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 committee.

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.
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.

Publications: See separate page for recent publications by graduate students.

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, in recent years it has been 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 information for new students 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.

The above requirements do not guarantee admission, which is competitive. Successful applications generally follow these recommendations:

  1. 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.
  2. ** Due to Covid-19 this requirement is currently suspended at the direction of the DMS Department Chair. 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.
  3. 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 assistantship will need a (paper) score of at least 600. The department gives preference to foreign applicants who also submit results of the Test of Spoken English (TSE); *
  4. Applicants must have completed at least a bachelors degree in mathematics or a closely related field from an accredited institution.
  5. 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 UAF academic calendar.

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.

Regarding Grades for Graduate Students:; Grades of A,B,C,D,F are possible in graduate courses, and correspond to numbers 4.0,3.0,2.0,1.0,0.0, respectively.

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 First, graduate assistantships (both teaching and research) are withdrawn after a warning:

A graduate student with a GPA (grade point average) less than 3.0 for one semester will be allowed to petition to continue as a graduate assistant for the next semester. A maximum one semester exception will be allowed per student. (2014-15 catalog, pages 204)

Next, the Advancement to Candidacy form must show courses which represent a GPA of 3.0:

The GPA for all courses listed on the Advancement to Candidacy form must be at least 3.0, and no graduate courses with grades below C, or undergraduate courses with grades below B, can be used. (2014-15 catalog, page 202)

Finally, as a requirement of maintaining "Good Standing" as a graduate student,

Maintain a cumulative GPA of 3.0 in courses taken since admission to graduate school. Before advancing to candidacy, however, a cumulative GPA of 3.0 is required. You must earn at least a B grade in 400-level courses. (2014-15 catalog, page 200)

Failure to meet one of these standards can, potentially, lead to dismissal; see pages 49 of the 2014-15 catalog.

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)

**All graduate students are required to also complete a 600 level seminar course in their final semester.

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 Modeling
Math 660 Advanced Mathematical Modeling
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 412 Differential Geometry
Math 617 Functional Analysis
Math 632 Algebra II
Math 663 Graph Theory
Math 665 Topics in Graduate Mathematics

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

Math 611 Mathematical Physics I
Math 614 Numerical Linear Algebra
Math 615 Numerical Analysis of Differential Equations
Math 660 Advanced Mathematical Modeling
Math 661 Optimization

Tentative Schedule of Course Offerings

  Fall odd (2019) Spring even (2020) Fall even (2020) Spring odd (2021)
Core MATH 641
Real Analysis		 MATH 645
Complex Analysis		 MATH 631
Algebra I		 MATH 651
Topology
elective
(pure)		 MATH 663
Graph Theory		 MATH 617
Functional Analysis		 MATH 658
Topics in Geometry		 MATH 632
Algebra II
elective
(applied)		 MATH 614
Numerical Linear Algebra		 MATH 660
Advanced Math Modeling		 MATH 661
Optimization		 MATH 615
Numerical Analysis of Differential Equations
  MATH 665
Topics in Grad. Math		   MATH 665
Topics in Grad. Math		  

Larger PDF of table here
LaTeX source for table here

Contact / Graduate Coordinator

Ed Bueler
Professor of Mathematics (Applied)
Dept of Mathematics and Statistics
University of Alaska
Fairbanks, AK 99775-6660
elbueler@alaska.edu

See the separate Faculty & Staff Directory.