The curriculum for the Master of Arts in Mathematics has been carefully constructed in order to provide students with a solid foundation in the basic tools and methodologies of their field of choice. Beyond the basic requirements, students-with the assistance of their advisors-can design a tailor-made program, which not only meets their specific needs and interests but is also geared toward their career goals. Throughout the program, students can be assured of continuing and effective mentoring through close contact with their advisors and professors.

Degree Requirements
I. Base Requirements: Students must complete a program of study consisting of at least 30 credit hours, which must be approved by their advisory committee (see also the Course Restrictions below). At least 15 of these credits must be 500/600-level MAT/STS courses (exclusive of thesis and seminar credits). Additionally, there are two subject requirements and a depth requirement:

(Depth) All students must take at least one two-semester sequence (STS 531/532, MAT 523/524, MAT 527/528, MAT 563/564, or MAT 577/578).

(Linear Algebra) All students must take one or more of: MAT 562 Linear Algebra, MAT 564 Abstract Algebra II, or a course in Linear Statistical Models.

(Real Analysis) All students must take MAT 523 Functions of a Real Variable I.

II. Choice of Option:

A. Thesis Option: Students choosing to write a thesis under the supervision of a member of the Graduate Faculty need to take a total of 5 credits of MAT 699 (Graduate Thesis), in addition to a 1-credit course on Responsible conduct of research (such as INT 601). The latter credit must be taken prior to enrolling in the fourth credit of MAT 699. Upon completion of the thesis, the student must present an oral defense.

B. Non-thesis Option: At least 24 credit hours must be at the graduate level, and at least 18 of these must be MAT/STS courses.

III. Seminar Requirement: All graduate students must successfully give at least two seminar talks. It is suggested that one seminar be given in each of the fall and spring semesters of the second year. As this is a credit-bearing requirement, it is necessary to register. The assigned course number is MAT 590. For students following the thesis option, one credit of MAT 590 is required, and the thesis defense fulfills the second seminar requirement. For students in the non-thesis option, MAT 590 must be taken twice, once for each of the two seminars given. The talks should be prepared in consultation with and under the supervision of the advisor. Students should submit a short advisor-approved abstract to the graduate coordinator at least one week in advance of the seminar day, for inclusion in the announcement. The evaluation will be handled by the advisor in consultation with the members of the student’s advisory committee. A clear statement of the problem should be given with a brief historical sketch. All technical terms, specific to the area of expertise, should be clearly defined before they are used.

IV. Course Restrictions With permission of the Graduate Coordinator in consultation with the advisory committee, degree credit may be given for MAT/STS courses at the 400-level or for classes in other departments which have a significant mathematical emphasis or particular relevance to the thesis project. However, the following classes cannot be used among the 30 credits for the MA degree in Mathematics:

*Undergraduate courses which are required for the BA degree in Mathematics at the University of Maine. This includes MAT 425, MAT 463, and STS 434.

*If both MAT 452 and MAT 527 are taken, only one of them can count toward the MA degree.

Student Advisory Committee
The student advisory committee will consist of the advisor together with at least two members of the graduate faculty. In addition, the graduate coordinator will serve as an ex officio member without the voting rights. The committee should be formed by the end of the first year via this form, and will meet with the student at least once each semester of the second year to get an overview of the student’s progress. Thesis Administration The student should have his/her program plan which would include the courses to be taken as well as the thesis topic, ready for discussion and approval by the student advisory committee by the start of the first semester of the second year of study. Ideally, the thesis should be formatted in LaTeX. The LaTeX class package for UMaine theses is found here. A copy of the thesis will be provided to the graduate coordinator at least one week in advance of the date of the defense. The coordinator will make the thesis available to any member of the faculty for perusal prior to the defense. All public announcements relating to the thesis as well as the seminars will be made by the coordinator.

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The Department offers a Master of Arts in Mathematics. The typical student chooses to focus their advanced study in one of three broad areas: applied mathematics, pure mathematics, or statistics. At the time of admission, students will be assigned a preliminary advisor to assist them in developing a course of study consistent with their specific goals, and monitor their progress until they can formally establish their own advisory committee before the end of the first year.

Degree Requirements

I. Base requirements:

Students must complete a program of study, consisting of at least 30 credit hours which must be approved by their advisory committee. At least 15 of these credits must be 500/600-level MAT/STS courses (exclusive of thesis and seminar credits). Additionally, there are two subject requirements and a depth requirement:

* (Depth) All students must take at least one two-semester sequence (STS 531/532, MAT 523/524, MAT 527/528, MAT 563/564, or MAT 577/578).

* (Linear Algebra) All students must take one or more of: MAT 562 Linear Algebra, MAT 564 Abstract Algebra II, or a course in Linear Statistical Models.

* (Real Analysis) All students must take MAT 523 Functions of a Real Variable I.

II. Choice of option:

A. Thesis Option: Students choosing to write a thesis under the supervision of a member of the Graduate Faculty need to take a total of 5 credits of MAT 699 (Graduate Thesis), in addition to a 1-credit course on responsible conduct of research (such as INT 601). The latter credit must be taken prior to enrolling in the fourth credit of MAT 699. Upon completion of the thesis, the student must present an oral defense.

