2012-2013 Undergraduate Academic Catalog

Page 257 2012–13 Undergraduate Catalog Introduction Admissions Academic Information Academic Departments Course Descriptions Financial Information Appendix Index MATH-3050 4 hours Algebraic Structures for Secondary Education Majors –Fa An introduction to the basic ideas of number theory, abstract algebra, and linear algebra. Factorization of integers, congruence modulo m, Fermat’s Theorem, groups, rings, integral domains, fields, vector spaces, systems of linear equations, determinants and inverses, linear transformations, eigenvalues, and eigenvectors. Does not count toward B.A. or B.S. majors in mathematics. Prerequisites: MATH-2210 Logic and Methods of Proof; MATH-1720 Calculus II. MATH-3110 Probability and Statistics I –Fa 3 hours Probability models, random variables, probability distributions, estimation, and hypothesis tests are studied from theoretical and practical viewpoints. Prerequisite: MATH-1720 Calculus II. MATH-3240 Introduction to Operations Research –Fa 3 hours Formulation and analysis of mathematical models for the optimal solution of decision making problems under certainty. Course content includes linear programming; the simplex method, duality and sensitivity analysis. This course applies probabilistic analysis to such nondeterministic models as queueing models, elements of dynamic programming, and Markov decision analysis. Prerequisites: MATH-3610 Linear Algebra; MATH-3110 Probability and Statistics; or permission of the instructor. (even years) MATH-3500 Number Theory –Fa 3 hours Introduction to most of the topics of elementary number theory such as modular arithmetic, prime factorizations, linear diophantine equations, the Chinese remainder theorem, quadratic reciprocity, Pythagorean triples, number theoretic functions, and related topics. Concrete examples will illustrate the concepts and abstract reasoning will develop the theories considered in the course. Prerequisite: MATH-2210 Logic and Methods of Proof. (odd years) MATH-3550 Discrete Math: Graph Theory –Fa 3 hours Introduction to the basic concepts of graph theory and discrete mathematics problem-solving. Topics covered include elements of graph theory, covering circuits, graph coloring, trees and searching, and network algorithms. Prerequisite: MATH-2210 Logic and Methods of Proof. (odd years) MATH-3560 Discrete Math: Combinatorics –Sp 3 hours Study of combinatorial reasoning, focusing on enumeration. Intended to develop a proficiency in methods of enumerative problem solving. Topics chosen from areas such as counting methods for arrangements and selections, permutations and combinations, generating functions, partitions, and recurrence relations. Prerequisite: MATH-2210 Logic and Methods of Proof. (odd years) MATH-3610 Linear Algebra –Sp 3 hours Introduction to the algebra of linear equations, including determinants, matrices, vector spaces, eigenvalues, eigenvectors, and linear mappings. Prerequisite: MATH-1720 Calculus II or equivalent. MATH-3710 Advanced Calculus –Sp 3 hours Topics in function theory, vector analysis, differential calculus of several variables, vector differential calculus of several variables, integral calculus of several variables, vector integral calculus of several variables, and infinite series. Prerequisite: MATH-2710 Calculus III or equivalent or permission of instructor. (even years) MATH-3740 Complex Variables –Sp 3 hours Introduction to complex arithmetic, differentiation: analytic functions, Cauchy-Riemann equations, harmonic functions, elementary functions and their mapping properties, integration: Cauchy’s Theorem, Cauchy’s Integral Formula, Taylor and Laurent series, poles, residues, and the residue theorem. Prerequisite: MATH-1720 Calculus II. (odd years) MATH-3750 Introduction to Dynamical Systems –Sp 3 hours Topics include one-dimensional flows and bifurcations, phase portraits, linearization and classification of equilibrium points, limit cycles, chaos, one-dimensional maps, and fractals. Prerequisite: MATH-2740 Differential Equations. (even years) MATH-3760 Numerical Analysis –Sp 3 hours Analysis of computational error, solutions of equations of one variable, interpolation, numerical differentiation and integration, finite difference methods for solving ordinary differential equations, solving linear algebraic systems, and least squares approximations. Prerequisite: CS-1210 C++ Programming; MATH- 2710 Calculus III; MATH-2740 Differential Equations. (odd years) MATH-3800 Research Methods –Sp 1 hour This course will introduce the mathematics major to the various resources and methods available for researching topics in mathematics. This could include the use of library resources at Cedarville University, use of Internet resources, WWW searches, and a tour of the library at a larger university, where journals and indices of importance can be referenced. Prerequisites: MATH-2210 Logic and Methods of Proof; ENG-1400 English Composition. (Fee: $50) MATH-4110 Probability and Statistics II –Sp 3 hours Second course of a two-course sequence covering basic concepts of statistics. Topics chosen from the following: hypothesis tests, regression analysis, quality control, and non-parametric statistics. Prerequisites: MATH-3110 Probability and Statistics I. MATH-4210 Mathematical Methods for Physicists –Fa 3 hours Advanced mathematical methods used in the solution of physics problems. Topics include curvilinear coordinates, vector analysis, and solutions to partial differential equations using Fourier, Bessel and Legendre functions. Prerequisites: MATH- 2710 Calculus III; MATH-2740 Differential Equations. (even years) MATH-4410 3 hours Euclidean and Non-Euclidean Geometry –Sp Rigorous treatment of the foundations of Euclidean geometry; an introduction to hyperbolic geometry with emphasis on its Euclidean models. Prerequisites: MATH-2210 Logic and Methods of Proof. MATH-4450 Topology –Fa 3 hours An introduction to elementary point set topology with emphasis on illustrating how the familiar concepts of closed and open intervals, continuity of functions, distances, and various geometrical properties have been generalized from classical mathematics. Topics include: metric spaces, topological space theory, separation axioms, covering properties, compactness, connectedness, metrizability, and complete metric spaces. Prerequisite: MATH-2210 Logic and Methods of Proof. (even years) MATH-4610, 4620 Abstract Algebra I and II –Fa, Sp 3 hours/sem Introduction to and development of the basic ideas of algebraic systems, groups, rings, integral domains, fields, and other advanced topics. Prerequisite: MATH-2210 Logic and Methods of Proof. (even years) MATH-4710, 4720 Real Variables I and II –Fa, Sp 3 hours/sem Introduction to the real number system’s algebraic order, completeness, and cardinality properties, the topology of Cartesian spaces Rn and functions including continuity and uniform continuity, connectedness, convexity, compactness, various types of convergence, limits, differentiability, and Riemann integration, measurability, and Ln. Prerequisites: MATH-2210 Logic and Methods of Proof. (odd years) Course Descriptions | MATH-3050 – MATH-4710