# Graduate Course Catalog 2015-2016

# Graduate School

### » http://www.gradschool.unh.edu/

## Mathematics and Statistics (MATH)

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*This program is offered in Durham.*

**Degrees Offered: M.S., M.S.T., Ph.D.**

**Certificate Offered: Industrial Statistics**

The Department of Mathematics and Statistics offers programs leading to a master of science for teachers (M.S.T.) in mathematics, master of science in mathematics, master of science in mathematics with an option in applied mathematics, and a master of science in mathematics with an option in statistics. Students in the master of science in applied mathematics option may choose to study for the integrated applied mathematics (IAM) program. Click here for additional information.

The department also offers doctor of philosophy programs in mathematics, applied mathematics, statistics, and mathematics education. Students in the doctor of philosophy in applied mathematics programs pursue the degree requirements of the integrated applied mathematics program (__click here for additional information__).

In general, the master's degree programs offer the student a high level of preparation for professional employment as well as appropriate preparation for programs leading to the Ph.D. The Ph.D. programs prepare the student primarily for a career in university teaching and research.

The graduate programs have limited enrollment, allowing students to work closely with faculty members in their areas of expertise. Research within the department is currently being conducted in many areas of the mathematical sciences, including: operator theory, Hilbert spaces, geometric function theory, complex analysis, ring theory, commutative algebra, homological algebra, quantum groups, tensor categories, combinatorics, topology, algebraic topology, category theory, nonlinear dynamics and chaos, data compression, chaotic prediction and control, spectral analysis, asymptotic analysis, mathematical control theory, environmental statistics, spatial and spatio-temporal statistics, Bayesian and computational statistics, wavelets in statistics, teaching and learning of mathematics, teaching and learning of probability and statistics, mathematics curriculum and teacher education, calculus learning, and undergraduate mathematics education.

Additionally, a graduate certificate in industrial statistics is offered.

**Admission Requirements**

Applicants for the M.S. and Ph.D. degrees must have completed significant undergraduate coursework in mathematics, preferably in algebra, analysis, and topology. Applicants for the M.S. with applied mathematics option must have completed significant coursework in analysis or applied analysis. Applicants for the M.S. with statistics option will typically have an undergraduate degree in the mathematical, physical, biological, or social sciences or in engineering; must have completed mathematical coursework at least through multivariate calculus; and must have knowledge of basic statistics and basic linear algebra at the undergraduate level. Applicants for the degree of master of science for teachers (M.S.T.) usually possess a background equivalent to at least a minor in mathematics and must have completed education courses sufficient for certification, or have three years teaching experience, or currently hold a full-time teaching position.

**Degree Requirements**

**M.S. Degree Requirements**

** Pure Mathematics Option
**This program requires 30 credit hours, consisting of at least 10 semester courses approved by the department and chosen from courses in MATH 801-899, MATH 931-978 and IAM courses 830-962. The following stipulations apply:

- At least five of the 10 courses must be chosen from MATH 931-978 or from 900-level IAM courses.
- At least three courses must be chosen from MATH 931-956.
- Courses in MATH 900 through MATH 929 may not be used to satisfy course requirements.
- With approval of the graduate committee, two non-MATH graduate-level courses taken at UNH may be used to satisfy course requirements.

As a concluding experience, the student will take an oral exam before a committee of three faculty members. The committee membership is suggested by the student and is approved by the graduate program committee.

** Applied Mathematics Option
**This program requires 30 credit hours, consisting of the courses MATH 931, IAM 933, an approved two-course sequence in applied mathematics (such as MATH 967/977). In addition to these courses, the student chooses either a thesis or project option. The thesis option consists of 6 credits of Master's Thesis (MATH 899) and four elective courses. The project option consists of 3 credits of Master's Project (MATH 898) and five elective courses. The elective courses need not be in mathematics, but must be at the 800 level or higher, and at least one must be a technical course in statistics or some other department. The broad elective flexibility allows the student's application interests to have a substantial role in the content of the program. The student's full program plan must be proposed in writing to the applied mathematics faculty and approved prior to the student's second semester of study. There is no comprehensive examination in this option.

** Statistics Option
**This program requires 30 credit hours, consisting of at least ten semester courses approved by the department, which includes completion of a project (MATH 898) consisting of a substantial application of statistical methodology to a real problem. Most of the courses will be taken from the department's statistics courses in the range MATH 837-979 and must include all of MATH 839, 840, 855, and 856, unless some of these or equivalent courses were taken prior to enrollment in the program. At most, three of the required ten courses may also be taken from the department's approved nonstatistics courses (in the range MATH 837-979) and/or approved courses offered in other departments. MATH 898, the Master's Project, is conducted under the supervision of a faculty adviser and concludes with a written report and a public oral presentation. MATH 898 may be taken for 3 to 6 credits, depending on the level of substantial research and methodological development required for project completion; the appropriate number of credits is determined by the statistics faculty. A master's committee of at least two statistics faculty members oversees the student's progress and determines credit for the project. There is no comprehensive examination in this option.

