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PHD MATHEMATICS (STRAIGHT PROGRAM)

Requirements for Admission

In addition to the requirements of the University for admission into the Graduate School of Arts and Sciences, the particular requirements of the Department of Mathematics must be met.

Particular Entrance Requirements for the Doctor of Philosophy in Mathematics. Straight Ph.D. Program

The applicant for the straight Ph.D. Program should have a background in the four areas specified below at the level indicated:

1. Algebra at the level of Herstein

2. Linear Algebra at the level of Herstein

3. Advanced calculus/real analysis at the level of Rudin or Apostol

4. Complex analysis at the level of Churchill

Normally, the applicant is tested by an exam to determine his competence in these four areas. However, the Department may waive this requirement in exceptional cases.

A student who is deficient in these requisites may be accepted into the straight Ph.D. program, subject to the approval of a Mathematics Graduate Committee, provided he/she takes courses at the masteral level specified by the Committee, to cover the deficiencies.

Acceptance Into a Program of Study

The applicant may be accepted into the Ateneo’s mathematics programs (the Master of Science or the Doctor of Philosophy Programs) only after he/she is issued an evaluation by the Department of Mathematics and is recommended to the Graduate School for acceptance into the Master of Science in Mathematics, Straight Ph.D. Program, or Ph.D.-After-M.S. Program. The applicant’s deficiencies and (extra) units to be credited towards the M.S. or Ph.D. shall be determined after acceptance by the Graduate School and before formal enrolment in any courses.

A student who is enrolled in the Master of Science in Mathematics Program, but who wishes to join Straight Ph.D. Program, must apply to the Department of Mathematics and the Administration for a change of status.

Requirements for the Straight Program Doctor of Philosophy in Mathematics

The student in the Straight Ph.D. Program must

1. Complete a total of sixty three (63) units of graduate courses in mathematics including to Core Programs of the Master of Science and Doctor of Philosophy in Mathematics;

2. Spend a minimum of two-and-one-half years in full-time graduate work with the Department;

3. Pass two special examinations: a comprehensive examination based on the M.S. Core Program and a Ph.D. qualifying examination;

4. (a) Be certified by the Department of Languages as having passed a reading
test in French or German or obtain 6-units credit in Japanese.

(b) Or, in place of (a), obtain 3-units credit in a computer language course
equivalent to CS 21A or AMC 21.

5. Submit a thesis which is considered by the Department an original contribution to existing knowledge. This thesis will count for twelve (12) units toward the total of seventy-five (75) units required. (See Summary of Requirement below.)

Core Program for the Doctor of Philosophy in Mathematics

Ma 257 – Algebra I (Ph.D. level) 3
Ma 258 – Algebra II (Ph.D. level) 3
Ma 259 – Linear Algebra (Ph.D. level) 3
Ma 271 – Real Analysis I 3
Ma 272 – Real Analysis II 3
Ma 273 – Complex Analysis I (Ph.D. level) 3
Ma 281 – Combinatorics I
(Basic graduate course) 3
Ma 282 – Combinatorics II
(Geometry and the classical groups) 3

Electives

To complete unit requirements for the Ph.D. in Mathematics, the student normally follows one of the two tracks listed below

Track I: Analysis Seminars

Ma 295 – Seminar: Functional Analysis I 3
Ma 295 – Seminar: Functional Analysis II 3
Ma 295 – Seminar: Complex Analysis II 3
Ma 295 – Research Seminar I 3
Ma 295 – Research Seminar Ii 3

Track II: Algebra & Combinatorics Seminars

Ma 295 – Seminar I 3
Ma 295 – Seminar II 3
Ma 295 – Seminar III 3
Ma 295 – Seminar IV 3
Ma 295 – Seminar V 3

M.S. or Ph.D. students can take certain core courses or electives in the other schools in the U.P.-Ateneo-De La Salle Consortium provided they follow the normal administrative requirements, which includes obtaining the permission of the Chairman, Ateneo Mathematics Department.

Summary of Requirements

Core Program (M.S.) 24
Core Program (Ph.D.) 24
Electives 15
Thesis 12





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