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Graduate Studies
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Home > Graduate Studies > Degree Requirements

All graduate students should be aware that they are responsible for the general degree requirements as imposed by the Graduate School. Students should familiarize themselves with the rules and regulations concerning academic standards, degree requirements, program approval procedures, etc. as stated in the Graduate School Catalog of the University of Minnesota. The information listed here is intended to supplement those requirements as listed in the UMD Graduate Catalog, and concerns primarily the additional requirements made by the Department of Mathematics and Statistics.

The Master of Science in Applied and Computational Mathematics is offered with both the Thesis (Plan A—see Catalog) and Non-thesis (Plan B—see Catalog) option. Both options are designed to provide the student and his/her advisor the flexibility to fashion an individual program that emphasizes mathematics relevant to the student's personal interests and objectives.

The Master's degree is designed primarily as a two-year program. The Department of Mathematics and Statistics requires that each candidate complete a minimum of 35 approved credits with a combined grade point average for these credits of 2.8 or higher. At least 25 of these credits must be under MATH or STAT designator (including MATH 8777 Thesis credits or MATH 8994 Directed Research credits). At least 14 of these (not including MATH 8777 Thesis credits or MATH 8994 Directed Research credits) must be under the MATH designation. At least 6 credits must be taken outside the major (see below).

Course and examination requirements are listed below. In addition, students must demonstrate an intermediate level competency in a modern scientific programming language (such as FORTRAN, C, C++, SAS). There is no foreign language requirement.

Graduate Teaching Assistants' reappointment is regulated by GTA Reappointment Policy.

Course Requirements

1. Theoretical Core

a. Linear Algebra: 5327 Advanced Linear Algebra (3 credits) (This requirement can be waived by DGS if the student has already taken a similar course prior to coming to UMD.) In addition, two courses from:

b. Analysis: Math 5201 Real Variables (4 credits)

c. Probability and Statistics: Stat 5571 Probability (4 credits)

d. Algebra and Discrete Math: Math 5371 Abstract Algebra I (3 credits)

2. Special Courses
    • Math 8980 Graduate Seminar. Moreover, every student must attend at least 16 Graduate Colloquium presentations (14 if you started before 2014).
3. Breadth

Students not taking all three Core Area courses in (1 b), (1 c), (1 d) must include in their program of study at least one course in the unrepresented Area.

4. Computation

Each student's program of study must include at least one course that makes significant use of computation. They are:

    1. Math 5233 Mathematical Foundations of Bioinformatics
    2. Math 5830 Numerical Analysis: Approximation & Quadrature
    3. Math 5840 Numerical Analysis: Systems & Optimization
    4. Math 5850 Numerical Differential Equations
    5. Stat 5411 Analysis of Variance
    6. Stat 5511 Regression Analysis
    7. Stat 5515 Multivariate Statistics
    8. Stat 5521 Applied Time Series Analysis
5. Related Field

The Graduate School requires that at least 6 credits be taken outside the major for both Plan A and Plan B programs. The Program in Applied and Computational Mathematics requires that these credits outside the major be taken from approved math related fields with designations other than MATH. STAT is an allowed related field except STAT 5571 Probability, which does not count towards the 6 credit requirement. Eligibility of courses other than STAT is determined by DGS. Moreover, 6 credits from a single field (courses with the same prefix) are sufficient for a minor. For students not seeking a minor, the credits may be taken from different fields.

Students planning a teaching career may consider getting Community College Teaching Certificate in collaboration with CEHSP. The courses offered there can be counted towards their minor.


6. Research Plan
The student may select from two alternatives:
a. Plan A: Master's Degree with Thesis
  1. Math 8777 Thesis Credits (10 credits). The thesis must be defended before the candidate's Examining Committee and presented to the department in a seminar or colloquium. In addition to the copies required by the Graduate School, the candidate must provide the advisor with a hard-bound copy and submit a pdf file of the thesis to the department. Guidelines for fomatting etc. are here.
  2. Electives from Mathematics, Statistics or approved related areas to reach a minimum of 35 credits. Your program must include a minimum of 14 credits with a Math designator (not including Math 8777 Thesis credits).
b. Plan B: Master's Degree without Thesis
  1. Math 8994 Directed Research (4 credits). Under this option, the student must complete an approved project that must be presented to the department in a seminar or colloquium, and prepared for publication as a departmental technical report. A pdf file of the final version must be submitted to the department. Starting the first semester after submission of their Graduate Degree Plan Form, Plan B students must register for 2 credits of Math 8994 Directed Research in every semester until they defend their project. In exceptional situations, they may register for 1+3 or 3+1 credits during the first two semesters after submission of their Graduate Degree Plan Form. (For students without Full Time status this requirement will be adjusted individually.) A maximum of 4 credits can count towards the total number of credits required by the program. For fomatting you can use the Thesis guidelines here.
  2. Two courses from one of the following areas of concentration (close to the project topic)
    • Applied Analysis: Math 5260, Math 5270, Math 5280, Math 5810
    • Probability and Statistics: Stat 5221, Stat 5411, Stat 5511, Stat 5515, Stat 5531, Stat 5572, Stat 8611
    • Algebra and Discrete Math: Math 5330, Math 5365, Math 5366, Math 5384, Math 5372
    • Computation: Math 5233, Math 5830, Math 5840, Math 5850
    Some courses are offered every other year only. Check the list here.
  3. Electives from Mathematics, Statistics or approved related areas to reach a minimum of 35 credits. Your program must include a minimum of 14 credits with a Math designator (not including Math 8994 Directed Research credits).


