# 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 288A | Pedagogy of Mathematics | 2 |

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

MATH 200 | Algebra I | 5 |

MATH 201 | Algebra II | 5 |

MATH 202 | Algebra III | 5 |

MATH 204 | Analysis I | 5 |

MATH 205 | Analysis II | 5 |

MATH 206 | Analysis III | 5 |

MATH 208 | Manifolds I | 5 |

MATH 209 | Manifolds II | 5 |

MATH 210 | 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:

MATH 203 | Algebra IV | 5 |

MATH 207 | Complex Analysis | 5 |

MATH 211 | Algebraic Topology | 5 |

MATH 212 | Differential Geometry | 5 |

MATH 213A | Partial Differential Equations I | 5 |

MATH 213B | Partial Differential Equations II | 5 |

MATH 214 | Theory of Finite Groups | 5 |

MATH 215 | Operator Theory | 5 |

MATH 216 | Advanced Analysis | 5 |

MATH 217 | Advanced Elliptic Partial Differential Equations | 5 |

MATH 218 | Advanced Parabolic and Hyperbolic Partial Differential Equations | 5 |

MATH 219 | Nonlinear Functional Analysis | 5 |

MATH 220A | Representation Theory I | 5 |

MATH 220B | Representation Theory II | 5 |

MATH 222A | Algebraic Number Theory | 5 |

MATH 222B | Algebraic Number Theory | 5 |

MATH 223A | Algebraic Geometry I | 5 |

MATH 223B | Algebraic Geometry II | 5 |

MATH 225A | Lie Algebras | 5 |

MATH 225B | Infinite Dimensional Lie Algebras | 5 |

MATH 226A | Infinite Dimensional Lie Algebras and Quantum Field Theory I | 5 |

MATH 226B | Infinite Dimensional Lie Algebras and Quantum Field Theory II | 5 |

MATH 227 | Lie Groups | 5 |

MATH 228 | Lie Incidence Geometries | 5 |

MATH 229 | Kac-Moody Algebras | 5 |

MATH 232 | Morse Theory | 5 |

MATH 233 | Random Matrix Theory | 5 |

MATH 234 | Riemann Surfaces | 5 |

MATH 235 | Dynamical Systems Theory | 5 |

MATH 238 | Elliptic Functions and Modular Forms | 5 |

MATH 239 | Homological Algebra | 5 |

MATH 240A | Representations of Finite Groups I | 5 |

MATH 240B | Representations of Finite Groups II | 5 |

MATH 246 | Representations of Algebras | 5 |

MATH 248 | Symplectic Geometry | 5 |

MATH 249A | Mechanics I | 5 |

MATH 249B | Mechanics II | 5 |

MATH 249C | Mechanics III | 5 |

MATH 252 | Fluid Mechanics | 5 |

MATH 254 | Geometric Analysis | 5 |

MATH 256 | Algebraic Curves | 5 |

MATH 260 | Combinatorics | 5 |

MATH 280 | Topics in Analysis | 5 |

MATH 281 | Topics in Algebra | 5 |

MATH 282 | Topics in Geometry | 5 |

MATH 283 | Topics in Combinatorial Theory | 5 |

MATH 284 | Topics in Dynamics | 5 |

MATH 285 | Topics in Partial Differential Equations | 5 |

MATH 286 | Topics in Number Theory | 5 |

MATH 287 | 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.