Mathematics M.A.

Introduction

The objectives of the mathematics M.A. program give students advanced fundamental knowledge in the areas of algebra, analysis, and geometry in order to prepare them for admission in top Ph.D. programs, for work in industry, or for a teaching career at community colleges. Students will possess the ability to solve problems and communicate solutions and concepts clearly and in rigorous mathematical language.

Master's students are expected to complete their degree within two years. Students admitted to the M.A. program may apply to the Mathematics Department to transfer to the Ph.D. program upon passing the required preliminary examinations at the Ph.D. level.

Requirements

Course Requirements

The following course:

MATH288A

Pedagogy of Mathematics

2

Students are required to complete four of the following courses from the three core sequences:

MATH200	Algebra I	5
MATH201	Algebra II	5
MATH202	Algebra III	5
MATH204	Analysis I	5
MATH205	Analysis II	5
MATH206	Analysis III	5
MATH208	Manifolds I	5
MATH209	Manifolds II	5
MATH210	Manifolds III	5

Students are also required to complete five additional courses in mathematics

Courses in a related subject may be substituted by approval from the graduate vice chair. Sample courses include:

MATH203	Algebra IV	5
MATH207	Complex Analysis	5
MATH211	Algebraic Topology	5
MATH212	Differential Geometry	5
MATH213A	Partial Differential Equations I	5
MATH213B	Partial Differential Equations II	5
MATH214	Theory of Finite Groups	5
MATH215	Operator Theory	5
MATH216	Advanced Analysis	5
MATH217	Advanced Elliptic Partial Differential Equations	5
MATH218	Advanced Parabolic and Hyperbolic Partial Differential Equations	5
MATH219	Nonlinear Functional Analysis	5
MATH220A	Representation Theory I	5
MATH220B	Representation Theory II	5
MATH222A	Algebraic Number Theory	5
MATH222B	Algebraic Number Theory	5
MATH223A	Algebraic Geometry I	5
MATH223B	Algebraic Geometry II	5
MATH225A	Lie Algebras	5
MATH225B	Infinite Dimensional Lie Algebras	5
MATH226A	Infinite Dimensional Lie Algebras and Quantum Field Theory I	5
MATH226B	Infinite Dimensional Lie Algebras and Quantum Field Theory II	5
MATH227	Lie Groups	5
MATH228	Lie Incidence Geometries	5
MATH229	Kac-Moody Algebras	5
MATH232	Morse Theory	5
MATH233	Random Matrix Theory	5
MATH234	Riemann Surfaces	5
MATH235	Dynamical Systems Theory	5
MATH238	Elliptic Functions and Modular Forms	5
MATH239	Homological Algebra	5
MATH240A	Representations of Finite Groups I	5
MATH240B	Representations of Finite Groups II	5
MATH246	Representations of Algebras	5
MATH248	Symplectic Geometry	5
MATH249A	Mechanics I	5
MATH249B	Mechanics II	5
MATH249C	Mechanics III	5
MATH252	Fluid Mechanics	5
MATH254	Geometric Analysis	5
MATH256	Algebraic Curves	5
MATH260	Combinatorics	5
MATH280	Topics in Analysis	5
MATH281	Topics in Algebra	5
MATH282	Topics in Geometry	5
MATH283	Topics in Combinatorial Theory	5
MATH284	Topics in Dynamics	5
MATH285	Topics in Partial Differential Equations	5
MATH286	Topics in Number Theory	5
MATH287	Topics in Topology	5

Other Requirements

Additional requirements for the M.A. degree are dependent on the student’s chosen track: the thesis track or the comprehensive examination track.

Thesis Track

Students are required to complete a master’s thesis. A master’s thesis does not have to consist of original research results. At the minimum, it should show mastery of a specific subject area that goes beyond the knowledge taught in the core sequences in algebra, analysis, or geometry. This track is recommended for students that want to transfer into a top Ph.D. program.

The student, in consultation with the graduate vice chair, is responsible for selecting a master’s thesis reading committee. The majority of the membership of a thesis reading committee shall be members of the Santa Cruz Division of the Academic Senate. The Graduate Division must approve the committee.

The Nominations for Master’s Thesis Reading Committee Form must be completed and submitted by the end of the second week of the quarter in which the degree will be granted. The form can be found on the Graduate Division website or can be provided by the Mathematics Department. The form should be turned in to the graduate adviser and program coordinator for review and submission to the Graduate Division.

More information about thesis submission can be found at the Graduate Division website.

Comprehensive Examination Track

Students are required to obtain a second-level pass on one of three written preliminary examinations: algebra, analysis, or geometry. A second-level pass signifies that the student has a very good understanding of the basic concepts, but not necessarily enough to conduct independent research.

Applying for Graduation

M.A. students must complete the Application for the Master’s Degree form by the appropriate quarter’s deadline listed in the current Academic calendar.

The application can be found on the Graduate Division website or can be provided by the Mathematics Department. The application should be turned in to the graduate adviser and program coordinator for review and submission to the Graduate Division.