# Master of Arts in Mathematics (MA) - Online

## Outline Requirements for the M.A.

The Master of Arts in Mathematics (MA) degree can be completed entirely online. To obtain this degree, a student needs to pass 11 courses with a GPA of 3.0 or better. One of these courses is the tutorial course Math 6315. At least seven of the other courses are online mathematics courses at the 5000 level. The other three courses may be online mathematics courses at the 5000 level or other elective courses such as those in the mathematics education graduate program.

The time taken to complete this degree depends on individual preference and the number of courses taken in any particular semester. Every summer a large selection of 5000 level courses is available. The program can be completed comfortably in 2 years, and it must be completed in no more than 5 years.

For more detailed descriptions of these requirements including a list of 5000 level mathematics courses, please read below *(**link to the current catalog**)*.

*Note: Due to University and Federal regulations, admission to this program is available only to US Citizens and Lawful Permanent Residents*.

### Introduction

The Master of Arts Program in Mathematics was established in 2002. Classes in this program were first offered in Fall 2003. The primary purpose of the program is to prepare students to teach mathematics at the secondary school and junior/community college levels. The program also provides advanced degree credentials for teachers who wish to take on supervisory positions in mathematics or in mathematics administration.

### Format

All of the courses in the program are offered online, and the entire program can be completed in that format. It is also possible to take approved on-campus courses as alternatives to online courses.

There is a regular schedule of online (asynchronous) classes each semester, including the summer sessions. As a result, there is little difficulty in combining a full-time teaching or work position with the program’s course work.

### Prerequisites For Admission

To be admitted to the program, a student must have completed a bachelor’s degree with a 3.0 GPA over the last 60 hours of course work, and should have a solid background in mathematics. A student need not have majored in mathematics to be admitted. However, it is expected that the student has completed a standard 3-semester calculus sequence and at least 3 additional mathematics courses at the junior or senior level, preferably in courses such as abstract algebra, linear algebra, advanced calculus, differential equations, or geometry.

*The Graduate Record Examination (GRE) is **waived** for all Masters programs within the Department of Mathematics.

### Program Description

The program requires **33 semester hours** of course work including:

- A minimum of 21 semester hours in mathematics.

- Completion of at least one course in each of the groups: Algebra, Analysis, Probability & Statistics, and Applied Mathematics. See below for a list of the course groups, as well as course descriptions.

- A 3-semester hour Master’s tutorial.
- In order to enroll in a Master's Tutorial course 6315 and satisfy the Tutorial requirement, students should first contact one of the instructors who previously taught classes in the MA program and request to take the Tutorial course with him/her. If the instructor agrees, they will assign a project and provide the course section number so that student is able to enroll into the course. If you have any questions, please contact Prof. Gary Etgen or the Director of Graduate Studies.

- A maximum of 9 semester hours of approved elective course work can be taken from other departments.
- We will not automatically accept for elective credit courses taken in any other College or department. For a course to be acceptable in the MA program, it must have some mathematical content. Students must fill out a petition in advance requesting that a particular course be approved for elective credit in the MA program. Some details such as syllabus or topics covered should be attached. Students must fill out the Graduate General Petition form and submit it for approval to the graduate advisor.

**Course Groups:**

**I. Algebra Courses**

MATH 5330: Abstract Algebra

MATH 5331: Linear Algebra

MATH 5336: Discrete Mathematics

MATH 5383: Number Theory

**II. Analysis Courses**

MATH 5333: Analysis

MATH 5350: Introduction to Differential Geometry

MATH 5334: Complex Analysis

*MATH 53XX: Analysis II*

**III. Probability & Statistics**

MATH 5382: Probability

MATH 5385: Statistics

MATH 5386: Regression Analysis

**IV. Applied Mathematics**

MATH 5332: Differential Equations

MATH 5341: Mathematical Modeling

MATH 5344: Scientific Computing with Excel

**V. Other Courses**

MATH 5310: History of Mathematics

MATH 5379: Axiomatic Geometry

MATH 5389: Survey of Mathematics

**Course Descriptions**

**Note**: The following mathematics graduate courses at the 5000 level apply toward the Master of Arts in Mathematics degree; they apply neither toward Master of Science in Mathematics nor the Master of Science in Applied Mathematics degrees.

**MATH 5310 - History of Mathematics. ***Prerequisite: Graduate standing.* **Description: **Mathematics of the ancient world, classical Greek mathematics, the development of calculus, notable mathematicians and their accomplishments.

