# MAT - Math

## MAT-100 Analysis of Data and Research

An introduction to a variety of applications of descriptive statistical concepts using spreadsheets for basic statistical analysis. Topics include research concepts, statistical analysis, graphical representation of data, measures of central tendency and variation, and the normal probability distribution.

3

## MAT-100B Statistics for Business Research and Data Analysis

An introduction to business applications of descriptive statistical concepts using spreadsheets for basic statistical analysis. Topics include research concepts, statistical analysis, graphical representation of data, measures of central tendency and variation, and the normal probability distribution.

3

## MAT-101 Introductory Algebra

A study of introductory algebra plus applications in geometry. This course is intended for those students who need improvement in skills of mathematics and preparatory work before taking college mathematics courses. Topics include polynomials and solving and graphing systems of linear equations and inequalities. This course does NOT satisfy the general education math/computer requirement. Only open to students who have not satisfied the math preparatory requirement.

3

## MAT-104 Sample Surveying

A course in elementary survey sampling that uses the survey questionnaire as the main focus of learning. This course will introduce the basic concepts and techniques of statistics while using practical lessons in survey design and development. Team work will be a significant part of the course along with using statistical computer software in conjunction with collection, summarization, analysis, and interpretation of real data. This course meets the general education math/computer requirement. Prerequisite: Satisfaction of mathematics preparatory requirement.

3

## MAT-107 Contemporary Mathematics

A study of contemporary mathematical topics including basic statistics and problems that relate to human flourishing in different contexts. Emphasis is on translating real-world scenarios into mathematical models, solving by either algebraic techniques or mathematical software, and communicating the results. This course meets the general education math/computer requirement. Prerequisite: Satisfaction of mathematics preparatory requirement.

3

## MAT-108 Modern Concepts of Mathematics

An introductory course for non-math majors, this course uses applications from the world today to combine critical thinking with mathematical skills. Quantitative problem solving techniques and decision-making methods are applied toward both personal and professional experiences in everyday living.

3

## MAT-109 Foundations of College Math

This introductory math course prepares students for college-level algebra content. Foundational concepts covered in this course include algebraic expressions, equations, inequalities, polynomials, factoring, rational expressions and exponents, and graphs. (This course must be passed with a "C" or higher in order for a student to take MAT-116)

3

A study of the basic arithmetic and algebra used most commonly in general business operations.

4

## MAT-111 Mathematics for Elementary Teachers

A mathematics content-based course for the prospective elementary school teacher that combines practical application of experiencing mathematics and critical thinking for problem solving. Topics reflect the NCTM standards for mathematics content at the elementary level, such as numeration systems, set theory, the real number system, algebra, geometry, measurement, probability and statistics. This course meets the general education math/computer requirement. Prerequisite: Satisfaction of mathematics preparatory requirement. Only open to elementary education majors.

3

## MAT-112 General Statistics

An introduction to elementary concepts in descriptive and inferential statistics using applications from various disciplines. Students will gain experience with usage of statistical software. Topics include data collection and summarization, random variables and probability distributions, linear correlation and regression, confidence intervals, and hypothesis testing. This course will meet General Education requirements. Prerequisite: Satisfaction of the mathematics preparatory requirement.

3

## MAT-113 College Algebra With Modeling

A study of algebraic, exponential, and logarithmic functions from analytic, graphical, and numerical points of view. Additional topics include solutions of equations, inequalities, and systems of linear equations; curve fitting; and algebraic operations. Emphasis on problem solving and modeling, supplemented by mathematical software. This course will meet General Education requirements. Prerequisite: Satisfaction of the mathematics preparatory requirement.

3

## MAT-114 Trigonometry

Topics to be covered include trigonometric functions, analytic trigonometry, polar coordinates, and conic sections. Prerequisite: MAT-113 or equivalent.

3

## MAT-116 Contemporary College Algebra

This skills-driven course will enable students to use mathematical language and models to describe real world mathematical relationships. Students will become familiar with equations and inequalities, functions and graphs, polynomial functions, systems of equations and inequalities, and exponential functions. Students will become competent with technical tools used to visualize algebraic relationships. Prerequisite: MAT-109 with a grade of "C" or higher.

3

## MAT-118 Quantitative Reasoning

The focus of this course is the development of quantitative reasoning skills and critical thinking skills. Students will have opportunities to apply mathematical, proportional, geometric, and statistical reasoning to various real world situations. Topics include algebraic expressions, linear equations and inequalities, proportions, probability, and descriptive statistics.

3

## MAT-120 College Algebra/Trigonometry

A course intended to strengthen algebraic and trigonometric concepts and to prepare students for higher level college courses such as calculus. Topics to be covered include systems of equations, inequalities, functions and their graphs, trigonometric identities, analytic trigonometry and conic sections. This course will meet Genearal Education requirements. Prerequisite: Satisfaction of the mathematics preparatory requirement.

