# Mathematics

For centuries, knowledge of mathematics has been essential for the study and practice of science and engineering. It is essential in many other areas of study as well. Students in such fields as psychology, sociology, economics, computer science, actuarial science, and information science are using algebra, calculus, matrix theory, and differential equations to express concepts more clearly and precisely, to analyze and interpret complex relationships, and to arrive at conclusions concerning the meaning and significance of data.

The courses offered in mathematics are intended to meet a variety of needs. Some students will wish to concentrate in mathematics in preparation for teaching the subject, for pursuing a career in business or industry, or for further study at the graduate level. Others will want only to take courses which will provide the mathematical skills needed for concentrated study in other areas.

## Courses

### MT099: BASIC MATH

Credits 4
Designed to develop mathematical skills that are a prerequisite for MT100. Students perform operations on whole numbers, fractions, and negative numbers. Topics include exponents, using the order of operations to simplify expressions, solving linear equations, and an introduction to graphing. Calculators are prohibited.

### MT100: BEGINNING ALGEBRA

Credits 2
A review of high school algebra. Includes solving first degree equations, simplifying polynomials, the rectangular coordinate system, and graphing lines. May include factoring, solving literal equations, solving, and graphing linear inequalities, and/or solving simultaneous equations. Students scoring a 16 or below on the ACT test must take MT099 before taking MT100, unless placement indicates placement in MT100.

### MT102: MATHEMATICS FOR TEACHERS I

Credits 4
An elementary study of the basic properties and underlying concepts of number systems. This content course emphasizes problem-solving techniques and a structural study of the whole numbers, the integers, rational numbers, decimals, and real numbers.

### MT103: MATHEMATICS FOR TEACHERS II

Credits 4
A structural study of statistics, probability, and geometry. Geometric concepts useful to K-8 teachers are developed. Geometric topics covered include geometric constructions, congruence, similarity, translations, rotations, and tessellations.

### MT105: INTRODUCTION TO COMPUTER PROGRAMMING

Credits 4
This course is for students who are interested in learning how to solve problems using computer programming. No programming experience is required or assumed. Students will learn how to use algorithmic problem solving in a variety of coding styles, using a modern object-oriented language. The focus is on building skills that students can transfer to other settings, including data science and scientific computing.

### MT106: LIBERAL ARTS MATH

Credits 4
Students become problem solvers of practical real-life problems. Topics covered include statistical methods in science and business, probability theory; coding techniques which provide for efficient handling of inventory data and data compression; techniques for detecting and correcting errors which occur when electronically transmitting identification numbers; alternative voting systems, and fair division procedures applied to mergers, divorce settlements, inheritance, and other potential adversarial situations.

### MT107: INTERMEDIATE ALGEBRA

Credits 4
A continuation of a review of high school algebra and an introduction to more advanced topics. Includes operations with real numbers, factoring, exponents and radicals, functions, and solutions of equations and inequalities.

### MT109: COLLEGE ALGEBRA

Credits 4
A study of rational and polynomial functions and their graphs and techniques for solving rational and polynomial equations. Includes logarithms, inequalities, complex numbers, sequences, and matrices and determinants, as time permits. Provides essential background in pre-calculus mathematics to prepare students for Calculus I. Emphasis is given to exploring and analyzing the behavior of functions and the connections among those functions and real-world problems.

### MT111: TRIGONOMETRY

Credits 2
A study of the circular and angular trigonometric and inverse trigonometric functions and their graphs, and trigonometric forms of complex numbers. Emphasizes solving real-world problems using trigonometric functions. Includes the unit circle and right triangle applications. Provides essential background in pre-calculus mathematics to prepare students for Calculus I and Physics.

### MT131: INTRODUCTION TO STATISTICS

Credits 4
Students learn the fundamental tools used to analyze sets of data and the standard methods for displaying data.

### MT140: CALCULUS I

Credits 4
An introduction to the basic concepts of limits and derivatives of functions of a single real variable. Includes plane analytic geometry, differentiation, curve sketching, maxima and minima problems, applications of the derivative, and an introduction to anti-derivatives and integration. Emphasis is on the behavior of functions and their derivatives and the use of these to model real-world systems. Graphing technology is used as an important tool for both the learning and exploring of concepts as well as for applications-based problem solving.

### MT141: CALCULUS II

Credits 4
A continuation of Calculus I. Differentiation and integration of trigonometric, exponential, logarithmic, and hyperbolic functions, and an in-depth look at methods of integration, and applications of the integral. Emphasis is placed on the behavior of functions, their derivatives and their integrals and the use of these to model real-world systems. As in Calculus I, graphing technology is used as an important tool.

