# Mathematical Sciences

## Master of Science in Mathematics

There are four options available in this program:

Applied and Computational Mathematics

Probabilty and Statistics

Mathematics for Teachers

Industrial Mathematics Professional Science Master's

All options require a four-year undergraduate degree from an accredited college or university with a satisfactory grade point average, and the official score report of the Aptitude Test of the Graduate Record Examination. For the Applied and Computational Mathematics and the Probability and Statistics options, the undergraduate degree must be in mathematics or a related discipline. For the Mathematics for Teachers option, three semesters of calculus (12 credits) are required. Applicants lacking some prerequisites may be accepted as matriculated with conditions. The Applied and Computational Mathematics, Probability and Statistics, and Mathematics for Teachers programs consist of thirty credit hours approved by the Graduate Curriculum Committee. The Industrial Mathematics Professional Science master's option requires 37 credit hours, including a paid internship. These credit requirements include both required courses and electives (which may be offered in other departments). Up to six credits at the 400 level may be considered for inclusion in the program of study. In addition, in all options except the Industrial Mathematics Professional Science Master's Option, three or six credits may, with the permission of the student advisor and Graduate Committee, be obtained by thesis. Most courses are offered on a regular basis in the late afternoon and early evening so that all programs can be completed on a part-time basis.

### Applied and Computational Mathematics

The M.S. Option in Applied and Computational Mathematics focuses on techniques of mathematical modeling and the basic tools needed to investigate problems from both a theoretical and computational viewpoint. Courses range from classical applied mathematics and state of the art courses in signal processing to modern applications of software in problem solution.

Required courses:

92.501 Real Analysis I

92.530 Applied Mathematics I

92.563 Computational Mathematics I.

### Probability and Statistics

This option is a professionally oriented program that provides the necessary mathematical skills to solve many of the data analysis problems of government, industry, science, engineering, and management. Courses range from theory based courses in probability through to applied hands-on course in statistical programming, including a course in the use of SAS statistical software.

Required courses:

92.501 Real Analysis I

92.509 Introduction to Probability & Statistics

together with one of

92.584 Stochastic Processes

92.587 Probability Theory

92.588 Mathematical Statistics

and one of

92.519 Introduction to Probability & Statistics II

92.591 Linear Statistical Modeling & Regression

92.593 Experimental Design

### Mathematics for Teachers

The Master of Science in Mathematics for Teachers Program aims to give students a balanced combination of theory and practice, to enhance their appreciation and understanding of Mathematics as a science, and to provide them with the tools necessary to instill in their own students an interest in the subject. Courses in Mathematical Analysis, Discrete Mathematics, Linear Algebra, Number Theory, Geometry, and Probability and Statistics are designed to introduce the student to several important areas of Mathematics. Courses in Problem Solving, History of Mathematical Science, Mathematical Modeling, and Computers in the Classroom are intended to provide a deeper awareness of the contexts in which mathematical activity takes place and of the mental processes and technological aids employed by people in solving practical problems. Note that this is not a teaching certification program - contact the Graduate School of Education for information about certification.

Required courses:

92.500 Discrete Structures

92.520 Problem Solving

### Industrial Mathematics Professional Science Master's

**Admission Requirements
** Incoming students will be expected to have completed the equivalent of an undergraduate degree in mathematics. Applicants with degrees in other sciences or engineering may be admitted if they demonstrate significant background in mathematics.

Degree Requirements - Total Number of Credits: 37

**Mathematics Courses** (15 credits)

**Required**:

- 92.501 Real Analysis I
- 92.509 Introduction to Probability & Statistics
- 92.530 Applied Mathematics I
- 92.563 Computational Mathematics

**Elective - One course from the following list:**

- 92.511 Complex Variables I
- 92.513 Number Theory
- 92.515 Intro Chaos & Dynamic System
- 92.521 Abstract Algebra I
- 92.526 Topology
- 92.531 Applied Mathematics II
- 92.545 Partial Differential Equations I
- 92.548 Mathematics Of Signal Processing
- 92.549 Math of Tomography
- 92.551 Calculus of Variations
- 92.552 Wavelet Analysis
- 92.564 Numerical Linear Algebra
- 92.572 Optimization
- 92.579 Reliability and Life Data
- 92.580 Discrete Mathematics for Eng and OR
- 92.581 Graph Theory
- 92.582 Time Series Analysis
- 92.589 Sampling Theory and Methods
- 92.590 Statistical Quality Control
- 92.592 Multivariate Statistics
- 92.595 Information Theory

**Science Cluster - One cluster of 12 credits from the following.
** (Variations on these clusters or different ones can be proposed with the guidance of the student's advisor.)

**Algorithms Cluster**

- 92.580 Discrete Math for Science and Engineering
- 91.503 Algorithms
- 91.504 Advanced Algorithms: Computational Geometry
- 91.544 Machine Learning and Data Mining

**Random Processes Cluster**

- 92.584 Stochastic Processes
- 16.509 Linear Systems Analysis
- 16.548 Coding and Information Theory
- 16.584 Probability and Random Processes

**Physics Cluster**

- 92.533 Mathematical Methods of Quantum Mechanics
- 95.535 Introductory Quantum Mechanics I
- 95.553 Electromagnetism I
- 95.554 Electromagnetism II

**Statistics Cluster**

- 92.576 Statistical Programming using SAS
- 92.588 Mathematical Statistics
- 92.591 Linear Statistics Modeling and Regression
- 92.593 Experimental Design

**Epidemiology/Biostatistics Cluster**

- 92.576 Statistical Programming in SAS
- 92.591 Linear Statistics Modeling and Regression
- 19.575 Introduction to Biostatistics and Epidemiology
- 19.689 Advanced Regression Modeling

**Internship** (1 credit)

The university will arrange for paid internships lasting a minimum of 340 hours for students in the program. The internship will be scheduled for a period some time after the student completes 18 credit hours in the program. At the end of the internship, the students will submit a paper and give an oral presentation on their work. Allowances will be made for students who already have a position in business, industry or government to allow them to use work in their current position as an internship.

**Professional Courses** (9 credits - one required plus two elective courses)

**Required Professional Course:**

- 66.688 Advanced Professional Communication,

plus **two** additional courses (6 credits) from a list approved by the PSM Coordinating Committee, including:

- 64.650 Innovation and Emerging Technologies
- 62.630 Market Research for Entrepreneurs
- 61.640 Financing Innovation and Technology Ventures
- 66.630 New Product Development
- 66.635 Project Management
- 64.655 Corporate Entrepreneurship