4

## MAT-130 Applied Calculus

Students will use derivatives and integrals on applications for business and science. This course provides classroom based lecture format. Intended for non-mathematics majors. A student may not earn credit in both MAT-130 and MAT-253. Prerequisite: MAT-113 or equivalent or permission of Division Chair.

3

## MAT-108ES Modern Concepts of Mathematics

An introductory course for non-math majors, this course uses applications from the world today to combine critical thinking with mathematical skills. Quantitative problem solving techniques and decision-making methods are applied toward both personal and professional experiences in everyday living.

3

## MAT-109ES Foundations of College Math

This introductory math course prepares students for college-level algebra content. Foundational concepts covered in this course include algebraic expressions, equations, inequalities, polynomials, factoring, rational expressions and exponents, and graphs. (This course must be passed with a "C" or higher in order for a student to take MAT-116)

3

## MAT-204 Applied Statistics I

An in-depth introduction to descriptive and inferential statistical procedures including graphical and numerical data summary, basic principles of sampling and experimental design, random variables and probability distributions, estimation and hypothesis testing, contingency table analysis, and correlation and regression. Emphasizes conceptual understanding of statistical procedures and their implementation using statistical software. Prerequisite: Satisfaction of the mathematics preparatory requirement. Students may not earn credit in more than one of MAT-100, MAT-112, or MAT-204.

3

## MAT-211 Mathematics for Elementary Teachers II

A continuation of MAT-111. This mathematics content course reflects the NCTM standards and includes extensive coverage of geometry and measurement along with selected topics from probability, data analysis, and modeling. Emphasizes mathematical reasoning, problem solving, and communication. Prerequisite: MAT-111 or permission of the Division.

3

## MAT-223 Introduction to Mathematics Via Discrete Processes

An introductory mathematics course designed to raise awareness of the mathematics discipline and acquaint students with a range of intellectual and professional activities within the mathematical science community. The mathematical content of the course focuses on discrete processes. Topics include set theory, logic and proof, mathematical induction, combinatorics, and graph theory. Open to mathematics and mathematics education majors as well as others interested in mathematical career possibilities.

3

## MAT-231 Mathematics for Middle School Teachers

A course for future teachers of middle school mathematics. Emphasizes problem solving and technology usage in geometry and measurement, discrete probability, and other selected topics. Open only to Elementary Education majors and Mathematics Education majors; Prerequisite: Sophomore standing or above.

3

## MAT-253 Calculus I

An introduction to differential and integral calculus of a single variable using polynomial, logarithmic, exponential and trigonometric elementary functions. A study of the concepts of limit, continuity, derivative, and integral using interdisciplinary applications and computer software.

4

## MAT-254 Calculus II

Differential and integral calculus with applications in area, volume, and surfaces. Additional topics of study include techniques of integration, parametric equations and polar coordinates, and infinite series representation of functions. Prerequisite: MAT-253 or equivalent.

4

## MAT-255 Calculus III

A study of multivariable calculus including continuity and differentiability of functions of several variables, partial derivatives, extrema, multiple integrals, line integrals, surface integrals, and Stoke's Theorem. Prerequisite: MAT-254 or equivalent.

4

## MAT-280 Linear Algebra

An introduction to the theory and application of linear algebra. Topics include systems of linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors, and linear transformations. Prerequisite: MAT-253.

3

## MAT-282 Transition to Advanced Mathematics

A course to develop students' ability in mathematical reasoning by applying logic and set concepts to problems in probability, functions and relations, number theory, and geometry. In addition, it is to increase background knowledge in these content areas in preparation for subsequent advanced courses. Intensive practice in reading and writing mathematics and constructing mathematical proofs. Prerequisite: MAT-253; Prerequisite or corequisite: MAT-223.

4

## MAT-293 Introduction to Mathematical Proofs

This introduction to mathematical proofs course is designed to encourage mathematical reasoning and critical thinking. Topics include direct proofs, indirect proofs, and strategies for creating proofs.

1

## MAT-294 Mathematical Figures and Properties

This course is designed to enable students to understand geometric models that describe real world phenomena. Foundational concepts include points, parallel and perpendicular lines, angles, triangles, and area.

2

## MAT-296 Studies in Mathematics

A course in topics of current interest in mathematics. See schedule for specific content. Prerequisite: Permission of Division Chair.

1 to 3

## MAT-253TU Calculus I

An introduction to differential and integral calculus of a single variable using polynomial, logarithmic, exponential and trigonometric elementary functions. A study of the concepts of limit, continuity, derivative, and integral using interdisciplinary applications and computer software.

