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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:

MATH 288APedagogy of Mathematics

2

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

MATH 200Algebra I

5

MATH 201Algebra II

5

MATH 202Algebra III

5

MATH 204Analysis I

5

MATH 205Analysis II

5

MATH 206Analysis III

5

MATH 208Manifolds I

5

MATH 209Manifolds II

5

MATH 210Manifolds 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:

MATH 203Algebra IV

5

MATH 207Complex Analysis

5

MATH 211Algebraic Topology

5

MATH 212Differential Geometry

5

MATH 213APartial Differential Equations I

5

MATH 213BPartial Differential Equations II

5

MATH 214Theory of Finite Groups

5

MATH 215Operator Theory

5

MATH 216Advanced Analysis

5

MATH 217Advanced Elliptic Partial Differential Equations

5

MATH 218Advanced Parabolic and Hyperbolic Partial Differential Equations

5

MATH 219Nonlinear Functional Analysis

5

MATH 220ARepresentation Theory I

5

MATH 220BRepresentation Theory II

5

MATH 222AAlgebraic Number Theory

5

MATH 222BAlgebraic Number Theory

5

MATH 223AAlgebraic Geometry I

5

MATH 223BAlgebraic Geometry II

5

MATH 225ALie Algebras

5

MATH 225BInfinite Dimensional Lie Algebras

5

MATH 226AInfinite Dimensional Lie Algebras and Quantum Field Theory I

5

MATH 226BInfinite Dimensional Lie Algebras and Quantum Field Theory II

5

MATH 227Lie Groups

5

MATH 228Lie Incidence Geometries

5

MATH 229Kac-Moody Algebras

5

MATH 232Morse Theory

5

MATH 233Random Matrix Theory

5

MATH 234Riemann Surfaces

5

MATH 235Dynamical Systems Theory

5

MATH 238Elliptic Functions and Modular Forms

5

MATH 239Homological Algebra

5

MATH 240ARepresentations of Finite Groups I

5

MATH 240BRepresentations of Finite Groups II

5

MATH 246Representations of Algebras

5

MATH 248Symplectic Geometry

5

MATH 249AMechanics I

5

MATH 249BMechanics II

5

MATH 249CMechanics III

5

MATH 252Fluid Mechanics

5

MATH 254Geometric Analysis

5

MATH 256Algebraic Curves

5

MATH 260Combinatorics

5

MATH 280Topics in Analysis

5

MATH 281Topics in Algebra

5

MATH 282Topics in Geometry

5

MATH 283Topics in Combinatorial Theory

5

MATH 284Topics in Dynamics

5

MATH 285Topics in Partial Differential Equations

5

MATH 286Topics in Number Theory

5

MATH 287Topics in Topology

5

Other Requirements

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

Thesis Track (Plan I)

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 their faculty advisor, 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 (Plan II)

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.