# Master of Science in Mathematics Program

## Outline Requirements for MAM

The Master of Science in Mathematics (MAM) degree is for students who take most of their courses 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 the number of courses taken in any particular semester. Every summer a large selection of 5000 level courses is available.

For more detailed descriptions of these requirements including a list of 5000 level mathematics courses, please read below.

## 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 be possible to take approved on-campus courses as alternatives to online courses.

There is a regular schedule of online classes each semester, including the summer sessions. As a result, there is little difficulty in combining a full-time teaching 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 all course work and should have a good 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 has had at least 9 semester hours of mathematics 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 required for admission.

## 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.

• 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 MAM 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 our Prof. Gary Etgen or the Director of Graduate Studies.

• A maximum of 9 semester hours of approved elective course work (elective courses are optional) 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 MAM 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 MAM 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 Ms. Neha Valji.

## Courses

MATH 5310: History of Mathematics. *Prerequisites*:Three semesters of calculus, or consent of instructor. Mathematics of the ancient world, classical Greek mathematics, the development of calculus, notable mathematicians and their accomplishments.

MATH 5330: Abstract Algebra. *Prerequisites*:Three semesters of calculus, or consent of instructor. The theory of groups is used to discuss the most important concepts and constructions in abstract algebra.

MATH 5331: Linear Algebra with Applications. *Prerequisites*:Three semesters of calculus, or consent of instructor. 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. *Prerequisites*:MATH 5331 or consent of instructor. 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 by projects.

MATH 5333: Analysis. *Prerequisites*:Three semesters of calculus, or consent of instructor. A survey of the concepts of limit, continuity, differentiation and integration for functions of one variable and functions of several variables; selected applications are used to motivate and to illustrate the concepts.

MATH 5334: Complex Analysis. *Prerequisites*:MATH 5333 or consent of instructor. Complex numbers, holomorphic functions, the Cauchy theorem and the Cauchy integral formula, the calculus of residues.

MATH 5336: Discrete Mathematics. *Prerequisites*: Three semesters of calculus, or consent of instructor. Discrete Mathematics and Its Applications, Kenneth H. Rosen, fifth edition. McGraw Hill, Chapters 1, 3, 7, plus the Zermelo Fraenkel Axioms and equivalence of sets.

MATH5337: Models Of Computation. *Prerequisites*:Three semesters of calculus, or consent of instructor. The algebra of Boolean functions, logic gates, languages and grammars, finite state machines, the Kleene algebra of regular sets, Turing machines and the halting problem.

MATH 5350:Introduction To Differential Geometry. *Prerequisites*:Three semesters of calculus, or consent of instructor. Multi-variable calculus, linear algebra, and ordinary differential equations are used to study the geometry of curves and surfaces in 3-space. Topics include: Curves in the plane and in 3-space, curvature, Frenet frame, surfaces in 3-space, the first and second fundamental form, curvature of surfaces, Gauss’s theorem egregium, and minimal surfaces.

MATH 5379:Axiomatic Geometry. *Prerequisites*:Three semesters of calculus, or consent of instructor. A review of the axiomatic approach to Euclidean Geometry and an introduction to non-Euclidean Geometries. Some finite geometries, Hyperbolic Geometry and Spherical Geometry are introduced. A student version of The Geometer’s Sketchpad is required for the homework assignments.

MATH 5382:Probability. *Prerequisites*:Three semesters of calculus and one semester of linear algebra, or consent of instructor. 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*:Three semesters of calculus, or consent of instructor. 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. *Prerequisites*:Three semesters of calculus, or consent of instructor. 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., EXCEL, Minitab) will be given.

MATH 5386:Regression And Linear Models. *Prerequisites*:Three semesters of calculus, one semester of linear algebra, and MATH 5385, or consent of instructor. Simple and multiple linear regression, linear models, inferences from the normal error model, regression diagnostics and robust regression, computing assignments with Matlab, R, Minitab, or SAS.

MATH 5389:Survey Of Mathematics. *Prerequisites*:Three semesters of calculus, or consent of instructor. 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.

**Courses under development**:

MATH 53xx: Mathematical Modeling

MATH 53xx: Technology In Mathematics Classes

MATH 53xx: Analysis II

MATH 53xx: Scientific Computing With Excel

**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 5337: Models of Computation

MATH 53XX: Mathematical Modeling

MATH 53XX: Technology in Mathematics Classes

MATH 53XX: Scientific Computing with Excel

**V. Other Courses**

MATH 5310: History of Mathematics

MATH 5379: Axiomatic Geometry

MATH 5389: Survey of Mathematics