# MAT-Mathematics

## MAT100 - Fund of Mathematics

This 3- credit course was designed to enhance the student’s knowledge, understanding and appreciation of mathematics. Topics are selected from among a variety of areas and fields in mathematics: problem solving, set theory, logic, numeration systems, elementary number theory, Euclidean geometry, probability and statistics. The student will examine the language, notation and applications relative to each area of mathematic. The prerequisite for this course is passing Part A of the University’s math placement exam (11 or higher) or SAT- Math scores of 440 or higher. [Offered in-class/Web, fall and spring; Web only, summer]. (3 crs.)

## MAT104 - Tentative Math

This course is to be used by Student Retention for incoming freshman and transfer students who need a Mathematics course on their schedule.

## MAT110 - Applications of Math

This course will provide the student with an application-oriented mathematics curriculum. Students will use cooperative learning to solve real-world problems using technology and multimedia resources. The course will be taught from a student discovery and investigative standpoint incorporating the use of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics. The topics covered include statistics, circuits, probability, linear programming and dynamic programming. Prerequisite: Must pass Part A of the University math placement test (11 or higher) or SAT- Math 440 or higher. [Offered in-class/Web, fall and spring; Web only, summer]. (3 crs.)

## MAT120 - Elementary Topics in Math I

This is the first course of a sequence of two mathematics content courses specifically designed for PreK - Grade 8 teacher education candidates by providing an overview of fundamental mathematical concepts. The content covered includes basic algebraic work with equations and inequalities in one unknown, systems of equations, problem-solving, sets, concepts of logic, binary operations, systems of numeration, number theory, rational numbers, real numbers, measurement, and use of calculators and computers. Prerequisite: DMA 092 for education majors; pass Part A of the University math placement test for non majors (11 or higher). [Offered in-class/Web, fall; in-class only, spring; Web only, summer]. (3 crs.)

## MAT130 - Elementary Topics in Math II

This is the second course of a sequence of two mathematics content courses specifically designed for PreK - Grade 8 teacher education candidates by providing an overview of fundamental mathematical concepts. The content covered includes metric and non-metric geometry, coordinate geometry, introduction of statistics and probability, problem-solving, and computer use. Prerequisite: DMA 092 for education majors; pass Part A of the University math placement test for non-majors (11 or higher). [Offered in-class only, fall; in-class/Web spring; Web only, summer]. (3 crs.)

## MAT181 - College Algebra

Fundamental operations; factoring and fractions; exponents and radicals; functions and graphs; equations and inequalities; properties of graphs; systems of linear equations; synthetic division; and rational zeros of polynomials. Prerequisite: DMA 092 or pass Part B of the University math placement test (12 or higher) or SAT-Math 520 or higher. [Offered in-class/Web, fall and spring; Web only, summer]. (3 crs.)

## MAT191 - College Trig

This course is a thorough development of trigonometry. This course includes both circular and right-triangle geometry, evaluation of trigonometric functions, graphing trigonometric and inverse trigonometric functions, analyses of trigonometric graphs, verifying trigonometric identities, solutions of trigonometric equations, and applications of trigonometry. Prerequisite: MAT 181 or pass Part C of the University mathematics placement test (10 or higher) or SAT-math 580 or higher. [Offered in-class only, fall; in-class/Web spring; Web only, summer]. (3 crs.)

## MAT195 - Discrete Mathematical Structures for Computer Science

MAT 195. DISCRETE MATHEMATICAL STRUCTURES FOR COMPUTER SCIENCE. An introduction to the theories and structures of mathematics that are relevant in computer science. Topics include set theory, formal logic, mathematical induction, Boolean algebra, number theory, matrix algebra, combinatorics, probability, algorithmic analysis, complexity and graph theory. Prerequisite: MAT 181, pass Part C of the University mathematics placement test (10 or higher), or SAT-Math 580 or higher. [Offered in-class, spring]. (3 crs.)

