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MATH 4101 MATHEMATICS CAPSTONE COURSE The capstone course is a one credit hour course for Mathematics Education and Mathematics seniors. It is modular in structure, with each module bringing together several different mathematics subject areas in a more advanced and interconnected context. To some extent, it will be preparatory for pre-professional exams. Prerequisite: Senior Standing or departmental approval. F MATH 4133 INTRO TO MATHEMATICAL LOGIC A basic course in mathematical thought, simple and compound sentences, truth tables, deductive logic, mathematical systems, quantification, application of logic to puzzles and games. Prerequisite: MATH 3834. D MATH 4153 HISTORY OF MATHEMATICS A survey course on the historical development of mathematics, including a look at famous problems and their development over time. SE MATH 4213 DIFFERENTIAL EQUATIONS I Solutions of ordinary differential equations with applications. A continuation of MATH 4213. Advanced ordinary differential equations methods and an introduction to partial differential equations including Fourier series, Laplace’s equation, heat and wave equations. Prerequisite: MATH 4213. D MATH 4233 VECTOR ANALYSIS A comprehensive course in theory and applications of vector analysis with an introduction to vector spaces. Prerequisite: MATH 3834. D MATH 4653 MODERN ALGEBRA An introduction to group, ring, and field theory, with an emphasis on group theory; permutation groups, factor groups and homomorphism theorems. Supportive problem sets and applications. Prerequisite: MATH 3834. F MATH 4753 INTRODUCTION TO POINT SET TOPOLOGY Prerequisite: MATH 3834 or departmental approval. S MATH 4223 DIFFERENTIAL EQUATIONS II Elements of set theory, the real number system, mappings, metric spaces, and general topological spaces. Prerequisites: MATH 3834 and consent of instructor. D MATH 4853 ADVANCED CALCULUS A course in real analysis designed to strengthen and extend the theory behind the calculus sequence. Prerequisite: MATH 3834. S MATH 4873 COMPLEX VARIABLES Complex numbers and their algebra. Analytic functions. Cauchy-Riemann conditions, differential calculus of analytic functions. Prerequisite: MATH 3834. FE Math for Elementary Teachers The following courses are designed to prepare elementary and middle school teachers and CANNOT satisfy any mathematics requirement for programs other than Middle School Mathematics, Bachelors in Elementary Education, or Masters in Elementary Education. MATH 1433 STRUCTURAL CONCEPTS IN ARITHMETIC This course is specifically designed for elementary education, special education, and early childhood education majors. The content of this course includes whole numbers, operations, properties of whole numbers, standard and nonstandard algorithms, number theory, fractions, decimals, ratios, percents, estimation, integers, teaching/learning strategies, and mental math strategies. Emphasis is placed on conceptual understanding,
eigenvectors, and diagonalization. Prerequisite: MATH 2834 or departmental approval. S MATH 3673 ELEMENTARY NUMBER THEORY A study including primes and composites, number theoretic functions, Diophantine equations, congruence classes, and mathematical induction. Prerequisite: MATH 2834 or departmental approval. SE MATH 3713 COLLEGE GEOMETRY An axiomatic development of the essentials of Euclidean geometry and an introduction to non-Euclidean geometry. Content includes the foundations of Euclidean geometry (points, lines, angles, triangles, quadrilaterals, circles), parallelism in Euclidean geometry, transformations and isometries, and parallelism in non-Euclidean geometry (with the focus on hyperbolic geometry). Prerequisite: MATH 2834 or departmental approval. S MATH 3834 CALCULUS III A course in multivariable calculus and its applications. Topics include vectors in two and three dimensions; differential calculus of functions of several variables, gradient, and optimization; multiple integration and change of coordinates; vector fields, line integrals, surface integrals, Green’s Theorem, Gauss’ Theorem, and Stokes’ Theorem. Prerequisite: MATH 2834 or equivalent. F, S MATH 4001-4 INDIVIDUAL STUDY IN MATHEMATICS (TOPIC) Independent study of specific topic in mathematics for undergraduate students. Credit one to four semester hours. D MATH 4011-4 SEMINAR IN MATHEMATICS (TOPIC) Group study of specified topic in mathematics for undergraduate students. Credit one to four semester hours. D MATH 4013 SEMINAR IN MATHEMATICS The following courses are generally offered under this course number: Analytic Geometry Emphasizes the essential elements of analytic geometry with special attention to those topics that are needed in a college level calculus sequence. Content includes polynomial, rational, and transcendental functions. Polar and parametric equations, space coordinates and surfaces, lines and planes in space, applications to business, social and physical sciences, and curve fitting. Prerequisite: MATH 2834. D Linear Algebra for Secondary Teachers An introductory course on matrix algebra with applications to solutions of systems of linear equations, linear programming, vector spaces, determinants, linear transformations and applications. Prerequisite: MATH 2834. D Modern Algebra for Secondary Teachers Fundamental concepts of sets, mappings, binary operations, mathematical induction, divisibility and congruence mod n. Basic algebraic structures: groups, subgroups, cyclic groups, normal subgroups, homomorphism, and isomorphism. Introduction to rings, integral domains, and fields. Supportive problem sets and applications of special interest to teachers. Prerequisite: MATH 3834. D Survey of Geometry Euclid’s Postulates with emphasis on Euclid’s parallel postulate. Historical development of non-Euclidean geometry, with emphasis on the work of Saccheri, Gauss, and Lobachevsky. Circular inversion and orthogonal circles. The Beltrami-Poincare’ half-plane and Poincare’ disk models of hyperbolic geometry. The spherical model of elliptic geometry. Prerequisite: MATH 1834. D
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