# Mathematics (M.S.)

The M.S. in Mathematics is the most rigorous program at the Master’s level and is designed for students who intend to study at the Ph.D. level in mathematical sciences, as well as for other students who are looking for a challenge.

## Admission Requirements

Admission to this program is contingent upon admission to the Graduate School.

Except for the program leading to the degree of Master of Arts in Applied Mathematics, the entrance requirements for the master’s programs in mathematics and statistics include successful completion of twelve semester credits in mathematics beyond sophomore calculus (equivalent to MAT 2010, MAT 2020, MAT 2030, MAT 2250, and MAT 2350); this course work should include advanced calculus and linear or modern algebra. Credit accrued in courses such as the history of mathematics or the teaching of mathematics, in which the study of mathematics itself is not the primary purpose will not be counted toward this requirement. As preparation for graduate study, the Department of Mathematics strongly recommends undergraduate course work along the line of option A, described under Bachelor’s Degrees in the undergraduate bulletin.

The Master of Science in Mathematics is offered under the following options:

** Plan A**:

*Twenty-six credits in course work plus an eight credit thesis*.

** Plan B**:

*Twenty-nine credits in course work plus a three credit essay*.

** Plan C**:

*Thirty-two credits in course work*.

**Degree Requirements**

Code | Title | Credits |
---|---|---|

At least twenty-four credits in course work from the Department of Mathematics, including credits earned toward a thesis or essay under Plan A or Plan B options. | ||

Select one of the following (if not previously completed): | ||

Algebra I and Algebra II and Advanced Linear Algebra | ||

Advanced Linear Algebra and Advanced Algebra I | ||

Select one of the following (if not previously taken): | ||

Introduction to Analysis I and Introduction to Analysis II and Complex Analysis | ||

Complex Analysis and Real Analysis I | ||

Select one of the following: | ||

Topology I (if not previously taken) | ||

Topology II | ||

Select at least two of the following (other courses may be approved by the Departmental Graduate Committee on an individual basis): | ||

Statistical Computing and Data Analysis | ||

Numerical Methods I | ||

Numerical Methods II | ||

Advanced Calculus | ||

Partial Differential Equations | ||

Complex Variables and Applications | ||

Methods of Differential Equations | ||

Elementary Theory of Numbers | ||

Applied Linear Algebra | ||

Introduction to Topology | ||

Elementary Differential Geometry and its Applications | ||

Introduction to Probability Theory | ||

Introduction to Stochastic Processes | ||

Mathematical Models in Operations Research | ||

Introduction to Mathematical Statistics | ||

Methods of Optimization | ||

Linear Statistical Models | ||

Ordinary Differential Equations | ||

Partial Differential Equations | ||

Advanced Numerical Analysis | ||

Finite Element Methods | ||

Advanced Partial Differential Equations | ||

Advanced Algebra I | ||

Advanced Algebra II | ||

Topology II | ||

Algebraic Topology I | ||

Algebraic Topology II | ||

Real Analysis I | ||

Real Analysis II | ||

Introduction to Real Harmonic Analysis | ||

Advanced Probability Theory I | ||

Advanced Probability Theory II | ||

Advanced Statistics Theory I | ||

Advanced Statistics Theory II |

A final oral examination. All students in Plan C are required to take this examination. Students in Plan A or B may, upon recommendation of the thesis or essay adviser, be excused from the final oral examination by the Departmental Graduate Committee.

A public lecture on the thesis or essay for each student in Plan A or Plan B.

By the time twelve credits have been earned, each student must submit a Plan of Work, approved by a departmental adviser, to the director of the program. In the Plan of Work, the student must choose Plan A, Plan B, or Plan C. The Plan of Work must be approved by the Departmental Graduate Committee, at which time the student will be advanced to candidacy. Students are not allowed to take more than twelve credits in the program unless candidacy has been established.

NOTE: Candidates for the Master of Science in Mathematics are exempt from the requirement of the Graduate School that six credits in the major field must be in courses numbered 7000 and above.

NOTE: The following courses cannot be applied towards this degree:

Code | Title | Credits |
---|---|---|

MAT 5000 | Fundamental Concepts of Mathematics and Proof Writing | 3 |

MAT 5070 | Elementary Analysis | 4 |

MAT 6130 | Discrete Mathematics | 3 |

MAT 6140 | Geometry: An Axiomatic Approach | 3 |

MAT 6150 | Probability and Statistics for Teachers | 4 |

MAT 6170 | Algebra: Ring Theory Through Exploration, Conjecture, and Proof | 4 |

MAT 6180 | Algebra: Group Theory Through Exploration, Conjecture, and Proof | 3 |

MAT 6200 | Teaching Arithmetic, Algebra and Functions from an Advanced Perspective | 3 |

MAT 6210 | Teaching Geometry, Probability and Statistics, and Discrete Mathematics from an Advanced Perspective | 3 |