal is twofold:
    1. to show the committee that the student has sufficient background and
    2. to receive timely criticism from the committee regarding the general direction of research.
  2. The final version of the proposal must be submitted to the committee no later than April 15 of the required semester.
  3. The oral defense of the proposal must be no later than the last week of classes.

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