DRAFT August 1, 2003 (document subject to change)

The Master of Science Degree in Mathematics
with Specialization in
Applied and Computational Mathematics

Note: Entering students undergo a Diagnostic Interview

The MS in applied and computational mathematics is a new (generally terminal) masters program aimed at providing the graduate with the skills needed to deal with problems which typically arise in business and industrial situations.

The program is based on the following components:

DEGREE REQUIREMENTS

General Requirements

  1. At least 33 credit hours of course work are required to complete an M.S. in mathematics. At least 24 of these hours must be taken on campus.
  2. Outside hours must be at the 300 level or above and must be approved in advance by the graduate student's advisor.
  3. The program must contain at least 18 hours of coursework in mathematics at the 500 level or above (excluding M-x99).
  4. At most 1 hour of M584 (Supervised College Teaching) may be included in the student's program.

 

Course Requirements

1. Computing Skills

Each student must demonstrate the ability to work in a professional programming language (e.g., C++, Java, C, FORTRAN). Several of the courses in the Department of Mathematics and some of the courses from related areas include a significant computing component. In these courses, the students will execute their assignments in an appropriate computer language. Introductory courses in programming languages are available for students having no previous programming skills.
Each student is required to complete a total of four computational courses. Mathematics courses which may be used to satisfy this condition include the following:

Numerical Analysis

M561

(Numerical Linear Algebra)

M550

(Finite Difference Methods for Differential Equations)

M651

(Numerical Analysis)

M652

(Finite Elements)

M750-M751

(Numerical Methods and Modeling)

Optimization

 

M510

(Linear Programming and Networkl Flows)

M520

(Nonlinear Programming)

M620-M621

(Variational Methods and Optimization)

Pattern Analysis

 

M795J

 

Introduction to High Performance Computing

 

GS510-GS511

 

2. Modeling

Mathematical modeling is the term used to refer to the process of formulating in mathematical context a problem arising in some area of applications. Each student is required to complete at least two one-semester courses in modeling. Mathematics courses which may be used to satisfy this condition include the following:

M532

(Continuous Models for Physical Systems)

M750-M751

(Numerical Methods and Modeling)


Examples of courses outside the Department of Mathematics which could be used to satisfy this requirement include:

CE631

(Solutions to Ground Water Problems)

CE633

(Ground Water Contaminant Transport Modeling)

AT601-AT602

(Atmospheric Dynamics)

3. Statistical Skills

Students are required to complete at least 6 credit hours in statistics. There are a large variety of courses offered by the Statistics Department and students should seek the advise of their faculty advisor in making a selection. With special approval of the graduate committee, the student may be excused from this condition by courses taken in the undergraduate program. In this case the undergraduate hours may not be counted toward the 33 hour total.

 

4. Project Development and Communication (Industrial Mathematics Seminar)

Students will have the opportunity to develop problem solving and communication skills as part of an industrial mathematics seminar and the associated project assignment. The core requirements of this seminar include:

The plan A/B paper can be based on the subject matter from this course. The final examination can be based on the evaluation of the final project report written by the student. As part of the exam, each student will submit to his/her committee a written report detailing their role in the project.

5. Area of Specialization

Each student will design a program containing at least one area of specialization. An area of specialization consists of at least two related courses, not necessarily from within the Department of Mathematics. Selections from within the Department of Mathematics that would serve to fulfill this condition include:

M517-M518, M519

(Mathematical Analysis)

M561, M651

(Numerical Analysis)

M560

(Linear Algebra)

M550-M652

(Computational Methods for Differential Equations)

M750-M751

(Numerical Methods and Modeling)

M545-M546

(Partial Differential Equations)

M540, M640-M641

(Ordinary Differential Equations)

M510-M520

(Linear and Nonlinear Programming)

M620-M621

(Optimization)

M501-M502, M601-602

(Combinatorics)


Course selections from outside the Department of Mathematics that would serve to fulfill this condition could be chosen, for example, from course offerings in any of the following areas: Statistics, Computer Science, Atmospheric Science, Fluid Dynamics, Hydrology and Ground Water Engineering, Electrical Engineering

Final Project and Examination

The student is expected to select an advisor from among the Mathematics faculty during the second semester, and a Masters committee, including a permanent advisor, by the end of the third semester of residency. In conjunction with selecting a committee, Masters students must complete the GS6 form from the graduate school at this time.

The student must complete one of the following options for a Masters paper:

Plan A (thesis): The student completes a thesis that is not purely expository but reflects an element of originality on the part of the student. The student's program must contain at least 6 but not more than 9 credit hours of thesis research (M699).

Plan B (paper): The student writes an expository paper under the direction of an advisor. This paper must be approved by the advisor and the committee. Students will register for 3 credits of thesis research (M699).

The Final Examination: A final exam is required. The nature of this exam is determined by the student’s committee (subject to graduate school requirements). It may be written or oral, at the discretion of the student's committee, and may cover the student's entire program. Traditionally the exam is oral and covers the paper or thesis. The student may choose to present the report from the Industrial Mathematics Seminar as his/her topic of final examination. In this case registering for M699 is not required.

A written report of the examination will become part of the student's file.

Scholastic Standards

A 3.0 average must be maintained in all courses, and a 3.0 average in all mathematics courses at the 400 level and above. Independently of this, the scholastic standards of the Graduate School apply, see page 18 of the Graduate and Professional Bulletin.

 

Sample Programs in Applied and Computational Mathematics

 

First Year

Second Year

 

First Semester

Second Semester

First Semester

Second Semester

Sample A:

GS510

GS511

M699J

M561

 

M531

M532

M540

M546

 

Stat 1

Stat 2

M651

M652

Sample B:

M510

M520

M560

M699J

 

M517

M518

M620

M621

 

Stat 1

Stat 2

M750

M751

Sample C:

GS510

GS511

M699J

M550

 

M531

M532

AT601/CE631

AT602/CE633

 

Stat 1

Stat 2

M651

M652

Sample D:

GS510

GS511

M699J

M561

 

M501

M502

Comp Sci/EE

Comp Sci/EE

 

Stat 1

Stat 2

M651

M795J

M.S. students who wish to go on for a Ph.D. program, please note:

1. Departmental Qualifying Examination

2. Policy regarding GTA support and graduate study in the Department of Mathematics