Course Descriptions

MTH099 BASIC MATH (3). Helps students develop proficiency in fundamental mathematical skills as a prerequisite for MTH100. Includes: arithmetic operations on whole numbers, fractions and decimals, percentages, ratios and proportions, and an introduction to geometry and basic algebra. This course does not count in the 124 hours required for graduation. Each Fall/Each Spring.

MTH100 ALGEBRA I (3). 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 MTH099 before taking MTH100, unless placement testing indicates placement in MTH100. Each Fall/Each Spring.

MTH112 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 number, the integers, rational numbers, decimals, and real numbers. Each Fall.

MTH113 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. Each Spring.

MTH120 ALGEBRA II (3). 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: MTH 100 or math placement. Each Fall/Each Spring.

MTH122 FINITE MATHEMATICS (3). Students become problem solvers of practical real life problems. Topics covered are chosen from Euler and Hamiltonian circuit theory, scheduling tasks, linear programming, statistics, probability, coding information, social choice and decision making, and geometric size and shape. Prerequisite: MTH100 or math placement. Each Fall/Each Spring.

MTH150 ALGEBRA III (3). 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 precalculus mathematics to prepare students for Calculus I. Emphasis on exploring and analyzing the behavior of functions and the connections among those functions and real-world problems. Prerequisite: MTH120 or math placement. Each Fall/Each Spring.

MTH152 TRIGONOMETRY (3). 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 precalculus mathematics to prepare students for Calculus I. Prerequisite: MTH120 or math placement. Each Fall.

MTH162 STATISTICS FOR SCIENCE STUDENTS (4). Students learn the fundamental tools used to analyze sets of data and the standard methods for displaying data. Prerequisite: MTH120. Spring 2007.

MTH171 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. Prerequisites: MTH 150 or math placement. Each Fall.

MTH172 CALCULUS Il (4). A continuation of Calculus 1. 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. Prerequisite: MTH171. Each Spring.

MTH241 DISCRETE MATHEMATICS (3). 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 application. 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. Prerequisite: MTH150. Each Spring.

MTH305 LINEAR ALGEBRA (3). Matrices, vectors, and linear transformations. Matrices and determinants and their properties are developed and used in applications of vector space concepts. The use of technology is integral to the conceptual, the computational and the problem solving aspects of the course. Prerequisite: MTH172 or permission of the department. Each Fall.

MTH312 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. Prerequisite: MTH172. Each Fall.

MTH320 DIFFERENTIAL EQUATIONS (3). 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. Prerequisite: MTH 312. Spring of even numbered years.

MTH335 ABSTRACT ALGEBRA (3). 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, divisibilty, 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. Prerequisite: MTH172. Each Spring semester.

MTH345 HISTORY OF MATHEMATICS (3). This course is 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. General topics covered include: the birth of demonstrative mathematics, the dawn of Modern Mathematics, Descartes’ and Fermat’s Analytic Geometry, the exploitation of the Calculus, the liberation of Geometry and Algebra. Prerequisite: MTH172. Fall of odd numbered years.

MTH350 PROBABILITY (3). A theoretical basis for Statistics. Students discuss combinatorics and the classical definition of probability and then proceed to a more axiomatic approach to the subject. Discussions include the topics of sample spaces, events, conditional probability, random variables, probability distribution and density functions, mathematical expectations, moments and moment generating functions. The normal distribution and the central limit theorem are discussed in detail. Probability histograms, graphs and area beneath graphs are emphasized to provide an intuitive, geometrical understanding of the concepts. Prerequisite: MTH312. Fall of odd numbered years.

MTH360 MATHEMATICAL STATISTICS (3). An introduction to the basic concepts involved in analyzing sets of data derived from scientific experiments. A rigorous treatment of sampling, estimation of population parameters, using appropriate distribution functions, hypothesis testing, correlation and regression and analysis of variance using the concepts presented in the course on Probability. Students process a data set from a real-world application using computer technology and the concepts presented. Prerequisite: MTH350. Spring of even numbered years.

MTH370 MODERN GEOMETRIES (3). 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 of 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. Topics include: Axiomatics and Finite Geometries, Geometric Transformations, Constructions, Convexity, Topological Transformations, Projective Geometry and Non-Euclidean Geometries. Prerequisite: MTH171. Fall of even numbered years.

MTH380 NUMERICAL METHODS (3). An introduction to the methods of numerical approximation and error analysis. Topics include numerical techniques of integration and interpolation, iterative solutions of equations and systems of equations. Real-world problems from other disciplines such as engineering and physics are modeled and solved using computer technology. Prerequisites: MTH305 and familiarity with a programming language. Spring of odd numbered years.