2001-2002 Academic Catalog

CS-403 Software Engineering HI 3 hours Builds upon the software analysis and design skills learned in Software Engineering II. Focuses on more advanced topics including object-oriented design, formal methods, client/server software engineering, and CASE tools. Capstone course. Prerequisite: CS-320 Language Sun1ey; CS-402 Software E11gi11eeri11g II; ENGR-316 Microprocessors. CS-495 Independent Study in Computer Science 1-4 hours Independent research in the various branches of computer science and allied fields of application. Submission and approval ofa research proposal must precede registration. Prerequisite: a major i11 computer scie11ce a11dpermission ofthe research instructor. (Fee: $5/hour) CS-499 Topics in Computer Science 2-5 hours Study of topics of interest from the field of computer science, such as compiler themy, artificial intelligence, parallel computing, robotics, advanced algorithms, and numeric methods. Prerequisite: permission ofinstructor. (Fee: $50) Mathematics MATH-281 Analytic Geometry and Calculus I-A,W 5 hours First course of a three-course sequence covering basic concepts of analytic geometty and single variable calculus. Includes limits, derivatives, applications of the derivative, and single variable integration with introduction to numeric integration techniques. Prerequisite: GSCI-185 Precalculus or eq11ivale11t; permission of instructor. MATH-282 Analytic Geometry and Calculus II-W,Sp 5 hours The second course of a three-course sequence covering the basic concepts of analytic geometty and single variable calculus. Includes calculus-based development ofthe logarithmic and exponential functions along with other tt·anscendental functions, applications of integration, additional integration techniques, sequences, series, and expansion of functions into Taylor and power series. Prerequisite: MATH-281 Analytic GeometlJ' and Calculus I. MATH-283 Analytic Geometry and Calculus III-A,Sp 5 hours Third course of a three-course sequence covering basic concepts of analytic geometry and single variable calculus. Includes conic sections, plane curves, parametric equations, polar coordinates, vectors and geometty in three-space, vectors, and vector calculus. Prerequisite: MATH-282 A11alytic Geometry a11d Calculus II. MATH-301 Research Methods in Mathematics-Sp 2 hours This course will introduce the mathematics major to the various resources and methods available for researching topics in mathemat– ics. This could include the use of library resources at Cedarville University, use oflnternet resources, WWW searches, and a tour of the libra1y at a larger university, where journals and indexes of importance can be referenced. Prerequisites: MATH-303 Logic a11d Methods ofProof; ENG-140 English Composition II. (Fee: $35) MATH-303 Logic and Methods of Proof-A 5 hours Introduction to formal mathematical logic; emphasis on preparing students for the abstraction of upper-division courses. Special attention is given to the development of students' skills with a variety ofmethods ofproof, using examples from numerous areas. Prerequisite: MATH-282 Analytic Geometl)' a11d Calculus II. MATH-355 Discrete Mathematics: Graph Theory-W 4 hours Introduction to the basic concepts of graph themy and discrete mathematics problem-solving. Topics covered include elements of graph themy, covering circuits, graph coloring, trees and searching, and network algorithms. Forms an eight-hour sequence with MATH- 356 Discrete Mathematics: Combinatorics. Prerequisite: MATH-303 Logic a11d Methods ofProof (odd years) MATH-356 Discrete Mathematics: Combinatorics-Sp 4 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-303 Logic and Methods ofProof (odd years) MATH-360 Number Theory-A 5 hours Introduction to most of the topics of elementary number themy 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 courses. Prerequisite: MATH-303 Logic a11d Methods ofProof. (odd years) MATH-370 Introduction to Higher Mathematical Concepts-Sp 5 hours An introduction to the basic ideas of Number Theory, Abstract Algebra and Linear Algebra. Factorization ofintegers, congruence modulo 111, Fermat's Theorem, groups, rings, fields, vector spaces, systems of linear equations, determinants and inverses, unique factorization, and factoring polynomials over R, C and Z Does not count towards B.A. or B.S majors i11 mathematics. Prereq~lisites: MATH-303 Logic andMethods ofProof; MATH-283 Analytic Geo111et1y a11d Calculus III. MATH-374 Complex Variables-Sp 5 hours Introduction to complex arithmetic, differentiation: analytic fonctions, Cauchy-Riemann equations, harmonic fonctions, elemen– ta1y fonctions and their mapping properties, integration: Cauchy's Theorem, Cauchy's Integral Formula, Taylor and Laurent series, poles, residues, and the residue theorem. Prerequisite: MATH-283 Analytic Geo111et1y and Calculus III. (odd years) MATH-384 Probability and Statistics-W 5 hours Probability models, random variables, binomial, T, chi square and F distributions, sample spaces, estimation, and hypotheses tests are studied from theoretical and practical viewpoints. Prerequisite: MATH-283 Analytic Geometly and Calculus III. MATH-387 Differential Equations-A,W 5 hours Study of the standard techniques employed in the solution of differential equations with emphasis on those arising from physical problems. Prerequisite: MATH-283 Analytic Geomet1y and Calculus III. MATH-388 Advanced Calculus I-A,W 5 hours Introduction to differential calculus ofseveral variables, multiple integrals, vector analysis, line integrals, surface integrals, and an abbreviated introduction to linear algebra, matrix algebra, and determi– nants. Prerequisite: MATH-283 Analytic Geometl)' and Calculus III. MATH-389 Advanced Calculus II-Sp 5 hours Topics in fonction theory, vector analysis, differential calculus of several variables, vector differential calculus, integral calculus of several variables, vector integral calculus, and infinite series. Prerequi– site: MATH-388 Advanced Calculus I. MATH-394 Linear Algebra-Sp 5 hours Introduction to the algebra of linear equations, including determi– nants, matrices, vector spaces, eigenvalues, eigenvectors, and linear mapping. Prerequisite: MATH-282 Analytic Geomet1y and Calculus II. (even years) MATH-401 Capstone Experience in Mathematics-A,W 2 honrs The course will allow students to deeply research an important topic in mathematics, both individually and collectively, and to present their findings from libra1y research as well as personal work. Prerequisite: MATH-301 Research Methods in Mathematics, 25 hours of300- or 400-level courses, andpermission ofinstructor. (Fee: $20) MATH-411 Applied Statistics-Sp 3 hours Topics chosen from the following: regression analysis, queuing theory, invento1y themy, decision analysis, simulation, quality control, and reliability themy. Prerequisite: MATH-384 Probability andStatistics. MATH-441 Euclidean and Non-Euclidean Geometries-Sp 5 hours Rigorous treatment of the foundations ofEuclidean geometty; an introduction to hyperbolic geometry with emphasis on its Euclidean models. Prerequisite: MATH-303 Logic andMethods ofProof (even years) MATH-445Topology-A 5 hours Introduction to elementary point set topology; emphasis on illustrating how the familiar concepts of closed and open intervals, continuity of fonctions, and various geometrical properties have been generalized from classical mathematics. Topics include: mett·ic spaces, topological space the01y, separation axioms, covering properties, compactness, connectedness, metrizability, and complete metric spaces. Prerequisite: MATH-303 Logic and Methods ofProof (even years) MATH-461,462AbstractAlgebral,II-A,W 4 hours Introduction to sets and logic, and the development of algebraic systems, groups, rings, integral domains, fields, and other advanced topics. Prerequisite: MATH-303 Logic and Methods ofProof (even years)