## MAT199 - Pre-Calculus

An overview of the essential concepts and techniques of algebra and trigonometry required for the study of calculus. Topics include slope; lines; equations; analyses of graphs and graphing; logarithms; trigonometric identities; and algebraic, exponential, logarithmic and trigonometric functions. Functions, their graphs and related applications are emphasized. Prerequisite: MAT 181 or SAT-Math 640 or higher. [Offered in-class, fall and spring; Web only, summer]. (3 crs.)

## MAT205 - Statistics for the Health & Social Sciences

For health and Social science majors only; not counted toward a mathematics major. This course is intended to provide just-in-time algebra reviews necessary to complete statistical analysis for various health and social sciences related problems. The following topics will be covered: frequency distribution, percentiles, measures of central tendency and variability, normal distribution and curve, populations, samples, sampling distribution of means, sampling distributions of proportion, null and alternative hypotheses, type I and type II errors, tests of means, confidence intervals, decision procedures, correlation, chi-square, simple analysis of variance, and design of experiments. (3 crs.)

## MAT215 - Statistics

For non-mathematics majors; not counted toward a mathematics major. Frequency distribution, percentiles, measures of central tendency and variability, normal distribution, populations, samples, sampling distribution of means, sampling distribution of proportions, type I and II erros, hypothesis testing of means, confidence intervals, decision procedures, correlation, chi-square, simple analysis of variance, and design of experiments. Appropriate technology will be used. Prerequisite: MAT 181 or MAT 182; or pass Part A of the University math placement test (11 or higher). [Offered in-class/Web, fall and spring; Web only, summer]. (3 crs.)

## MAT225 - Business Statistics

Statistical techniques relevant to business applications. Primary emphasis is placed upon identification of appropriate statistical methods to use, proper interpretation and appropriate presentation of results. Topics include descriptive statistics, probability concepts, the normal probability distribution, estimation techniques, tests of hypotheses, simple and multiple linear regression. Statistical software is used to implement many of the statistical methods. Prerequisite: MAT 181 or pass Part C of the University math placement test (10 or higher). [Offered in-class/Web, fall and spring; Web only, summer]. (3 crs.)

## MAT272 - Discrete Mathematics

Introduction to theories and methods of mathematics relative to computer science but taught from a mathematics perspective. Topics include logic, set theory, elementary number theory, methods of proofs and proof writing (direct, indirect and math induction), combinatorics, probability, relations and functions, and graph theory. Prerequisite: MAT 181, pass Part C of the University mathematics placement test (10 or higher), or SAT-math 580 or higher. [Offered in-class, fall]. (3 crs.)

## MAT273 - Applied Calculus

The techniques of differentiation and integration are covered without the theory of limits and continuity. Applications in business and biological science are considered. Prerequisite: MAT 181 or MAT 199. [Offered in-class, spring]. (3 crs.)

## MAT281 - Calculus I

A study of modeling, functions, limits and continuity; the derivative; appliation of the derivative. Prerequisite: MAT 181 and MAT 191 or MAT 181 and MAT 199 or appropriate score on placement test. [Offered in-class, fall; Web only, summer]. (3 crs.)

## MAT282 - Calculus II

The integral; fundamental theorem of calculus; applications of the integral; inverse functions; logarithmic functions; hyperbolic functions; techniques of integration. Prerequisite: MAT 281 (3 crs.)

## MAT290 - Technology for Mathematics

This course, designed for both mathematics and science majors, and for prospective and practicing educators, details the use of technological tools in the study of mathematics and explores the effective and appropriate use of technology in the teaching, learning, and application of mathematics. The course is composed of three components: using graphing calculators; using calculator-based laboratories; using mathematical software. The course will be taught from a laboratory-based perspective. Prerequisite: MAT 281. [Offered in-class, spring]. (3 crs.)

## MAT303 - Geometry

This course is an analysis of axiomatic systems, axiomatic development of elementary Euclidean geometry and non-Euclidean geometry. Prerequisites: MAT 272. [Offered in-class, fall]. (3 crs.)

