Graduate Degrees, page 2
Department of Mathematics
College of Letters, Arts and Sciences

Doctor of Philosophy in Applied Mathematics

The program requires the maximum endeavor by the student for normally a minimum of four years of full-time work.

Screening Procedure

Appointment of a guidance committee and retention in the doctoral program are contingent on passing the preliminary qualifying examination by the end of the second semester. If a student fails the examination, the department, at its discretion, may permit the student to take it again during the third semester of graduate studies.

The preliminary qualifying examination is a written two hour examination covering a choice of the subject content of MATH 510ab Algebra or MATH 525a Real Analysis and MATH 520 Complex Analysis.

Course Requirements

The student must complete, with no grade lower than B, a minimum of 60 units of courses carrying graduate credit and approved by the guidance committee. These must include MATH 794ab Dissertation and eight courses from four of the following groups: MATH 510ab; MATH 525a, 520; MATH 535a, 540; MATH 555a, 565a; MATH 507a, 541b; MATH 502ab.

Transfer of Credit

No transfer of credit will be considered until the screening examination is passed. Normally a maximum of 30 units of graduate work at another institution may be applied toward the course requirements for the Ph.D. A grade of B- or lower will not be accepted and, at most, two grades of B will be accepted. A Ph.D. candidate may petition the department for transfer of additional credit, after he or she passes the qualifying examination.

Foreign Language Requirement

The student must demonstrate a reading comprehension of mathematics in two languages (other than English) in which there is a significant body of research mathematics (such as Chinese, French, German, Japanese and Russian) by passing a written examination, administered by the department, in translation of mathematical content.

Qualifying Examination

The written portion of the qualifying examination is comprehensive, consisting of two examinations administered by the department. A student, having selected the analysis option for the preliminary qualifying examination, must select the two examinations from the options: MATH 510ab, Algebra; MATH 535a and 540, Differential Geometry and Topology; MATH 555a and 565a, Partial and Ordinary Differential Equations; MATH 507a and 541b, Probability and Statistics; and MATH 502ab, Numerical Analysis. A student selecting the algebra option for the preliminary qualifying examination must select MATH 525a and 520, Real and Complex Variables, as one of the written examinations and the other examination from the options MATH 535a and 540; MATH 555a and 565a; MATH 507a and 541b; and MATH 502ab.

The oral portion of the qualifying examination covers one topic selected from department research areas in applied mathematics and approved by the guidance committee. The student must demonstrate research potential in this field.

Dissertation

Following passage of the qualifying examination and approval of a dissertation topic by the guidance committee, the student begins research toward the dissertation under the supervision of the dissertation committee. The primary requirement for the Ph.D. is an acceptable dissertation based on a substantial amount of original research conducted by the student.

Research Areas

Opportunities for research are offered in areas of applied algebra, applied functional analysis, applied topology, biomathematics, control theory, differential equations, discrete mathematics, econometrics, fluid dynamics, numerical analysis, optimization theory, probability, statistics and systems theory.

Doctor of Philosophy in Mathematics

The program requires the maximum endeavor by the student for normally a minimum of four years of full-time work.

Screening Procedure

Appointment of a guidance committee and retention in the doctoral program are contingent on passing the preliminary qualifying examination by the end of the second semester. If a student fails the examination, the department, at its discretion, may permit the student to take it again during the third semester of graduate studies.

The preliminary qualifying exam is a written two hour examination covering a choice of the subject content of MATH 510ab, Algebra, or MATH 525a and 520, Real and Complex Analysis.

Course Requirements

The student must complete with no grade lower than B a minimum of 60 units of courses carrying graduate credit and approved by the guidance committee. These must include MATH 794ab Dissertation and the eight courses from four of: MATH 510ab; MATH 525a and 520; MATH 535a and 540; MATH 555a and 565a; MATH 507a and 541b; MATH 502ab.

Transfer of Credit

No transfer of credit will be considered until the screening examination is passed. Normally a maximum of 30 units of graduate work at another institution may be applied toward the course requirements for the Ph.D. A grade of B- or lower will not be accepted, and, at most, two grades of B will be accepted. A Ph.D. candidate may petition the department for transfer of additional credit after passing the qualifying examination.

Foreign Language Requirement

The student must demonstrate a reading comprehension of mathematics in two languages (other than English) in which there is a significant body of research mathematics (such as Chinese, French, German, Japanese and Russian) by passing a written examination, administered by the department, in translation of mathematical content.

Qualifying Examination

The written portion of the qualifying examination is comprehensive, consisting of two examinations administered by the department. One must cover the subject content of the option, MATH 510ab, Algebra, or 525a, Real Analysis, and 520, Complex Analysis, not selected for the preliminary qualifying examination and the other is selected from the options: MATH 535a, Differential Geometry, and 540, Topology; MATH 555a and 566a, Differential Equations; MATH 507a, Probability, and 541b, Statistics; and MATH 502ab, Numerical Analysis.

The oral portion of the qualifying examination covers one topic selected from department research areas in mathematics and approved by the guidance committee. The student must demonstrate research potential in this field.

Dissertation

Following passage of the qualifying examination and approval of a dissertation topic by the guidance committee, the student begins research toward the dissertation under the supervision of the dissertation committee. The primary requirement for the Ph.D. is an acceptable dissertation which is based on a substantial amount of original research conducted by the student.

Research Areas

Opportunities for research are offered in the area of algebraic geometry, arithmetic geometry, combinatorics, complex geometry, control theory, differential equations, differential geometry, dynamical systems, functional analysis, geometric analysis, group theory, K-theory, nonlinear analysis, number theory, numerical analysis, optimization, probability, representation theory, ring theory and topology.

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Produced by the USC Division of Student Affairs, Office of University Publications, May 1, 1995
Joye Day
day@mizar.usc.edu