# MAT-Mathematics

## MAT100 - Survey 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. (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 mathematics course will cover how to apply mathematics to real-world situations such as determining methods of fair voting and apportionment, finding the shortest path, scheduling meetings, determining the best return on investments, and collecting data to show patterns. The prerequisite for this course is passing Part A of the mathematics placement exam. (3 crs)

## MAT120 - Elementary Topics in Mathematics I

This is the first course of a sequence of two mathematics content courses specifically designed for Pre-K to 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-education majors (11 or higher). (3 crs.)

## MAT130 - Elementary Topics in Mathematics II

This is the second course of a sequence of two mathematics content courses specifically designed for pre-K to 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 (3 credits). Prerequisite: DMA 092 for education majors; pass Part A of the University math placement test for non-education majors (11 or higher). (3 crs.)

## MAT181 - College Algebra

Fundamental operations; factoring and algebraic 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. (3 crs.)

## MAT191 - College Trigonometry

This course is a thorough development of trigonometry. It 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. (3 crs.)

## MAT195 - 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. Prerequisites: C or better in MAT 181 or passing score on part C of the mathematics placement examination. (3 crs.)

## MAT199 - Pre-Calculus

This course is a study of numerical, analytical, and graphical properties of functions. The course content includes polynomial, rational, irrational, exponential, logarithmic, and trigonometric functions. Additional topics include: inverse functions, complex numbers, and vectors. This course is designed as a preparation for calculus. Prerequisite: Grade of C or better in MAT 181, grade of C or better in MAT 191, or two years of high school algebra. (3 crs)

## MAT202 - Math Around the World

This course is intended for Liberal Arts majors (This course may NOT be used as a math course by secondary ed or BA in math students). Students will study the mathematical historical topics related to the region of the world. The course will be an online course and will include a required field trip to the region of the world being studied. An example: If the area of the world were Greece, topics may include the Greek ancient alpha numeric numeral system, studying the mathematics of Thales; Pythagoras; Euclid etc. Note: This course will only be run every two years in conjunction with MAT 468 Field Course in Mathematics. Prerequisites: College Algebra or math SAT score of 520 or pass part C of the math placement exam with a score of 10 or above, some high school geometry preferred (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 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. Prerequisite: MAT 181 or MAT 182. (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: Grade of C or better in MAT 181. (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: Grade of C or better in MAT 181, pass Part C of the University mathematics placement test (10 or higher), or SAT math score of 580 or higher. (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 (3 credits). Prerequisite: MAT 181 or MAT199. (3 crs.)

## MAT281 - Calculus I

A study of modeling, functions, limits and continuity; the derivative; application of the derivative. Prerequisite: MAT 181 and MAT 191 or MAT 181 and MAT 199 or appropriate score on placement test. (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 and MAT 290 Technology for Mathematics. (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; and using mathematical software. The course will be taught from a laboratory-based perspective. Prerequisite: MAT 281. [Offered in-class, spring]. (3 crs.)

## MAT303 - Geometry

Analysis of axiomatic systems, axiomatic development of elementary Euclidean geometry and non-Euclidean geometry. Prerequisites: Grade of C or better in MAT 181 or grade of C or better in MAT 191 or three years of high school mathematics AND grade of C or better in MAT 272 Discrete Math. ( 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: grade of C or better in MAT 282 and grade of C or better in MAT 303. (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 in one variable, cubic and biquadratic equations, limits of roots and rational roots, isolation and separation of roots, and the approximate evaluations of roots. Prerequisite: Grade of C or better in MAT 281. ( 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. Prerequisites: Grade of C or better in MAT 272 or Grade of C or better in MAT 195. (3crs)

## 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, natural homomorphism, and the three fundamental homomorphism theorems. Prerequisite: Grade of C or better in MAT 272 is required and MAT 341 Linear Algebra I is recommended . (3 cr.)

## 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.)

## MAT371 - Applied Categorical Data Analysis

This course provides an introduction to categorical data analysis. Topics include contingency table analysis, inference for contingency tables, models for binary response data including logistic regression and probit models, models for multinomial responses, loglinear models and mixture models for discrete data. Prerequisite: MAT 215 (3 crs.)