B. Non-thesis Option: At least 24 credit hours must be at the graduate level, and at least 18 of these must be MAT/STS courses. Two written qualifying examinations must be passed prior to graduation, chosen from analysis, algebra, and statistics. Decisions for retakes are up to the student’s committee in consultation with the Graduate Coordinator.

III. Seminar Requirement: All graduate students must successfully give at least two seminars. It is suggested that one seminar be given in each of the fall and spring semesters of the second year. As this is a credit-bearing requirement, it is necessary to register. The assigned course number is MAT 590. For students following the thesis option, one credit of MAT 590 is required, and the thesis defense fulfills the second seminar requirement. For students in the non-thesis option, MAT 590 must be taken twice, once for each of the two seminars given. The talks should be prepared in consultation with and under the supervision of the advisor. Students should submit a short advisor-approved abstract to the graduate coordinator at least one week in advance of the seminar day, for inclusion in the announcement. The evaluation will be handled by the advisor in consultation with the members of the student’s advisory committee. A clear statement of the problem should be given with a brief historical sketch. All technical terms, specific to the area of expertise, should be clearly defined before they are used.

IV. Course Restrictions:

With permission of the Graduate Coordinator in consultation with the advisory committee, degree credit may be given for MAT/STS courses at the 400-level or for classes in other departments which have a significant mathematical emphasis or particular relevance to the thesis project. The following classes cannot be used among the 30 credits for the MA degree in Mathematics:

* Undergraduate courses which are required for the BA degree in Mathematics at the University of Maine. This includes MAT 425, MAT 463, and STS 434.

* If both MAT 452 and MAT 527 are taken, only one of them can count toward the MA degree.

Admission to the Program

In addition to satisfactory performance of the candidate as an undergraduate, as evidenced by transcripts, letters of recommendation, and G.R.E. scores, the Department requires one semester of real analysis (equivalent to MAT 425) and one semester of abstract algebra (equivalent to MAT 463). Occasionally, students can be admitted with a deficiency in one of these areas if the deficiency is made up in the first year of graduate study. Prospective students are encouraged to follow the application procedure here: http://umaine.edu/mathematics/graduate-program/application-procedure/

Four Plus BA/MA Program
The Department offers the opportunity for ambitious mathematics majors to begin taking graduate courses during their senior year, with the possibility of double-counting these credits toward the BA and the MA. Students must apply for the program by February 1 of their junior year. Details may be found here: https://umaine.edu/mathematics/graduate-program/fourplus/

Teaching Assistantships A limited number of graduate teaching assistantships are available. Teaching assistants are expected to spend approximately 17 hours per week either teaching a course or assisting a faculty member and working in the Math Lab, an open tutorial center. Assistantships are awarded on a competitive basis among all applicants, and the decision to renew an assistantship is based on performance in the first year of the student’s program of study.

Graduate Faculty

Eisso Atzema, Ph.D. (Utrecht University, Netherlands, 1993), Lecturer. History of mathematics, geometry, mathematics education.

David M. Bradley, Ph.D. (University of Illinois, Urbana 1995), Professor. Classical analysis, number theory, special functions, difference differential equations.

Jack Buttcane, Assistant Professor (Ph.D. University of California, Los Angeles, 2012). Analytic number theory.

Tyrone Crisp, Ph.D. (University of Pennsylvania, 2012), Group representations, operator algebras, and connections between the two.

Robert Franzosa, Ph.D. (University of Wisconsin, 1984), Professor. Applied topology.

Ramesh C. Gupta, Ph.D. (Wayne State University, 1970), Professor. Statistics, biostatistics, probability, stochastic processes, reliability theory, mathematical models.

Brandon Hanson, Ph.D. University of Toronto, 2015. Number Theory

David Hiebeler, Ph.D. (Cornell University, 2001), Professor. Mathematical ecology and epidemiology, modeling and simulation.

Andrew Knightly, Ph.D. (University of California, Los Angeles, 2000), Professor and Graduate Coordinator. Number theory.

Franziska Peterson, Assistant Professor (Ph.D. University of Wyoming, 2016). Mathematics education.

Nigel Pitt, Ph.D. (Rutgers University, 1992), Professor. Analytic number theory.

Natasha Speer, Ph.D. (University of California, Berkeley, 2001), Associate Professor. Mathematics Education.

Peter Stechlinski, Ph.D. University of Waterloo, 2014. Assistant Professor. Dynamic modeling and simulation; control and optimization; mathematical biology.

Zheng Wei, Ph.D. (New Mexico State University, 2015), Assistant Professor. Statistics.

Associate Graduate Faculty

Keshav Aggarwal, Fixed-term Assistant Professor (Ph.D. Ohio State University, 2019). Number theory.

Timothy Boester, Fixed-term Assistant Professor (Ph.D. University of Wisconsin, 2008). Undergraduate mathematics education.

Shenhui Liu, Fixed-term Assistant Professor (Ph.D. Ohio State University, 2017). Number theory.

Julian Rosen, Fixed-term Assistant Professor (Ph.D. University of Michigan, 2013). Number theory, arithmetic geometry, Galois theory.

Byungjae Son, Fixed-term Assistant Professor (Ph.D. UNC Greensboro, 2017). Nonlinear differential equations, Mathematical ecology.