The Master of Science Degree in Applied and Computational Mathematics requires successful completion of two examinations. A written Comprehensive Examination covers the basic theoretical material included in each candidate's official program of study. At the end of the student's term of studies, there is an oral Final Exam.

Comprehensive Examination

This examination is required of all students. When sufficient demand exists, it is offered in the late Spring and Fall semesters each year. The material tested is the courses from the Theoretical Core. There are 8 problems, two in each subject. The student must solve four problems; precisely one problem in Advanced Linear Algebra and three problems in two or three of the remaining fields (Abstract Algebra, Real Variables, Probability) according to the student's choice. The exam is three hours long. It is typically given on Saturday, one week after the Final Exam week, at 9 AM in SCC 130.

This examination can be take in an oral format at the mutual agreement of both the student and the Graduate Program Committee when there is insufficient demand for a written examination.

Most students should be able to complete these courses during the first year, and must take the exam the first time it is offered once they have completed the courses from the Theoretical Core.

The Director of Graduate Studies coordinates the collection of problems, administration, and grading of the exam. To the extent possible, problems are solicited from and graded by the faculty who have taught the material to the students being examined.

The Graduate Program Committee reviews the graded exams and determines what constitutes a passing or failing grade. A student failing the exam is given a second chance. At the request of either the student or the Graduate Program Committee, this second exam may be replaced by a comparable oral examination. This Committee handles any student appeals or may request an immediate oral exam (based on material related to the written examination) of a "borderline" student. Every problem is worth 50 points. To pass with distinction, the student must have a score of 180 or higher.

Copies of old comprehensive examinations are available upon request in the Mathematics & Statistics office. These are an excellent resource to aid you in preparing for the examination.

Students need to fill the Application for Comprehensive Examination Form by April 20 or November 20 in their second semester even if they are not planning on taking it that semester (in that case they need to state the reasons for not taking it).

Final Examination

For Plan A students (Thesis option), this consists of a defense of the thesis. The members of the student's Examining Committee serve as examiners. While the format may vary, typically the defense consists of a short presentation (open to the full department) of the thesis, followed by a period (open only to Committee Members and invited faculty) of questions.

For Plan B students, the exam covers the student's Plan B Project, as well as the material from courses in the student's Area(s) of Concentration. The members of the student's Examining Committee serve as examiners. While, again, the format may vary, the examination typically is centered around the student's project, which must be in final form before the examination is held. The examination consists of a short presentation (open to the full department) of the project, followed by a period (open only to Committee Members and invited faculty) of questions.

It is departmental policy that Committee Members be provided final drafts of either the thesis (Plan A) or project technical report (Plan B) at least 10 days in advance of the corresponding defense or oral examination. Useful links for preparing the final draft of your thesis/project are here.

A pdf file with the final version of the thesis/project needs to be submitted to the department. For Plan A, another pdf file must to be submitted to the Graduate School. Instructions are here. A direct link is here.

Advisor and Examining Committee

  1. Finding an Advisor. Every student must find an Advisor by April 1 or November 1 (in the first semester following the semester in which he/she had completed 10 credits, typically during the second semester of study) and provide the Advisor's name to DGS by email to (Until then, DGS serves as advisor to all first year students.) The Advisor then suggests two other members of the Examining Committee, one from the major field and one from a related field or minor. Hence, one member must be from another department, or in Statistics. If the student is seeking a minor, one of the Committee Members must be from the minor field. After that, the student asks online for committee approval (the actual link is at the bottom of the page). You can also go directly to committee approval page.
  2. Examining Committee meeting and courses selection. [This is just recommended.] The whole committee then meets with the student. They discuss the student's plan of courses for the second year of study as well as the research area for the Thesis or Project. The advisor then approves the plan of courses.
  3. Graduate Degree Plan. After the completion of the plan for the second year, the student fills the Graduate Degree Plan (Form) and submits it to DGS by April 20 or November 20. All documents are then reviewed by the Director of Graduate Studies and submitted to Graduate School.
  4. Changes. For any course changes, the Graduate Degree Plan (Form) needs to be amended, approved by DGS and submitted to the Graduate School.


If you need to take a break in your study (semester, academic year, or even more), you should maintain your Active status by registering for GRAD 999 or MATH 8333 courses. To learn which one is better for you, see the policy. If you do not register for one of them, you may need to re-apply before you come back and you may lose your benefits and/or visa status. Information about readmission is here and the official policy is here, Ask your Advisor or DGS about details. Another option is to apply for a Leave of Absence (for up to two years). Related policy is here and the application form is here. There is also a guide to that policy here.

Graduate Teaching Assistants' reappointment is regulated by GTA Reappointment Policy.

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Last modified on 08/27/12 02:45 PM
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