Graduate Degrees
Admission Requirements
All applicants must take the Graduate Record Examinations General Test.
Master of Arts and Doctor of Philosophy in Mathematics and in Applied Mathematics
A substantial undergraduate background in mathematics which includes one year of real analysis (MATH 425ab), one semester of abstract algebra (MATH 410) and one semester of upper division linear algebra (MATH 471) is required. Students enrolled in one of the department's Master of Science or Arts programs must complete the Ph.D. screening procedure prior to admission to a Ph.D. program.
Master of Science in Applied Mathematics and Master of Science in Statistics
A substantial undergraduate background in mathematics which includes one semester of real analysis or advanced calculus and one semester of linear algebra is required.
Regular admission pending completion during the first year of graduate studies of prerequisite undergraduate mathematics may be considered for applicants who otherwise qualify for the program.
Degree Requirements
These degrees are under the jurisdiction of the Graduate School. Refer to the Requirements for Graduation section and the Graduate School section of this catalogue for general regulations. All courses applied toward the degrees must be courses accepted by the Graduate School.
Master of Science in Applied Mathematics
This program is intended for individuals who are seeking or currently hold positions which involve mathematical applications, or for mid-career people wishing to improve their skills in applied areas. Specific options in the program include: biomedicine, discrete mathematics, economics, finance and business economics, fluid dynamics, numerical analysis and computation, and systems and control. In addition, students may design their own option to suit specific needs.
On admission to the program, each student is assigned an option advisor. The advisor serves on the student's guidance committee and assists the student in determining the courses of study in the selected option. Courses of instruction are drawn from the Department of Mathematics and other participating departments which include: aerospace engineering, biomedical engineering, civil engineering, computer science, economics, electrical engineering, business administration, mechanical engineering, physiology and biophysics, and preventive medicine.
Course Requirements
| Required courses | Units |
| MATH 501 | Numerical Analysis and Computation | 3 |
| MATH 505ab | Applied Probability | 3-3 |
| MATH 570a | Methods of Applied Mathematics | 3 |
| MATH 601 | Optimization Theory and Techniques | 3 |
| plus at least 15 units of elected option courses. |
In addition, registration in MATH 594ab and a master's thesis is required for all students. This thesis is the end product of a practicum in the selected option. The practicum is supervised by the student's guidance committee.
For this program students are not required to take the screening examination or to satisfy a foreign language requirement.
Master of Science in Statistics
The object of this program is to provide academic instruction in statistical theory and methods with a fine mathematical base while emphasizing applications to real world problems. Some probability theory is included to provide a rigorous foundation. The program is intended for individuals who are seeking or currently hold positions which involve statistical methodology and practice. Each student orients his or her course of study toward a particular field of application through appropriate selections from the program listings plus elective courses from other disciplines.
Course Requirements
Thirty units of course work are required; in addition, a master's thesis and registration in MATH 594ab is required of all students. MATH 541ab must be taken during the first three semesters; this requirement may be waived for students with sufficient prior education in mathematical statistics. All students are required to take MATH 650. Up to 12 units may be selected from courses outside the department in the chosen field of application or emphasis.
A student in the program must pass a screening examination covering material from MATH 505a and MATH 541a. The examination will be given at the end of the student's first year in regular standing in the M.S. Statistics program.
Master of Arts in Mathematics and Master of Arts in Applied Mathematics
The objective of the Master of Arts program is to prepare students for research, teaching and other professional careers in mathematics and applied mathematics, respectively. In addition to the algebra requirement and differential geometry/topology option for the Master of Arts in Mathematics, the two programs differ in emphasis: the Master of Arts in Mathematics emphasizes the core courses in pure mathematics, and the Master of Arts in Applied Mathematics emphasizes courses in mathematics and affiliated fields which are fundamental in applied mathematics.
Relationship to Ph.D. Programs in Mathematics and in Applied Mathematics
The two year M.A. program is an expansion of the first year of graduate studies in the Ph.D. program in mathematics (respectively, the Ph.D. program in applied mathematics). The program provides a rigorous foundation in mathematics (applied mathematics) while affording students additional time for preparatory training. The comprehensive examinations for the M.A. program can serve as the preliminary qualifying examination for either Ph.D. program, and the written Ph.D. qualifying examinations serve as comprehensive examinations for the corresponding Master of Arts degree.
Requirements for the Master of Arts in Mathematics
At least 24 units are required, including:
| Required courses | Units |
| MATH 510ab | Algebra | 3-3 |
| MATH 525a | Real Analysis | 3 |
| MATH 520 | Complex Analysis | 3
|
|
| and one option from A, B, C or D |
| (A) |
| MATH 535a | Differential Geometry | 3 |
| MATH 540 | Topology | 3 |
|
| (B) |
| MATH 555a | Partial Differential Equations | 3 |
| MATH 565a | Ordinary Differential Equations | 3 |
|
| (C) |
| MATH 507a | Theory of Probability | 3 |
| MATH 541b | Introduction to Mathematical Statistics | 3 |
|
| (D) |
| MATH 502ab | Numerical Analysis | 3-3 |
The degree is completed with either departmental examinations (two written examinations selected from the two required components and the optional component) or a thesis demonstrating research ability in pure mathematics (the thesis option requires four additional thesis units selected from MATH 574abz).
Requirements for the Master of Arts in Applied Mathematics
At least 24 units are required, including:
| Required courses | Units |
| MATH 525a | Real Analysis | 3 |
| MATH 520 | Complex Analysis | 3 |
|
| and two options from A, B and C |
| (A) |
| MATH 555a | Partial Differential Equations | 3 |
| MATH 565a | Ordinary Differential Equations | 3 |
|
| (B) |
| MATH 507a | Theory of Probability | 3 |
| MATH 541a | Introduction to Mathematical Statistics | 3 |
|
| (C) |
| MATH 502ab | Numerical Analysis | 3-3 |
The degree is completed with either departmental comprehensive examinations (two examinations, one covering the required component, MATH 525a and 520, and the second covering one of the selected options) or a thesis demonstrating research ability in applied mathematics (the thesis option requires four additional thesis units selected from MATH 594abz).
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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