4

## MAT-304 Applied Statistics II

A continued study of estimation and hypothesis testing procedures from Applied Statistics I. Topics include simple, multiple, and logistic regression analysis of variance; nonparametric procedures; and time series. Prerequisite: BUS-320, MAT-204 or MAT-305.

3

## MAT-305 Statistics for Social Sciences

This is an upper-division course for the Social Sciences. Topics include measures of central tendency and dispersion and graphical representation of data. Other topics include inferential statistical theory and hypothesis testing for statistical significance. Bivariate and multivariate measure of statistical relationship include chi square, nominal and ordinal measures of association, correlation and regression, analysis of variance, and multiple correlation and regression techniques. Factor analysis and analysis of covariance are briefly introduced. Primarily for students concentrating in psychology, sociology, social work, criminal justice, or political science. Prerequisites: RSATM 500 or above or ACT 20 or above or MAT-112 or MAT-204.

3

## MAT-322 Mathematical Modeling I

An introduction to the principles and process of mathematical modeling. This course incorporates several projects in which students model open-ended scenarios from various disciplines. Relevant mathematical and statistical techniques, such as curve-fitting and optimization, and Monte Carlo methods, are included on an as-needed basis. Various software packages and lab experiments are also incorporated. Prerequisite: MAT-130 or MAT-253.

3

## MAT-324 Mathematical Modeling II

The development and extension of the modeling process using higher level mathematical concepts in calculus and differential equations. Problem-solving techniques for finding solutions to open-ended scenarios are discussed, developed, and demonstrated by the students using the modeling process, and statistical computer software. Interdisciplinary applications beneficial to both mathematics and science majors. For some students, an opportunity to participate in COMAP contest. Prerequisite: MAT-254 or equivalent.

4

## MAT-333 Modern Geometry

A critical study of the foundations of geometry in which Euclidean and non-Euclidean geometries are explored and compared. A sound logical basis is then built for Euclidean geometry within the framework of Hilbert's postulates. Prerequisite or co-requisite: MAT-282 or permission of the Division.

3

## MAT-342 Number Theory

A study of the theory of numbers that includes concepts about the fundamental theorem of arithmetic, theory of prime numbers, Diophantine equations, congruences, Euler's Theorem, and number theoretic functions. Prerequisite: MAT-223.

3

## MAT-344 Modern Abstract Algebra

An introductory study of significant algebraic structures and their properties. Introduction to group theory including cyclic groups, permutations, Lagrange's Theorem, product groups, First Isomorphism Theorem, and Finite Abelian Groups. Introduction to rings and fields, including polynomial rings and factorization. Prerequisite: MAT-282.

3

## MAT-351 Financial Mathematics I

An introduction to financial mathematics with emphasis on the theory behind formulas for present and accumulated values of cash flows. Topics include simple and compound interest, the time value of money, cash flows, yield rates, annuities, loans, and bonds. Also includes an introduction to financial economics, examining mathematical formulas for forwards, futures, options, hedging and swaps. This course prepares students for the second required examination (FM/2) in the Actuarial Profession. Prerequisites: MAT-253 and MAT-223.

3

## MAT-353 Differential Equations

A study of ordinary differential equations including classification, theory and common solution techniques of linear equations, basic numerical and qualitative methods, power series solutions, Laplace transform methods, linear systems, and applications. Prerequisites: MAT-254 and MAT-280.

3

## MAT-354 Introduction to Operations Research

An introduction to linear programming, integer programming, and dynamic programming. This course will be offered as needed. Prerequisite: MAT-280.

3

## MAT-363 Mathematical Statistics I

An introduction to the theory of probability and statistics using basic concepts of probability and its laws, probability distributions for discrete and continuous random variables, mathematical expectation, and sampling theory. Multivariate probability distributions are examined, along with methods of distribution functions, transformations and moment-generating functions. Prerequisites: MAT-255 and MAT-282.

4

## MAT-364 Mathematical Statistics II

A continued study of the theory of probability and statistics covering sampling distributions, The Central Limit Theorem, methods of estimation, and hypothesis testing. Analysis of variance and chi-square will be derived theoretically and then applied to various designs of experiments. Prerequisite: MAT-363.

3

## MAT-370 Statistical Research Design I

An introduction to experimental design using statistical inference as the basis for applying statistical tests to various parameters. Design of experiments will include single factor experiments using analyses of variance, randomized block and Latin Square Designs. Factorial experiments will be explored in depth, and regression techniques will be extended to include multiple regression. Prerequisite: MAT-304.

3

## MAT-371 Statistical Research Design II

A continuation of experimental design reinforcing elementary models and including complex design methods. Topics will include fixed, random and mixed models, nested experiments, and covariance analysis. A survey of factorial experiments will include split-plot designs, confounding and replication. Prerequisite: MAT-370.

