## Master's Degree

Students can pursue a Master's Degree in Mathematical Sciences with an emphasis in discrete mathematics, pure mathematics, statistics, or computational and applied mathematics. Applicants are not required to have an undergraduate degree in mathematics. Each concentration area has a set of required courses.

### Concentrations—Core Courses and Electives

All students pursuing an MS in mathematical sciences must choose one of four concentrations.

Computational and Applied Mathematics students develop expertise in the theory and application of ordinary and partial differential equations, linear algebra, and computational methods.

**Core courses:**

- MA5501 Theoretical Numerical Analysis
- MA5510 ODEs
- MA5565 PDEs
- MA5627 Numerical Linear Algebra
- MA5629 Numerical PDEs

**Elective courses (choose two):**

Students of Discrete Mathematics study design and coding theory, graph theory number theory, and algebra.

**Core courses:**

**Elective courses (choose two):**

- MA5201 Combinatorial Algorithms
- MA5280 Topics in Applied Combinatorics
- MA5302 Algebra II
- MA5320 Commutative Algebra
- MA5360 Number Theory
- MA6222 Advanced Topics in Design Theory
- MA6231 Advanced Topics in Coding Theory
- MA6280 Advanced Topics in Combinatorics, Algebra, or Number Theory
- MA6300 Advanced Topics in Algebra

The curriculum in Pure Mathematics consists of a blend of both theoretical and applied courses.

**Core courses:**

**Elective courses (choose four):**

- MA5222 Design Theory
- MA5231 Error-Correcting Codes
- MA5302 Algebra II
- MA5320 Commutative Algebra
- MA5360 Number Theory
- MA5501 Theoretical Numerical Analysis
- MA6222 Advanced Topics in Design Theory
- MA6231 Advanced Topics in Coding Theory
- MA6280 Advanced Topics in Combinatorics, Algebra, or Number Theory
- MA6300 Advanced Topics in Algebra
- MA6701 Probability

While providing a broad statistics background, the Statistics program also specializes in statistical genetics, computational methods, and functional data analysis.

**Core courses:**

- MA5711 Mathematical Statistics I
- MA5712 Mathematical Statistics II
- MA5731 Linear Models
- MA5741 Multivariate Statistical

**Elective courses (choose three):**

*Note: It is important to recognize that some of these courses are offered only in
alternate years. Students must plan carefully to complete the MS degree in the expected
two academic years.*

### Degree Options

There are three different options under which the MS in mathematical sciences can be earned: thesis, report, or coursework. Regardless of the option, students must complete the core courses in their chosen concentration.

This option requires a research thesis prepared under the supervision of the advisor. The thesis describes a research investigation and its results. The scope of the research topic for the thesis should be defined in such a way that a full-time student could complete the requirements for a master’s degree in 12 months or three semesters following the completion of coursework by regularly scheduling graduate research credits.

The minimum requirements are as follows:

Option Parts | Credits |
---|---|

Coursework (minimum) | 20 Credits |

Thesis research | 6-10 Credits |

Total (minimum) | 30 Credits |

Distribution | Credits |
---|---|

5000-6000 series (minimum) | 12 Credits |

3000-4000 (maximum) | 12 Credits |

Programs may have stricter requirements and may require more than the minimum number of credits listed here.

This option requires a report describing the results of an independent study project. The scope of the research topic should be defined in such a way that a full-time student could complete the requirements for a master’s degree in twelve months or three semesters following the completion of coursework by regularly scheduling graduate research credits.

Of the minimum total of 30 credits, at least 24 must be earned in coursework other than the project:

Option Parts | Credits |
---|---|

Coursework (minimum) | 24 Credits |

Report | 2-6 Credits |

Total (minimum) | 30 Credits |

Distribution | Credits |
---|---|

5000-6000 series (minimum) | 12 Credits |

3000-4000 (maximum) | 12 Credits |

Programs may have stricter requirements and may require more than the minimum number of credits listed here.

This option requires a minimum of 30 credits be earned through coursework. A limited number of research credits may be used with the approval of the advisor, department, and Graduate School. See degree requirements for more information.

