# 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:- MATH.5010 Real Analysis I
- MATH.5300 Applied Mathematics I
- MATH.5630 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:- MATH.5010 Real Analysis I
- MATH.5090 Introduction to Probability & Statistics

together with one of - MATH.5840 Stochastic Processes
- MATH.5870 Probability Theory
- MATH.5880 Mathematical Statistics

and one of - MATH.5190 Introduction to Probability & Statistics II
- MATH.5910 Linear Statistical Modeling & Regression
- MATH.5930 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:

MATH.5000 Discrete Structures

MATH.5200 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**:

- MATH.5010 Real Analysis I
- MATH.5090 Introduction to Probability & Statistics
- MATH.5300 Applied Mathematics I
- MATH.5630 Computational Mathematics

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

- MATH.5110 Complex Variables I
- MATH.5130 Number Theory
- MATH.5150 Intro Chaos & Dynamic System
- MATH.5210 Abstract Algebra I
- MATH.5260 Topology
- MATH.5310 Applied Mathematics II
- MATH.5450 Partial Differential Equations I
- MATH.5480 Mathematics Of Signal Processing
- MATH.5490 Math of Tomography
- MATH.5510 Calculus of Variations
- MATH.5520 Wavelet Analysis
- MATH.5640 Numerical Linear Algebra
- MATH.5720 Optimization
- MATH.5790 Reliability and Life Data
- MATH.5800 Discrete Mathematics for Eng and OR
- MATH.5810 Graph Theory
- MATH.5820 Time Series Analysis
- MATH.5890 Sampling Theory and Methods
- MATH.5900 Statistical Quality Control
- MATH.5920 Multivariate Statistics
- MATH.5950 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**

- MATH.5800 Discrete Math for Science and Engineering
- COMP.503 Algorithms
- COMP.504 Advanced Algorithms: Computational Geometry
- COMP.544 Machine Learning and Data Mining

**Random Processes Cluster**

- MATH.5840 Stochastic Processes
- EECE.509 Linear Systems Analysis
- EECE.548 Coding and Information Theory
- EECE.584 Probability and Random Processes

**Physics Cluster**

- MATH.5330 Mathematical Methods of Quantum Mechanics
- PHYS.5350 Introductory Quantum Mechanics I
- PHYS.5530 Electromagnetism I
- PHYS.5540 Electromagnetism II

**Statistics Cluster**

- MATH.5760 Statistical Programming using SAS
- MATH.5880 Mathematical Statistics
- MATH.5910 Linear Statistics Modeling and Regression
- MATH.5930 Experimental Design

**Epidemiology/Biostatistics Cluster**

- MATH.5760 Statistical Programming in SAS
- MATH.5910 Linear Statistics Modeling and Regression
- PUBH.5750 Introduction to Biostatistics and Epidemiology
- PUBH.6890 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:**

- MGMT.6880 Advanced Professional Communication,

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

- ENTR.6500 Innovation and Emerging Technologies
- MKTG.630 Market Research for Entrepreneurs
- FINA.6400 Financing Innovation and Technology Ventures
- MGMT.6300 New Product Development
- MGMT.6350 Project Management
- ENTR.6550 Corporate Entrepreneurship