3

## MAT-373 Numerical Analysis

A study of the operation, efficiency, and accuracy of numerical algorithmic processes. Topics include rates of convergence, analysis of error, solution of equations, interpolation, numerical integration and differentiation, solution of linear systems, and approximation/curve-fitting. Prerequisites: MAT-254, MAT-280 and CIS-125.

3

## MAT-391 Directed Studies in Math

This course prepares students to perform basic research in which they learn to use Off Campus Library Services (OCLS), electronic periodical indexes, and information resources. Students will identify and select appropriate material for inclusion in a college level research project which will be submitted at the conclusion of the course. (1 or 2 credit hours)

1 to 2

## MAT-396 Advanced Studies in Mathematics

A course in advanced topics of current interest in mathematics. Specific content varies term by term but will be announced before registration begins for the semester of offering. Prerequisite: Permission of Division Chair.

1 to 3

## MAT-399H Honors College Thesis/Project

Work with a faculty mentor and in cooperation with an Honors College advisor, producing a research thesis or creative project.

3

## MAT-404 Introduction to Statistical Learning With R

An introduction to Statistical Learning with extensive applications with the R programming language. Emphasis on various types of statistical models including Linear and Nonlinear Regression, Regression Trees, Clustering, Classification Trees, and Random Forests. An exploration of advanced techniques including Regularization (Ridge and Lasso), K-Nearest Neighbor, and Principal Component Analysis. Finally, an introduction to model evaluation including Cross-Validation and the Bias-Variance Trade-Off. This course helps to prepare students for the examination "Statistics for Risk Modeling" in the Actuarial Profession. Prerequisites: MAT-322 and one of MAT-363 or MAT-204

3

A continuation of MAT-344 Modern Abstract Algebra. Topics include advanced group theory, theory of factorization, extension fields, Galois theory, and selected applications. Prerequisite: MAT-344.

3

An advanced multivariate treatment of calculus for the mature student of mathematics. This course will present derivation of the properties of continuity, differentiation, integration and convergence using the fundamental concepts and theorems of analysis. Applications in differential geometry and vector calculus will build on previous calculus experience. Prerequisite: MAT-255.

3

## MAT-455 Point Set Topology

A study of metric spaces and general topological spaces. Continuity, connectedness, compactness, separation, completions, product spaces, and quotient spaces. Prerequisite: MAT-255 and MAT-282.

3

## MAT-456 Elementary Real Analysis

A theoretical study of single variable calculus. Topics include the real number system, sequences, limits, continuity, derivatives, Riemann integrals, and convergence of series. Emphasis will be placed on understanding, writing, and communicating proofs. Prerequisite: MAT-255 and MAT-282.

3

## MAT-457 Complex Variables

An introduction to functions of a single complex variable. Topics include complex numbers, analytic and harmonic functions, mappings, integration techniques and theory, series, and residues. Prerequisite: MAT-255 and MAT-282.

3

## MAT-475 Independent Learning-Mathematics

Individually arranged reading, problem solving, or research in higher mathematics or statistics. Prerequisite: Permission of Division Chair.

1 to 3

## MAT-481 History & Foundations of Mathematics

A classical historical approach to the study of the foundations of mathematics. Contributions of ancient cultures such as the Egyptians, Babylonians, Greeks, Chinese, Hindus and Arabs are considered, as well as the transmission of mathematics into Europe from antiquity through the twentieth century. A comprehensive overview of the various branches of mathematics, such as number theory, logic, geometry, analysis, probability, and statistics is given using concrete applications and high level abstract thinking. Prerequisite: MAT-282.

3

## MAT-485 Mathematics Internship

A mathematical/statistical work experience individually arranged with an employer or volunteer agency. Internships must be preapproved by the Mathematics Department Coordinator for suitable placement and determination of the number of credits. Requirements at the end of the experience include a presentation to the Department as well as student and employer evaluations, a journal, and a paper submitted to the Coordinator. The course may be repeated for credit; a maximum of 4 credits may be applied to a major within the Math Department. Prerequisite: Junior or senior status.

1 to 3

## MAT-490 Math Senior Seminar

A capstone course designed to integrate Christian faith, mathematics, philosophy, and other disciplines. Emphasis will be placed on researching and presenting advanced topics in mathematics. The relationships between the world changing mission of the university, truth, and the student's mathematical career will also be explored. The Major Field Achievement Test in Mathematics will be administered. Prerequisite: Senior standing in a major offered through the Mathematics Department.

2

## MAT-495 Research in Mathematics

Students will engage in a research project in conjunction with a faculty member. Designed for mathematics majors who plan on graduate level work. This course may be repeated for up to 4 credits total. Prerequisite: At least sophomore standing and permission of Division Chair.

1 to 4 