*M.S.T. Degree Requirements*

The program requires 30 credit hours of coursework, which must include MATH 900, 905, 906, 909, 913, 915, 918 and 925. In addition to the 22 credit hours from the required courses, at least eight additional credit hours must be taken from courses numbered MATH 900-929. A concluding experience consisting of a mathematics portfolio and a comprehensive problem set is required. The program courses will be a combination of regular summer courses and academic-year online courses; a typical student in the program might expect to take as many as four program courses online. .

**Ph.D. Requirements**

The following are the requirements for completing the Ph.D. programs.

**Candidacy**

Students are advanced to candidacy after meeting the following requirements:

**Doctor of Philosophy in Mathematics**

1. All of the courses MATH 951, 952, 953, 954, 955.

2. Mathematics Ph.D. students must pass written comprehensive examinations in algebra, analysis, topology and an elective subject. Elective subjects include functional analysis, algebraic topology, applied mathematics, statistics, advanced algebra, advanced complex analysis, advanced mathematics education, et al.

3. Advanced coursework in a minor field (usually within mathematics, but possibly in another area of the mathematical sciences), and a major field (that of the student's intended dissertation work) followed by successfully completion of oral examinations in their minor and major areas.

4. Experience in teaching equivalent to at least half-time for one year

*Doctor of Philosophy in Statistics *

1. All of the courses MATH 836, 839, 840, 855, 856..

2. Successful completion of written qualifying examinations in theory of statistics and in applied statistics

3. Advanced coursework in statistics: all of the courses MATH 941, 945, 946; three elective courses from among MATH 837, 841, 843, 844, 942, 944, 969, 979 (MATH 969 and 979 are topics courses and may be taken more than once)

4. Minor coursework: one course in analysis (either MATH 867 or MATH 953) and two ocurses in a focused minor area to be selected in consultation with the program advisor

5. Participation in the one-credit statistics seminar during at least three semesters

6. Successful completion of a dissertation proposal defense in the major field of statistics

*Doctor of Philosophy in Mathematics Education*

1. All of the courses MATH 951, 952, 953, 954, 955.

2. Successful completion of written comprehensive examinations in algebra, analysis, mathematics education and an elective subject.

3. Advanced coursework in the major field (mathematics education), including MATH 958, 968A, and 968B, and at least two semesters of MATH 978, and in a minor field (usually a related one, such as educational psychology or research methodology, but possibly in an area of mathematics) followed by qualifying examinations in each.

4. Successful completion of a dissertation proposal defense in the major field of mathematics education and a presentation in the minor field.

5. Experience in teaching equivalent to at least half-time for one year

*Doctor of Philosophy in Applied Mathematics*

1. Must take nine courses totaling 27 credits from the following list: PHYS 931, IAM Â 830, IAM 851, IAM 932, IAM 933, IAM 961, IAM 962. One of the following 2-course sequences can also apply: MATH 847/IAM 950, ME 807/ME 909 or PHYS 953/PHYS 951.

2. In addition, must take a minimum of three technical electives totaling 9 credits from the following list: IAM 940, ME 812, ME 911, and other approved courses.

3. Pass a three-part Ph.D. qualifying exam:

*Comprehensive exam in mathematical methods

*Comprehensive exam in numerical analysis and HPC

*Oral or written exam in specialization area

4. Seminar presentation of thesis proposal to dissertation committee.

**Dissertation**

Each Ph.D. student must submit a dissertation as follows:

Doctor of Philosophy in Mathematics: A dissertation that includes original results in mathematics.

Doctor of Philosophy in Statistics: A dissertation that includes original results in statistics.

Doctor of Philosophy in Mathematics Education: A dissertation that includes original results in mathematics education.

Doctor of Philosophy in Applied Mathematics: A dissertation that includes original results in Integrated Applied Mathematics.

**Certificate in Industrial Statistics**

The Department of Mathematics and Statistics offers a graduate certificate in the area of industrial statistics. For more information please visit the mathematics and#38; statistics website.

**Admissions Requirement**

Individuals holding a bachelor's degree are eligible to apply for admission to a graduate certificate program.

**Applying**

Please visit the Graduate School website for detailed instructions about applying to the certificate program.

**Certificate Requirements**

A graduate certificate in industrial statistics is awarded for completion of four courses as follows:

***Note that all of these have as a prerequisite an introductory statistics course, such as MATH 835, Statistical Methods for Research.*

### Three required courses chosen from:

Abbreviation | Course Number | Title |
---|---|---|

MATH | 836 | Advanced Statistical Methods for Research |

MATH | 837 | Statistical Quality Improvement (SQI) |

MATH | 839 | Applied Regression Analysis |

MATH | 840 | Design of Experiments I |

Note that all of these have as a prerequisite an introductory statistics course, such as MATH 835, Statistical Methods for Research. |

### One elective course chosen from the remaining course of the

Abbreviation | Course Number | Title |
---|---|---|

MATH | 841 | Biostatistics and Life Testing |

MATH | 843 | Time Series Analysis |

MATH | 844 | Design of Experiments II (DOE II) |

MATH | 855 | Probability and Stochastic Processes |

MATH | 941 | Bayesian and Computational Statistics |

MATH | 942 | Beyond ANOVA: Generalized Linear & Semi-parametric Smoothing Methods |

MATH | 944 | Spatial Statistics |

or any other approved special topics course in the area of industrial statistics Other special topics courses are occasionally offered and may be added to the list of elective courses. |