Master of Science

in Applied and Computational Mathematics

Department of Mathematics and Statistics

University of Minnesota Duluth

The basic intention of the master's program in applied and computational mathematics and statistics is to develop the student's critical professional thinking and intuition. It is designed for students seeking or currently engaged in careers in industry, business, education, or government. Students having recently obtained their undergraduate degrees can enter the program with the goal of obtaining employment at a relatively high level of responsibility and expertise. However, the program is also designed to upgrade the skills and knowledge of persons who are already engaged in positions in government, industry, business, and academia.

This guide is intended to provide prospective graduate students in mathematics and statistics with a concise description of the program and pertinent requirements. Also included is a tentative schedule of graduate courses.

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 Bulletin of the University of Minnesota. The information listed here is intended to supplement those requirements as listed in the 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) and Non-thesis (Plan B) 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 33 approved credits with a combined grade point average for these credits of 3.0 or higher. At least 14 of these (not including thesis credits) must be under the MATH designation.

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 or C++). There is no foreign language requirement.

Course Requirements

1. Theoretical Core:

Math 5327 Advanced Linear Algebra, if the student has not already had a similar course. In addition, the student must have two courses from:

a. Area: Analysis: Math 5201 Real Variables

b. Area: Probability and Statistics: Stat 5571 Probability

c. Area: Algebra and Discrete Math: Math 5371 Abstract Algebra I

2. Math 8980 Graduate Seminar and at least one additional 8000-level Mathematics or Statistics course. If 8000-level courses are not available then the student must attend Graduate Colloquia every semester.

3. Breadth: Students not taking all three Core Area courses in (1) must include in their program of study at least one course in the unrepresented Area.

4. Each studentís program of study must include at least one course that makes significant use of computation.

5. Related Field: The Graduate School requires that at least 6 credits be taken outside the major for Plan A programs and that at least 10 credits be taken outside the major for 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. For Plan A programs, 6 credits from a single field (courses with the same prefix) are sufficient for a minor.

6. Research Plan: The student may select from two alternatives:

Plan A: Masterís Degree with Thesis

Math 8777 Thesis Credits (10 credits). The thesis must be defended before the candidateís advisory committee and presented to the department in a seminar or colloquium. In addition to the copies required by the Graduate School, two bound copies of the thesis are required by the Department (one to the thesis advisor, and one to the Department Head.)

Plan B: Masterís Degree without Thesis

Math 8994 Directed Research (2 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.

7. For Plan B students, two courses from one of the following clusters:

a) Applied Analysis: Math 5260, Math 5270, Math 5280

b) Probability and Statistics: Stat 5511, Stat 5531, Stat 5572

c) Algebra and Discrete Math: Math 5330, Math 5365, Math 5366

d) Computation: Math 5830, Math 5840, Math 5850

8. Electives from Mathematics, Statistics or approved related areas to reach a minimum of 33 credits. Your program must include a minimum of 14 credits with a Math designator.

Advising mechanism and schedule

New graduate students are normally assigned a graduate advisor by the Director of Graduate Studies during their first semester of graduate work. Advisors typically are chosen from among the members of the Graduate Program Committee at the time the student applies. However, a student can request any member of the graduate faculty to act as his/her advisor, and this request will generally be honored.

Near the end of each semester, students should discuss their course programs for the following semester with their advisors. The advisor's approval must be obtained for both registration in courses and any subsequent additions or withdrawals.

Advisors will counsel students in picking the courses necessary for the completion of the degree requirements. They will also assist the students in the preparation of their official programs of study (submitted after completion of 10 credits -- typically, during their second semester of study). All students are advised to include only the minimum number of credits to satisfy the degree requirements in their official programs of study. This is to avoid potential problems should a student desire to pursue a second masterís degree. The Graduate School stipulates that a student may have a maximum of 8 semester credits in common between two Plan A masterís degrees, two Plan B masterís degrees, or a Plan A and Plan B masterís degree. It is the official programs of study that are used in determining potential credits in common. These programs will be reviewed by the Director of Graduate Studies, and then passed on to the Graduate School for final approval.

At the time a student prepares his/her official program of study, the student's advisor will help in selecting the members of the student's advisory committee. (See the graduate school form for a description of the make-up of the committee.) Note: Students using STAT as a related area must include on their examining committee at least one faculty member who has served as an instructor in one of their STAT courses. This faculty member cannot also act as the student's advisor.

It is the responsibility of the graduate student to identify a thesis advisor if he/she wishes to pursue the Plan A Option. The thesis advisor will take over the advisement responsibilities for the student, and will oversee the creation of the thesis committee.

Assistantship reappointment policy

Students who receive financial aid through the Department are expected to pursue a minimum of 8 approved credit hours per semester. Those students holding regular ("half-time") graduate teaching/research assistantships must demonstrate normal progress towards the degree by completing at least 16 approved credit hours a year with a combined grade point average for these credits of 3.0 or higher. Students satisfying these requirements in addition to carrying no more than 3 unresolved "I" grades are normally reappointed automatically (at or near the end of the Spring semester).

