## M.S. in Mathematics

### Overview

Students in the Master of Science in Mathematics program take courses with either a pure or an applied mathematical emphasis. In addition to advanced coursework in mathematics, students take a comprehensive examination, and they complete a project or thesis developed in consultation with the student's graduate advisor and graduate advisory commitee.Projects and theses have been done in the areas of graph theory, algebra, biomathematics, partial differential equations, numerical analysis, dynamical systems, and Lie groups, among other topics. Many projects and theses have led to publications in pure and applied mathematics journals.br>

Most students complete the program in two years plus associated summers. Graduates of this program have gone on to Ph.D. programs in Mathematics, Applied Mathematics, and other fields, and into teaching positions at the two-year college level.

Start your application at the UAF Admissions application page. Applications are evaluated when complete. To be competitive for financial support, applications should be complete at least six months before intended admission. Firm application deadlines are June 1 for fall admission and October 15 for spring (March 1 and Sept 1 for international applicants). The UAF catalog description of the program is online here.

### Outcomes for the Successful Graduate

Qualifications of Graduates: Graduates of the program will be qualified to do the following:- Advanced research in mathematics or a closely related field.
- Continue on to Ph.D. work in mathematics, applied mathematics, or statistics.
- Teach courses in mathematics or subjects with high mathematical content (e.g. introductory statistics) at the post-secondary (two-year college) level.
- Work in industry in applications of mathematics.

Teaching experience: All MS Mathematics students have an opportunity to work as tutors or teaching assistants. Many recent MS graduates have also had the opportunity to teach their own courses at the pre-calculus or calculus level. Almost all gain experience tutoring in sections of calculus classes or in the Math Lab.

### Sources of Funding

Most of our graduate students are supported by Teaching Assistantships, which provide a 9-month stipend, health insurance, and tuition for up to 10 credits (e.g. three courses, a full graduate load) per semester. While the stipend amount is set by the College of Natural Science and Mathematics annually, for 2014-15 it was approximately $18,000.The duties of a Teaching Assistant might include (i) working with calculus students on homework problems in a small recitation section, (ii) grading for a more advanced class, (iii) tutoring in the Math Lab, and/or (iii) teaching (lecturing for) a 100- or 200-level course. See also the Teaching Assistant Handbook put out by the Graduate School

A limited number of Research Fellowships or Assistantships may also be available through grant money procured by faculty inside and outside of the department. Also see the financial aid and funding page at the Graduate School.

Also, Summer Sessions of UAF may hire MS Mathematics students to teach mathematics in the summer, including at the calculus level. Interested students should speak to the Chair of DMS.

### Courses, Exams, and Thesis or Project

The program is built around four 600-level mathematics core courses (below). Further electives are expected, possibly including courses outside of the department in applied areas. While most students will complete the program in two years, students who matriculate with deficiencies--typically one or two 400-level courses--may require an extra semester or two to complete the program.The written comprehensive examination covers the content of three courses chosen by the student and his/her committee, but including at least two core courses. It is usually offered in the Spring semester. Students are encouraged to take it at the end of their first year, but it may be taken in the second year of the program.

The program must be taken with a thesis or project. A thesis is more formal and involves satisfying UAF's thesis format requirements. A uafthesis LaTeX package exists to help with this; see also uafthesis at github

An oral defense/presentation is required for both the thesis and the project. This will usually be done shortly before graduation in the Spring of the student's second year. Theses are archived by the library, but PDF final forms are desired for both theses and projects.

### Qualifications for Admission

To be admitted to the program, an applicant must complete the general UAF procedures for admission into a graduate program, along with the admission requirements specific to the MS Mathematics degree.See the Admissions "Apply Now!" page to start an application online.

The specific admission requirements are:

- Submit three letters of recommendation concerning the applicant's educational background and quantitative training.

- Submit complete transcripts for all college-level work.

- Submit a resume.

- Submit a written statement of goals.

- The department does not require any GRE, but recommends applicants provide GRE general scores.
- Complete and submit a TOEFL score of at least 600 (this requirement is only for foreign applicants who seek a teaching assistantship).
- The department gives preference to foreign applicants who also submit results of the Test of Spoken English.

- Although GRE scores are not required for admission for students
with a 3.0 undergraduate grade point average or better, we recommend
that students complete and submit GRE general and subject exam scores
to provide additional information for admission and funding decisions.

- Students are required to take the GRE Mathematics Subject exam
by the end of their first year of study if they have not done so in the
admission process. This is intended as an assessment tool for the
graduate program. The Department will pay (reimburse) current
students for this exam. Failure to complete the GRE test during the
first year will result in a loss of department funding, including
teaching assistantships.