**MATH 5330 - Abstract Algebra. ***Prerequisite: Graduate standing*. **Description: **Groups, rings and fields; algebra of polynomials, Euclidean rings and principal ideal domains.

**MATH 5331 - Linear Algebra with Applications. ***Prerequisite: Graduate standing*. **Description: **Systems of linear equations, matrices, vector spaces, linear independence and linear dependence, determinants, eigenvalues; applications of the linear algebra concepts will be illustrated by a variety of projects.

**MATH 5332 - Differential Equations**.** ***Prerequisite: MATH 5331 or consent of instructor.* **Description: **Linear and nonlinear systems of ordinary differential equations; existence, uniqueness and stability of solutions; initial value problems; higher dimensional systems; Laplace transforms. Theory and applications illustrated by computer assignments and projects.

**MATH 5333 - Analysis**. *Prerequisite: Graduate standing*. **Description: **A survey of the concepts of limit, continuity, differentiation and integration for functions of one variable and functions of several variables; selected applications.

**MATH 5334 - Complex Analysis.** *Prerequisite: MATH 5333 or consent of instructor*. **Description: **Complex numbers, holomorphic functions, linear transformations, Cauchy integral theorem and residue theorem.

**MATH 5336 - Discrete Mathematics**. *Prerequisite: Graduate standing*. **Description: **Logic and proof, sets and relations; elementary set theory; the axiom of choice. Does not apply toward the Master of Science in Mathematics or Applied Mathematics.

**MATH 5341 - Mathematical Modeling.** *Prerequisite: Graduate standing.* **Description: **Proportionality and geometric similarity, empirical modeling with multiple regression, discrete dynamical systems, differential equations, simulation and optimization. Computing assignments require only common spreadsheet software and VBA programming.

**MATH 5344 - Introduction to Scientific Computing.** Prerequisite: Graduate standing. **Description: **The course introduces core areas of numerical analysis and scientific computing along with basic themes such as solving nonlinear equations, interpolation and splines fitting, curve fitting, numerical differentiation and integration, initial value problems of ordinary differential equations, direct methods for solving linear systems of equations, and finite-difference approximation to a two-points boundary value problem. This is an introductory course and will be a mix of mathematics and computing.

**MATH 5350 - Intro To Differential Geometry.** *Prerequisite: Graduate standing*. **Description: **Curves, arc-length, curvature, Frenet formula, surfaces, first and second fundamental forms, Gauss’ theorem egregium, geodesics, minimal surfaces.

**MATH 5378 - Axiomatic Geometry.** *Prerequisite: Graduate standing*. **Description: **An axiomatic approach to Finite Geometries, Taxicab Geometry, Spherical Geometry, Hyperbolic Geometry and a review of Euclidean Geometry.

**MATH 5382 - Probability.** *Prerequisite: Graduate standing*. **Description: **Sample spaces, events and axioms of probability; basic discrete and continuous distributions and their relationships; Markov chains, Poisson processes and renewal processes; applications.

**MATH 5383 - Number Theory.** *Prerequisite: Graduate standing*. **Description: **Divisibility and factorization, linear Diophantine equations, congruences and applications, solving linear congruences, primes of special forms, the Chinese remainder theorem, multiplicative orders, the Euler function, primitive roots, quadratic congruences, representation problems and continued fractions.

**MATH 5385 - Statistics.** *Prerequisite: Graduate standing.* **Description: **Data collection and types of data, descriptive statistics, probability, estimation, model assessment, regression, analysis of categorical data, analysis of variance. Computing assignments using a prescribed software package (e.g., R or Matlab) will be given.

**MATH 5386 - Regression & Linear Models.** *Prerequisite: MATH 5385, or consent of instructor.* **Description: **Simple and multiple linear regression, linear models, inferences from the normal error model, regression diagnostics and robust regression, computing assignments with appropriate software. *( Notes: This course is approved for VEE Applied Statistical Methods (topic: Regression). Approval code: 4458-11008)*

**MATH 5389 - Survey of Mathematics**. *Prerequisite: Graduate standing*. **Description: **A review and consolidation of undergraduate courses in linear algebra, differential equations, analysis, probability, and abstract algebra. Students may not receive credit for both MATH 4389 and MATH 5389.

**MATH 5397 - Selected Topics in Mathematics.** *Prerequisite: Graduate standing*. **Description: **May be repeated with approval of chair when topics vary.

### Contacts:

**Garry Etgen, PhD**., Professor and Program Scientific Advisor

**Note: The correct designation for degrees on the transcript, will be denoted as: Mathematics, M.A.*