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2022-23 UCSC General Catalog
2021-22 UCSC General Catalog
2020-21 UCSC General Catalog
2019-20 UCSC General Catalog

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.

MATH288A | Pedagogy of Mathematics | 2 |

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 |

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 |

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

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.

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.