## MAT304 - History of Mathematics

This course is a historical summary of the development of mathematics. Emphasis is placed on relating mathematics to the development of world culture and its relationship with all aspects of our culture. The lives and discoveries of many mathematicians are discussed. Methods of incorporating the history of mathematics into high school mathematics courses are a major focus of the course. This is a writing-intensive course. Prerequisites: MAT 303 and MAT 282. [Offered in-class, spring] (3 crs.)

## MAT305 - Theory of Equations

This course deals with the development of the theory involved in solving algebraic equations. It includes complex numbers as an algebraic system, polynomials inone variable, cubic and biquadratic equations, limits of roots and rational roots, isolation and seperation of roots, and the approximate evaluations of roots. Prerequisite: MAT 281. {Offered in-class spring} (3 crs.)

## MAT341 - Linear Algebra I

This course covers systems of linear equations and matrices, determinants, vectors in n-space, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications. Prerequisite: MAT 272. [Offered in-class, fall and spring]. (3 crs.)

## MAT345 - Cryptography I

This course is intended to provide an introduction to Cryptography with the Number Theory portion tied in. The following topics will be covered: Modular Arithmetic, Classical Cryptography, Public Key Cryptography, and Introduction to Complexity. Prerequisite: MAT 195 or MAT 272 and MAT 282. (3 crs.)

## MAT351 - Abstract Algebra I

Fundamental concepts of logic; natural numbers, well-ordering property, induction, elementary concepts of number theory; groups, cosets, Lagrange's theorem, normal subgroups, factor groups; homomorphism, isomorphism, and related topics, including Cayley's theorem. Prerequisite: MAT 272. [Offered in-class, spring]. (3 crs.)

## MAT361 - Nonparametric Statistics

This course provides an introduction to nonparametric statistics. It includes the introduction of nonparametric inference testing including the Wilcoxon Test, the Mann-Whitney test, the Ansari-Bradley test, the Kruskal-Wallis test, the Kendall test and the Theil test along with their associated estimators. Students will also learn how to run analyses within a statistical software program. Prerequisite: MAT 215 (3 crs.)

## MAT381 - Calculus III

Indeterminate forms, L'hospital's rule, improper intregrals, arc length, area of a surface of revolution, parametric equations (tangents, arc length, areas, and tangents), vectors, dot products, cross products, vector-valued functions, vector equations of lines and planes in three space, polar corrdinates (graphs, areas, and arc length), conics, sequences, bounded sequences, series, integral test and estimates of sums, comparison tests, alternating series, absolute convergence (ratio and root tests), power series, taylor series, and taylor remainder theorem. Prerequisite: MAT 282 {offered in class Fall and Spring} (3 crs.)

## MAT382 - Calculus IV

Vector analysis in two and three dimensions. Topics include theory of curves and surfaces; partial derivatives; multiple integrals; and Greens, Stokes and the Divergence theorems. Prerequisite: MAT 381. [Offered in-class, spring]. (3 crs.)

## MAT400 - Mathematical Modeling

This course provides an introduction to mathematical modeling. Students will be presented with real-world problems from a variety of fields, such as physics, biology, earth science, meteorology, engineering, economics, etc. Students will learn how to select appropriate mathematical models to model the real-world situation, use the model to solve a real-world problem, interpret the results of the solution(s), and communicate their work orally and in written format. This course serves as a capstone course for students in mathematics. This is a writing-intensive course. Prerequisites: MAT 215, MAT 341 and MAT 381. Offered in-class, fall. (3 crs.)

## MAT406 - Differential Equations

Ordinary differential equations and their solutions. The existence and uniqueness of solutions. Various types of differential equations and the techniques for obtaining their solution. Some basic applications, including numerical techniques, computer solution techniques are discussed. Prerequisite: MAT 381. [Offered in-class, Fall]. (3 crs.)