## MAT373 - Time Series and Stochastic Processes

This course provides an introduction to stochastic processes. The course covers Poisson processes, renewal theory, Markov chains and continuous-time Markov chains, martingales, random walks and Brownian motion. Prerequisite: MAT 215 (3 crs.)

## MAT376 - Applied Regression

This course is an introductory-level course in regression analysis. This course begins with simple linear regression and associated one-way analysis of variance tables for regression analysis along with diagnostic measures for simple linear regression. The course continues with more complicated regression models including general regression models, multiple regression, generalized linear models and a brief introduction to nonlinear estimation. The course will cover the necessary linear algebra for completing regression. An appropriate statistical package will be used to complete analysis. (3 crs.)

## MAT381 - Calculus III

Continuation of integration techniques, indeterminate forms and improper integrals, parametric and polar curves, and conic sections, infinite series, and the theory of infinite series and power series. Prerequisites: Grade of C or better in MAT 282. ( 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. Prerequisites: Grade of C or better in MAT 38l. ( 3 crs.)

## MAT391 - Statistical Packages

This course provides an in-depth look at statistical packages used to complete a variety of statistical analysis. The course will focus on current and highly used packages such as SAS, SPlus, R and MINITAB. The course will provide a basic introduction to each package and will also cover more in-depth topics within each package as applicable. Prerequisite: MAT 376. (3 crs.)

## MAT400 - Mathematical Modeling

This course provides an introduction to mathematical modeling for mathematics majors. Students will be presented with real-world problems from a variety of fields such as physics, biology, space travel, carpentry, 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 and communicate their work orally and in written format. This course serves as a capstone course for students in mathematics. Prerequisites: Grade of C or better in MAT 215 and grade of C or better in MAT 341 and grade of C or better in MAT 381. (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. Prerequisites: Grade of C or better in MAT 381. (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 valuable experience in the applications of mathematics that should enhance their job opportunities upon graduation. Prerequisites: Completion of 64 credits with a 2.50 GPA or better and department chair permission. (3 cr.)

## 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. Prerequisites: Grade of C or better in MAT 341. (3 crs)

## MAT451 - Abstract Algebra II

This course is a continuation of MAT 351 Abstract Algebra I. It continues the covering of algebraic structures such as fields, rings and groups. It is a blend of theory and application. Prerequisite: MAT 351 or consent of the instructor Prerequisite: MAT 351. (3 crs.)

## MAT461 - Statistical Analysis I

Basic concepts of both discrete and continuous probability theory. The concepts of a random variable is stressed, including distributions and mathematical expectation. A number of important probability models are studied in detail. Prerequisites: MAT 215 and MAT 282 . (3 crs.)

## MAT462 - Statistical Analysis II

Statistical theory and application of statistical estimation techniques and hypothesis and hypothesis testing methods. Simple linear regression, multiple linear regression and basic experimental design. R statistical software used. Prerequisite: Grade of C or better in MAT 461. (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" and “The Mathematicians of Europe," “The Mathematics of Wallstreet." Prerequisites: Mathematics major, must have completed 64 credits or have permission of department chair or course instructor. (3 crs.)

## MAT471 - Applied Multivariate Statistics

This course covers the basics for several multivariate statistical analyses. The course begins with a review of univariate and bivariate statistics and continues on to cover multiple regression, multivariate analysis of covariance, discriminant analysis, logistic regression and survival analysis.Prerequisite: MAT 461. (3 crs.)

## MAT474 - Complex Analysis

The course 1. introduces the essential concepts in 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: C or better in MAT 382 or the permission of the department chair or the course instructor. (3 crs.)

## MAT481 - Real Analysis I

Logic and techniques of proofs; relations, functions, cardinality, and naïve set theory; development of real numbers from natural numbers through topology of the line; convergence and related ideas dealing with functions (sequences and series) including continuity. Prerequisites: Grade of C or better in MAT 272 and grade of C or better in MAT 381. (3 cr.)

## 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.)