A graduate program may require an oral or written examination before conferring the degree and may require more than the minimum credits listed here:

Distribution | Credits |
---|---|

5000-6000 series (minimum) | 18 Credits |

3000-4000 (maximum) | 12 Credits |

## PhD Program

The doctoral program has three areas of concentration: computational and applied mathematics, discrete mathematics, and statistics. The doctoral program requires advanced coursework (beyond the master's degree) and successful completion of the Qualifying and Comprehensive Examinations. Students must demonstrate the ability to independently conduct research. Doctoral students work closely with a major advisor and must have their research proposal and dissertation approved by their graduate committee.

### Overview of Program Requirements

To complete a doctoral degree, students must complete the following milestones:

- Complete all coursework and research credits (see credit requirements below)
- Pass Qualifying Examination
- Pass Research Proposal Examination
- Prepare and Submit Approved Dissertation
- Pass Final Oral Defense

The minimum credit requirements are as follows:

Degrees | Credits |
---|---|

MS-PhD (minimum) | 30 Credits |

BS-PhD (minimum) | 60 Credits |

Individual programs may have higher standards and students are expected to know their program's requirements. See the Doctor of Philosophy Requirements website for more information about PhD milestones and related timelines.

The PhD degree is offered in the following concentrations:

- computational and applied mathematics
- discrete mathematics
- statistics.

It is important to note that this list is not chronological; indeed, not all students will complete the requirements in the same order.

- Choose a concentration and complete the core MS course work in that concentration.

Computational and Applied Mathematics students develop expertise in the theory and application of ordinary and partial differential equations, linear algebra, and computational methods.

**Core courses:**

- MA5501 Theoretical Numerical Analysis
- MA5510 ODEs
- MA5565 PDEs
- MA5627 Numerical Linear Algebra
- MA5629 Numerical PDEs

**Elective courses (choose two):**

Students of Discrete Mathematics study design and coding theory, graph theory number theory, and algebra.

**Core courses:**

**Elective courses (choose two):**

- MA5201 Combinatorial Algorithms
- MA5280 Topics in Applied Combinatorics
- MA5302 Algebra II
- MA5320 Commutative Algebra
- MA5360 Number Theory
- MA6222 Advanced Topics in Design Theory
- MA6231 Advanced Topics in Coding Theory
- MA6280 Advanced Topics in Combinatorics, Algebra, or Number Theory
- MA6300 Advanced Topics in Algebra

While providing a broad statistics background, the Statistics program also specializes in statistical genetics, computational methods, and functional data analysis.

**Core courses:**

- MA5711 Mathematical Statistics I
- MA5712 Mathematical Statistics II
- MA5731 Linear Models
- MA5741 Multivariate Statistical

**Elective courses (choose three):**

- Find an
**advisor**and form a PhD dissertation committee. (Note that the committee must include one faculty member from another department.) - Complete at least two 6000-level courses in your concentration.
- Complete the "breadth" requirement by taking a sequence of two courses in another concentration.

- MA5222 Design Theory

MA5231 Error-correcting Codes - MA5301 Algebra I

MA5302 Algebra II - MA5501 Theoretical Numerical Analysis

MA5510 Ordinary Differential Equations - MA5510 Ordinary Differential Equations

MA5565 Partial Differential Equations - MA5501 Theoretical Numerical Analysis

MA5629 Numerical Partial Differential Equations - MA5565 Partial Differential Equations

MA5629 Numerical Partial Differential Equations - MA5711 Mathematical Statistics I

MA5712 Mathematical Statistics II

- Pass the
**qualifying examination**. This is a written exam covering advanced undergraduate material; it must be passed by the end of the fourth semester (summer semesters do not count) in the PhD program. - Pass the
**comprehensive examination**. This multi-part exam covers graduate course work; it must be passed by the end of the eighth semester in the PhD program (summer semesters do not count). - Present a dissertation proposal to the satisfaction of your dissertation committee. (Note: Depending on your committee, this proposal may be written or oral. Check with your advisor.)
**Write a dissertation**detailing the results of a substantial and original research project.- Defend the dissertation with a public presentation and examination by your committee.