# Mathematics, MS

## Requirements

The Master of Science in Mathematics program consists of 36 hours of graduate coursework, from the three areas specified below. In accordance with University policy, a GPA of at least 2.75 must be maintained with no more than two passing grades of "C+" or lower being utilized in satisfying the degree requirement.

### Core Coursework (15 hours)

Coursework for the MS degree must include the following five core courses:

MATH 50253 | Abstract Algebra I | 3 |

MATH 50403 | Complex Analysis | 3 |

MATH 50503 | Real Analysis I | 3 |

MATH 60513 | Multivariable Analysis | 3 |

MATH 60223 | Applied Linear Algebra | 3 |

An advanced student may be waived from any or all of these required courses by passing the corresponding Ph.D. preliminary exam(s) or otherwise showing proficiency in the material, as determined by the department.

### Specialized Coursework (12 hours)

In addition to the five core courses, at least four courses are to be chosen from either the Pure Mathematics Option or the Applied Mathematics Option (refer to course listings below).

#### Pure Mathematics Option:

This track of the MS Program is intended to prepare students for careers in academia. Each student selecting this track will take at least four of the pure mathematics courses listed below:

MATH 50323 | Differential Geometry | 3 |

MATH 50703 | Number Theory | 3 |

MATH 60263 | Abstract Algebra II | 3 |

MATH 60313 | Topology | 3 |

MATH 60323 | Algebraic Topology I | 3 |

MATH 60413 | Advanced Complex Analysis | 3 |

MATH 60503 | Real Analysis II | 3 |

MATH 60523 | Measure Theory | 3 |

MATH | Any MATH 70000 level 3 hour course | 3 |

#### Applied Mathematics Option:

This track of the MS Program is intended for students planning to use mathematics in careers outside academia. Each student selecting this track will take at least four applied mathematics courses from the list below:

MATH 50613 | Partial Differential Equations | 3 |

MATH 50623 | Applied Mathematics I | 3 |

MATH 60103 | Graph Theory | 3 |

MATH 60543 | Numerical Analysis | 3 |

MATH 60553 | Modern Fourier Analysis | 3 |

MATH 60603 | Game Theory | 3 |

MATH 60613 | Differential Equations of Mathematical Physics | 3 |

MATH 60633 | Applied Mathematics II | 3 |

MATH 60643 | Dynamical Systems and Applications | 3 |

Up to 6 hours of the applied mathematics courses may be substituted with graduate coursework taken in the departments of Biology, Chemistry, Computer Science or Physics and Astronomy, or from the School of Geology, Energy & the Environment, with approval from the student's graduate advisor in the Department of Mathematics.

### Master's Thesis or Electives (9 hours)

The student may choose either to write a master's thesis (three hours of MATH 70980 and three hours of MATH 70990) and complete three hours of approved elective coursework, or to complete nine hours of approved elective coursework. Based on the recommendation of the department, the dean appoints a Master's Advisory Committee of at least three members, including the thesis advisor as chair. For the student to be eligible for the degree, the Master's Advisory Committee must approve the thesis upon its completion. The thesis need not contain original research but must demonstrate a deep and thorough understanding of some area of mathematics.