Course Requirements

Core Courses

All degrees offered in the Department have certain core requirements which students are expected to complete during their first year of study. In lieu of taking core courses, students may demonstrate proficiency in the subject matter by examination.

Required Core Courses

Students seeking a Ph.D. in Mathematical Sciences who intend to concentrate in Applied Analysis or Logic are required to take the following core courses:

	21-610 Algebra
	21-621 Introduction to Lebesgue Integration (Half Semester)*
	21-640 Functional Analysis
	21-651 General Topology.

Students seeking a Ph.D. in Mathematical Sciences who intend to concentrate in Scientific Computing or Mathematical Finance are required to take the following core courses:

	21-621 Introduction to Lebesgue Integration (Half Semester)*
	21-640 Functional Analysis
	21-660 Introduction to Numerical Analysis
	21-690 Fundamentals of Optimization.

Requirements for a Ph.D. in the ACO program are detailed in the catalog for that program or may be found on the ACO Program Home Page.

Recommended Courses

Students who wish to write a thesis in applied analysis are strongly recommended to take four or five of the following courses:

	21-623 Complex Analysis
	21-630 Ordinary Differential Equations
	21-660 Introduction to Numerical Analysis I
	21-690 Fundamentals of Optimization
	21-720 Measure and Integration
	21-724 Sobolev Spaces

Students who intend to write a Ph.D. dissertation in logic are encouraged to take courses from the following list:

	21-602 Introduction to Set Theory
	21-603 Introduction to Model Theory
	21-700 Mathematical Logic II
	21-703 Model Theory II
	21-804 Seminar in mathematical logic
	21-805 Lambda-calculus

Additional logic courses are offered in this Department and by the Department of Philosophy and the School of Computer Science. Students interested in logic should request the separate brochure describing the interdisciplinary program in Pure and Applied Logic.

An M.S. in Mathematical Sciences may be obtained by completing a total of 96 units and either of the two groups of core courses listed above.

Ph.D. students enrolled in the ACO or PAL program may obtain an M.S. in those disciplines by completing 96 units and the course requirements for those disciplines.

*Students who have not previously taken a rigorous "real analysis" course may be required to take 21-620 (Half Semester) before enrolling in 21-621.

Course Load

The normal course load for a graduate student is three or four courses per semester, with teaching and research assistants typically taking only three courses (36-48 units) per semester. Since the university has set three courses (36 units) per semester as the minimal load for a full-time student, all teaching and research assistants must be enrolled in at least this number of courses or be engaged in a commensurate level of reading and research.

All degree requirements are subject to periodic review and revision.

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