### MT233: DISCRETE MATHEMATICS

Credits 4
An introduction to discrete mathematical elements and processes. Includes sets, functions, concepts of logic and proof, Boolean algebra, combinatorics, algorithmic concepts, and graph theory and its applications. Students in this course often encounter their first experiences with formal mathematical proof techniques. Emphasis is placed upon applications of the many elements of discrete mathematics in a variety of real-world settings. The use of technology is incorporated for the benefit of both the learning of concepts as well as the solving of real-world applications problems.

### MT328: MODERN GEOMETRIES

Credits 4
The knowledge of Euclidean Geometry acquired in high school is used as a basis for generalization. Familiar Euclidean concepts and theorems are modified and extended to produce other geometries with unusual and interesting properties. Structure and formal proof are stressed. The non-Euclidean geometries' component for the course provides an opportunity to see that a modern theoretical model of the universe which depends on a complex non-Euclidean geometry supports Einstein's general theory of relativity.

### MT330: LINEAR ALGEBRA

Credits 4
This course gives an introductory treatment to solving multi-dimensional systems of equations using matrix methods. Solution through the determination of the inverse, as well as other approaches are developed. Matrices and determinants and their properties are developed and used in applications of vector space concepts.

### MT332: CALCULUS III

Credits 4
The third course in the Calculus sequence. Students continue to investigate the application of the Calculus to the solution of problems of both physical and historical importance including the resolution of Zeno's paradox, convergence and divergence of infinite sums, motion in the plane and in space, the shortest time curve between two points (the brachistochrone problem) and centers of mass. Topics include parameterization of curves, vectors, sequences, infinite sums, power series, approximation of functions using the Taylor polynomial, solid analytic geometry, partial derivatives and gradients, multiple integrals, and their application to areas in the plane and volumes beneath surfaces. This course demonstrates how the Calculus unified seemingly diverse concepts from geometry, algebra, the study of motion and other physical problems.

### MT334: SCIENTIFIC COMPUTING

Credits 4
This course is for students with some programming experience who are interested in learning how to solve scientific and mathematical problems using computer programming. The focus is on tools and techniques that are used in applied scientific fields, including data science and machine learning.

### MT335: ABSTRACT ALGEBRA

Credits 4
This course presents an axiomatic approach to the study of algebraic systems. It begins by investigating the most fundamental concepts behind integer arithmetic. It then shows how all other arithmetic operations involving integers are justified from these basic concepts which are called postulates. Other topics involving integers such as proof by induction, divisibility, congruence, and modular arithmetic are also discussed. A general discussion of algebraic systems such as groups, rings, integral domains, and fields includes the tools used to analyze algebraic systems such as sets, mappings between sets, relations defined on sets, permutations, homomorphisms and isomorphisms. These tools are used to compare algebraic systems defined on sets of integers, rational, real, and complex numbers. Examples involving matrices, coding theory and applications to computer science are used to illustrate the concepts.

### MT338: HISTORY OF MATHEMATICS

Credits 4
A careful study of the major contributions to mathematics from throughout the world and how these contributions are blended into the mathematical structure in which we now function.

### MT341: APPLIED MATHEMATICS

Credits 4
Students will be exposed to the applications of mathematics that occur in a variety of workplace settings. Topics will include higher-order curve fitting used in business and science, predictive techniques in both business and science, financial mathematics (including quantitative modeling and opportunity costs), complex variables, game theory, quantitative decision making, math modeling with Excel, and a basic introduction to databases and programming. Projects will be selected based on student backgrounds and employment objectives. This course will prepare students to use and develop hands-on quantitative tools in today’s work environment.

### MT358: CALCULUS BASED PROBABILITY AND STATISTICS

Credits 4
Students discuss combinatorics and the classical definition of probability and then proceed to a more axiomatic approach to the subject. Discussions include topics such as sample spaces, events, conditional probability, random variables, probability distribution and density functions, and mathematical expectations. The normal distribution and the central limit theorem, as well as probability histograms, graphs, and area beneath curves as probabilities are all discussed. A rigorous treatment of sampling, estimation of population parameters, hypothesis testing, correlation and regression and analysis of variance are also covered.

### MT359: DIFFERENTIAL EQUATIONS WITH NUMERICAL METHODS

Credits 4
Methods for solving first and second order differential equations and linear differential equations of higher order. Includes standard techniques such as change of variables, integrating factors, variation of parameters, and power series. An introduction to numerical methods is also included. An introduction to the application of calculus connecting mathematics to real-world situations in other disciplines is given. Physical systems in physics, chemistry and engineering are modeled using differential equations.