- Foreign applicants for whom English is a second language will need to complete and submit a TOEFL score of at least 550 (paper score), 79 (internet score), or 230 (computer score). Applicants seeking a teaching assistanceship will need a (paper) score of at least 600. The department gives preference to foreign appicants who also submit results of the Test of Spoken English (TSE); *
- Applicants must have completed at least a bachelors degree in mathematics or a closely related field from an accredited institution.
- Transcripts should include a background in mathematics courses requiring proofs. Specifically, we expect coursework for the undergraduate degree to include the completion of the following courses or their equivalent with a grade of B or better: **

- A course in advanced calculus or introductory analysis (e.g. Math 401);
- A course in abstract algebra (e.g. Math 405);
- A course in linear algebra (e.g. Math 314);

* - Exceptions MAY be made by the graduate admissions committee.

** - Exceptions to these requirements MAY be made by the graduate admissions committee. Students who are admitted with deficiencies will be asked to remedy these deficiencies as soon as possible after their arrival on campus.

### Program Requirements from UAF

**Deadlines:**See the Graduate School's deadlines page.

**Graduate Committee: **The applicant
must select a graduate
advisory committee including at least three faculty members,
at least two of whom are mathematics faculty. One member who is on
the mathematics faculty must be committed to chair or co-chair the
committee. The
inclusion
of a faculty member from another discipline is encouraged for those
students
working on a thesis/project in an applied area. Students will
need to form a (provisional) graduate committee by the
end of their first semester. The graduate advisory committee
can decide, in accordance with
university policy, whether specific transfer graduate courses may be
allowed
as part of the program (at most 9 credits). The student
and
his/her committee should complete the Appointment/Change
of Graduate Committee Form.

Graduate Study Plan:
One of the first actions of the student and his/her graduate
committee is to meet with the student to create a Graduate
Study Plan. Among
other things, the Graduate Study Plan lists the courses the student
will
be taking to complete their Master's degree.

**University Requirements: **The student must satisfy the
general
university requirements, in particular, complete a minimum of 30
semester
credits of which at least 24 credits must be at the 600 level,
including
those earned for thesis (maximum of 12 credits) or projects (maximum of
6 credits). At least 21 of these credits must be taken in
Mathematics.

Annual Report: Each
year the student and his/her committee should complete an
Annual
Report. This report provides an opportunity to confirm that
the student is making satisfactory progress toward the degree, or to
flag any issues or difficulties that have arisen.

Advancement to Candidacy:
Once the student and committee have achieved finally agreement upon
courses, topics on the comprehensive exam, and project/thesis title, an
Advancement
to Candidacy form must be submitted to the Graduate School
This form will be checked upon application for graduation, and the
courses the student has actually taken must match the form. Thus
it
should not be submitted prematurely, however it must be submitted at least one semester before graduation.

Written Comprehensive Examination:
See the separate page on the MS
comprehensive examination.

The UAF catalog says three things about grades for graduate students. First, graduate assistantships (both teaching and research) are withdrawn after a warning:

In summary, graduate students must maintain a 3.0 GPA to stay out of trouble.

### Departmental Requirements

In addition to the
university
requirements, the M.S. Mathematics program requires the
following:
## I. Complete the Core Mathematics Courses: |
||

Math 631 |
Algebra I |
4 credits |

Math 641 |
Real Analysis |
4 credits |

Math 645 |
Complex Analysis |
4 credits |

Math 651 |
Topology |
4 credits |

16 credit subtotal |

II. Complete at least 8 additional credits of approved
elective courses in Mathematics or a closely related field; at most 6
credits can be at the 400 level; see below
for suggestions |

8+ credit subtotal |

III. Complete an approved Project or Thesis |
||

Math 698 |
Research
(on Project) |
6 credits |

Math 699 |
Thesis |
6-12 credits |

6-12 credit subtotal |

**= at least 30 CREDITS TOTAL**

**(includes at least 24 credits at the 600 level)**

### Suggested Electives

The following are
common electives for MS students. These lists are neither
exclusive nor exhaustive.Possible electives for students
planning to** teach mathematics at the post-secondary
(two-year college) level:
**

**Math 460 Mathematical Modelling**

Math 660 Advanced Mathematical Modelling

Math 661 Optimization

Math 663 Graph Theory

Stat 651 Statistical Theory I

Possible electives for a student
in a **pre-Ph.D. program in mathematics:**

Math 617 Functional Analysis

Math 632 Algebra II

Math 663 Graph Theory

Math 665 Topics in Graduate Mathematics

**pre-Ph.D. program in applied mathematics**:

Math 614 Numerical Linear Algebra

Math 615 Numerical Analysis of Differential Equations

Math 660 Advanced Mathematical Modelling

Math 661 Optimization

### Contact / Graduate Coordinator

**Ed Bueler**

Associate Professor of Mathematics (Applied)

Dept of Mathematics and Statistics

University of Alaska

Fairbanks, AK 99775-6660

(907) 474-7693

Fax: (907)-474-5394

elbueler@alaska.edu

See the separate Faculty & Staff Directory.