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

Four of the following core sequence courses:

A three-course sequence in each of the three fields of algebra, analysis, and geometry-topology (manifolds) will be offered each year. Master's students are required to complete four courses from the core sequence course list.

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

No more than three courses may be independent study or thesis research courses. Independent study and thesis courses must be approved by the graduate vice chair to count toward the additional course requirement.

Third-level core sequence courses that were not used to satisfy the four core course requirements may also be used to satisfy this requirement upon approval by 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

Capstone Requirement

The capstone requirement for the M.A. degree are dependent on the student’s chosen track, to be one of the following:

Thesis Track (Plan I)

Students are required to complete a master’s thesis as their program capstone. 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 first- or second-level pass on one of three written preliminary examinations as their program capstone. 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.

Preliminary examinations are given for each core sequence in the fields of algebra, analysis, and geometry-topology at the beginning and end of each academic year. The exams will be designed and graded by recent instructors of each core sequence.

Topics for the preliminary examinations are defined on the departmental graduate student website.

Timeline to Degree

A master's student should complete their chosen program capstone by the end of spring quarter of their second year. A student who may be experiencing academic difficulty will first develop an academic support plan with the department before being recommended for academic notice or disqualified from the program in alignment with the following timeline:

  • If a capstone is not completed after the grading of the spring preliminary exam offered in a student's second year, an academic support plan will be developed with the student and graduate vice chair. Students pursuing the Comprehensive Exam Track should retake the exam the following fall. Students pursuing the Thesis Track should complete their thesis over the summer.
  • If a capstone is not completed after the grading of the fall preliminary exam offered in a student's third year, the student will be recommended for academic notice, and their academic support plan reassessed to follow through the spring of the student's third year, at the end of which the student should retake the spring preliminary exam or complete their thesis in spring.
  • If a capstone is not completed after the grading of the spring preliminary exam offered in a student's third year, the student may be disqualified from the program or can appeal to the department to continue on the master's route.

Applying for Graduation

M.A. students must complete the Application for the Master’s Degree form and the Thesis Reading Committee form (if applicable) 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.