# Course Descriptions

MT099 BASIC MATH (2). Designed to develop mathematical skills that are a prerequisite for MT100.

MT100 ALGEBRA I (2). Review of high school algebra and an introduction to more advanced topics. Includes solving first degree equations, simplifying polynomials, factoring, solving literal equations, the rectangular coordinate system and graphing lines, solving simultaneous equations, solving and graphing linear inequalities, and solving quadratic equations. Students scoring 16 or below on the ACT test must take MT099 before taking MT100, unless placement testing indicates placement in MT100.

MT102 MATHEMATICS FOR TEACHERS I (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. [Skill: Q] Prerequisite: MT099 or math placement in MT100 or higher level of math.

MT103 MATHEMATICS FOR TEACHERS II (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. [Skill: Q] Prerequisite: MT099 or math placement in MT100 or higher level of math.

MT106 SOCIAL TOPICS IN MATHEMATICS: MATHEMATICS WITHOUT ALGEBRA (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. Prerequisite: MT100 or math placement.

MT107 ALGEBRA II (4). A continuation of the study of algebraic concepts and techniques begun in a first year algebra course. Includes operations with real numbers, factoring, exponents and radicals, functions, solutions of equations and inequalities, and rational expressions. Prerequisite: MT100 or math placement.

MT109 ALGEBRA III (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. [Skill: Q] Prerequisite: MT107 or math placement.

MT111 TRIGONOMETRY (4). 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, right triangle applications, verification of identities, and exponential and logarithmic functions. Provides essential background in pre-calculus mathematics to prepare students for Calculus I. [Skill: Q] Prerequisite: MT107 or math placement.

MT131 INTRODUCTION TO STATISTICS (4). Students learn the fundamental tools used to analyze sets of data and the standard methods for displaying data. [Skill: Q] Prerequisite: MT107 or placement in MT109 or higher.

MT140 CALCULUS I (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. [Skill: Q] Prerequisite: MT109 or math placement.

MT141 CALCULUS II (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. [Skill: Q] Prerequisite: MT140 or math placement.

MT233 DISCRETE MATHEMATICS (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. [Skill: Q] Prerequisite: MT109.

MT328 MODERN GEOMETRIES (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. [Skills: Q,T] Prerequisite: MT140.

MT330 LINEAR ALGEBRA (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. [Skills: Q,T] Prerequisite: MT141.

MT332 CALCULUS III (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. [Skills: Q,T] Prerequisite: MT141.

MT335 ABSTRACT ALGEBRA (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. [Skill: Q] Prerequisite: MT141.

MT338 HISTORY OF MATHEMATICS (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. [Skill: Q] Prerequisite: MT141.

MT358 CALCULUS BASED PROBABILITY AND STATISTICS (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. [Skills: Q,T] Prerequisite: MT332or permission of instructor.

MT359 DIFFERENTIAL EQUATIONS WITH NUMERICAL METHODS (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. [Skills: Q,T] Prerequisite: MT332 or permission of instructor.