## MAT419 - Math Internship

This course is designed for the BA in Mathematics majors who are seeking work experience in the Mathematics area. This intern experience will enable students to apply their knowledge of Mathematics in the real workplace. The internship will provide students with the valuable experience in the applications of Mathematics that should enhance their job opportunities upon graduation. Prerequisite: Students should have completed 64 credits with a good GPA plus have sufficient background to meet the needs of the particular internship in which they will be participating. (3 crs.)

## MAT441 - Linear Algebra II

Extends the concepts learned in Linear Algebra I. The content is not fixed, but usually includes the following topics: linear transformations, change-of-bases matrices, representation matrices, inner-product spaces, eigenvalues and eigenvectors, diagonalization, and orthogonality. Prerequisite: MAT 341. [Offered in-class, spring-even yrs. only]. (3 crs.)

## MAT451 - ABSTRACT ALGEBRA II

Study of rings, ideals, quotient rings, integral domains and fields; ring homomorphisms; polynomial rings, division algorithms, factorization of polynomials, unique factorization, extensions, fundamental theorem; finite fields. Prerequisite: MAT 351. (3 crs.)

## MAT461 - Statistical Analysis I

Basic concepts of both discrete and continuous probability theory. The study of random variables, probability distributions, mathematical expectation and a number of significant probability models. Introduction to statistical estimation and hypothesis testing. Prerequisite: MAT 282 and MAT 215 or MAT 225. [Offered in-class, fall]. (3 crs.)

## MAT462 - Statistical Analysis II

Continuation of MAT 461. Statistical theory and application of statistical estimation techniques and hypothesis testing methods. Simple linear and multiple linear regression models. Statistical techniques are implemented with microcomputer statistical software. Prerequisite: MAT 461. [Offered in-class, spring-odd yrs. only].(3 crs.)

## MAT468 - Field Experience in Math

Prerequisites: Mathematics major, completed 64 credits or permission of Dept. Chairman or course instructor. The class is not scheduled to run every semester and will be run approximately once every two years. It gives the student an opportunity to delve into a topic of special interest to him/her. It also affords him/her an opportunity to experience research procedures in the field. The selection of the topic or topics to be examined will vary according to the research interests of faculty and students. The course is an online course that includes a required field trip related to the topic of the course. Examples of possible topics may be “The Mathematics of Egypt," “The Mathematicians of Europe," “The Mathematics of Wallstreet."

## MAT474 - Complex Analysis

The course introduces the essential concepts in the Complex Analysis such as: Complex Numbers, Functions of complex variables, their Limits, Continuity, Derivatives, Integrals and Cauchy Integral Formula. 2. Shows students the importance of Complex Analysis Theory in pure mathematics, applied mathematics and Engineering Applications. 3. Develops the elements of Complex-Variable Functions in a rigorous and self contained manner. Prerequisites: MAT 382 or the permission of the department chairperson or the course instructor (3 crs.)

## MAT481 - Real Analysis I

This course covers logic and techniques of proof; relations, functions, cardinality and naive set theory; development of real numbers from natural numbers through topology of the line; and convergence and related ideas dealing with functions (sequences and series), including continuity. Prerequisites: MAT 272 and MAT 381. [Offered in-class, fall]. (3 crs.)

## MAT482 - Real Analysis II

This course covers logic and techniques of proof; relations, functions, cardinality and naive set theory; development of real numbers from natural numbers through topology of the line; and convergence and related ideas dealing with functions (sequences and series), including continuity. Prerequisite: MAT 481 . [Offered in-class, fall]. (3 crs.)

## MAT496 - Senior Research Project

This course, which should be taken near the end of the student's bachelor's degree program, involves an in-depth investigation of a mathematical or computer science topic (theoretical computer science being mathematical in nature). The investigation will culminate in the presentation of a senior paper. Prerequisite: Permission of mathematics and computer science departments. (3 crs.)