2021-22 Undergraduate Academic Catalog

MATH-2510 Discrete Math for Computer Science –Sp 3 hours An introduction to mathematical foundations of computer science, including propositional and predicate calculus, methods of proof, sets and relations, recurrences, graphs and trees, and program correctness and proofs. This course does not satisfy any requirements for the B.A. or B.S. in mathematics or the B.A. in integrated mathematics education. Prerequisite: MATH-1710 Calculus I. MATH-2520 3 hours Discrete Math and Probability Principles for Computer Science –Sp An introduction to mathematical foundations of computer science, including propositional and predicate calculus, methods of proof, sets and relations, recurrences, program correctness and proofs, probability models, random variables, probability distributions, estimation, and hypothesis testing. This course does not satisfy any requirements for the B.A. or B.S. in mathematics or the B.A. in integrated mathematics education Prerequisites: MATH-1720 Calculus II; EGCP-1010 Digital Logic Design. MATH-2710 Calculus III –Fa, Sp 3 hours Introduction to differential and integral calculus of several variables, multiple integrals, vector analysis, line integrals, and surface integrals. Prerequisite: MATH-1720 Calculus II or equivalent or permission of instructor. MATH-2740 Differential Equations –Fa, Sp 3 hours Study of the standard techniques employed in the solution of differential equations with emphasis on those arising from physical problems. Prerequisite: MATH-1720 Calculus II or equivalent. MATH-2800 LaTeX for Technical Documents –Sp 1 hour In this course students will be introduced to the typesetting language of LaTeX through the use of tutorials, example documents, and homework assignments. They will learn to easily prepare professional-looking theses, conference papers, and journal papers. They will also learn how to create professional- looking presentations, homework, quizzes, examinations, syllabi, resumés, and curriculum vitae. 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. (even years) MATH-3110 Probability and Statistics –Sp 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-3120 Theory of Probability –Sp 3 hours Topics include combinatorial analysis, axioms of probability, conditional probability, independent events, Bayes’ Formula, random variables, expected value, variance, discrete distributions, continuous distributions, joint distributions, the Law of Large Numbers, and the Central Limit Theorem. Prerequisites: MATH- 2710 Calculus III; MATH-2210 Logic and Methods of Proof 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; 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) Page 302 2021–22 Undergraduate Academic Catalog Course Descriptions MATH-2510 – MATH-3800 SCIENCE AND MATHEMATICS