The PhD in Mathematics

Degree of Ph.D. in Mathematics

The Purpose of the doctoral program is to prepare specialists capable of doing research and creative, independent, original work in the fields of mathematics represented by the three options. To obtain the Ph.D. degree in mathematics, a student must display a high levei of scholarship shown by the ability to do original research and should possess a broad knowledge of the major fieids of modern mathematics.

Requirements

Information concerning the degree of Ph.D. can be found in the Graduate Program Rules (2011). The following is a brief summary of the degree requirements (you can also look at this diagram of the PhD curriculum):

Ph.D. Total Credits: 69

Qualifying Exams

Students must take written quafifying examinations.

1. An exam in Real and Complex Analysis, based on the corresponding core courses of the first year.
2. An exam in Modern and Linear Algebra, based on the corresponding core courses of the first year.
3. An exam specific to the chosen option in one of the following areas:
   1. Pure Mathematics Option: Real Analysis and Complex Analysis, Topology, Functional Analysis.
   2. Discrete Mathematics Option: Graph Theory, Linear Programming, Applied Algebra, Enumerative and Algebraic Combinatorics, Discrete Algorithms, Combinatorial Optimization, Convex Polytopes, Matroid Theory.
   3. Computational Mathematics Option: Mathematical Analysis, Probability and Statistics, Data Structures and Algorithms, Computational Analysis

MA Degree – Syllabi

Detailed syllabi may be requested in the Office of Graduate Studies of the Department of Mathematics.

• Syllabi — MA and Ph.D.

Admission to Candidacy

Before petitioning to admission to candidacy, a student must have:

1. Demonstrated a competent knowledge of Spanish and English. A reading knowledge of French, German, or Russian is strongly recommended.
2. Maintained a B average or better in formal course work, with grades of at least B in the courses related to the chosen option.
3. Passed the written qualifying examinations at the doctoral level, as described in Section V of the Departmental Rules.
4. Passed the oral examination for advancement to the Ph.D. candidacy.
5. Satisfied the specific requirements of the option committee governing the field of principal interest.
6. Obtained the consent of a faculty member who will accept the responsibility 0€ directing a dissertation.

The Ph.D. Dissertation

The dissertation prepared must represent a substantial, original, and independent contribution of the student to the existing mathematical knowledge. It must be defended in an oral examination, by a committee consisting of five members, at least one of whom must belong to the graduate faculty of the department of mathematics of another university. All members of the committee must be specialists in the field of the dissertation.