Any student with grade point average below 3.0 or with more than 3 unresolved "I" grades is placed on "probation". If on probation at reappointment time, a student may be granted a reappointment on a semester-by-semester basis, with future reappointments contingent either on the student's removing his/her probationary status or satisfying other stipulations as indicated by the Graduate Program Committee.

Examinations

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 will be 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 2 courses from the "theoretical core" (student's choice) and 5327 Advanced Linear Algebra, as well as prerequisite material from calculus, vectors and matrices, discrete mathematics, introduction to probability and statistics, and intermediate analysis.

This examination can be take in an oral format at the mutual agreement of both the student and the Graduate Faculty 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". However, students are encouraged to take the examination even if they are enrolled in one or more of these courses at the time of the examination. (In such a situation, the questions for that material will be designed and/or graded with the understanding that the student may not have seen all the material normally covered in the course.)

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.

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.

"Final" examination:

For Plan A students (Thesis option), this consists of a defense of the thesis. The members of the student's thesis 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 "areas of concentration". The examination committee consists of the student's advisory committee plus invited faculty (eg, project advisor or faculty from the "area(s) of concentration"). 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.

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.

Financial Aid

Each year the Department of Mathematics and Statistics attempts to identify sources of financial aid to help support graduate student studies over the summer months. When funds are available, they have been allocated so as to promote productive summer activity by those students who have made sufficient progress towards the completion of the degree.

In the past, available funds have been offered on a competitive basis. While all students are encouraged to apply, the highest priority is given to those who have identified thesis/project topics and who hope to work on these over the summer. These awards have no associated teaching responsibilities. They are announced typically near the end of the Spring semester, and distributed early in the Spring semester.

Students wishing to apply for a summer fellowship should submit a (typed) proposal to the Graduate Program Committee. This proposal is to be written by the student and should address of the following points:

1. Brief description of summer research plans, including the names of any associated UMD faculty.

2. Preparation for research (past course work, grade point average, literature work, seminar attendance, current research, etc.).

3. Available financial support. While financial need will be taken into consideration, those students who have already arranged for some sort of summer support are not to be considered at a disadvantage. Partial or supplemental fellowship awards will be considered by the Committee. In particular, students are encouraged to seek independent career-related employment as a means of broadening their backgrounds.

A copy of a Proposal for Summer Research Support is attached as a guide for both format and depth of detail. The statement of financial needs, as well as an approved Program of Study must accompany the proposal. In general, preference for summer support is given to students who have passed or have registered to take the comprehensive examination.

It should be emphasized that this support is not intended to be a reward for past service, but rather is given in anticipation of substantial effort on your project or thesis. You are expected to maintain contact with your advisor over the summer and to keep your advisor appraised of your progress. Moreover, for those students who have found additional funding from other university sources, the Departmentís summer support is not intended as a means of raising a studentís summer salary over the %100 GRA level. As such, the Department retains the right to reduce its summer fellowship support of a graduate student in order to maintain a total university level of support of not more than 100% time.

Tentative Schedule of Graduate Course Offerings for 2003-4, 2005-6, ?

	Fall	Spring
Core / Seminars:	Math 5371 Abstract Algebra	Math 5327 Advanced Linear Algebra
	Stat 5571 Probability	Math 5201 Real Variables
	Math 8980 Seminar
Algebra/Discrete Math:	Math 5365 Graph Theory	Math 5330 Number Theory
		Math 5372 Abstract Algebra II
Continuous Modeling:	Math 5260 Dynamical Systems	Math 5270 Modeling with Dyn Sys
	Math 5830 Num. Analysis App & Quad	Math 5840 Num. Analysis Sys & Opt
Stochastic Modeling:	Stat 5411 Analysis of Variance	Stat 5531 Probability Models
	Stat 5515 Multivariate Statistics	Stat 5572 Statistical Inference
		Stat 5511 Regression Analysis

Tentative Schedule of Graduate Course Offerings for 2004-5, 2006-7, ?

	Fall	Spring
Core / Seminars:	Math 5201 Real Variables (2004)	Math 5327 Advanced Linear Algebra
	Math 5371 Abstract Algebra	Math 5201 Real Variables (2006, ?)
	Stat 5571 Probability
	Math 8980 Seminar
Algebra/Discrete Math:	Math 5365 Graph Theory	Math 5366 Enum. Combinatorics
	Math 5384 Algebraic Coding Theory	Math 5372 Abstract Algebra II
Continuous Modeling:	Math 5280 Partial Differential Eqns	Math 5850 Numerical Diff Eqns
	Math 5830 Num. Analysis App & Quad	Math 5810 Linear Programming
Stochastic Modeling:	Stat 8611 Linear Models	Stat 5531 Probability Models
	Stat 5515 Multivariate Statistics	Stat 5572 Statistical Inference
		Stat 5511 Regression

Under-enrolled courses are subject to cancellation. Should there be courses that you consider important to your program which are not on the schedule above, contact the Director of Graduate Studies as soon as possible. If there is sufficient demand, this schedule can be modified.