2017-18 Undergraduate Catalog

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) MATH-4800 3 hours Capstone Experience in Mathematics –Fa, Sp The course will allow students to deeply research an important topic in mathematics, both individually and collectively, and to present their findings from library research as well as personal work. Prerequisites: MATH-3800 Research Methods in Mathematics; 15 hours of courses beyond MATH-1720 Calculus II; permission of instructor. (Fee: $20) MATH-4880 Topics in Mathematics –Fa, Sp 1–3 hours Some typical topics are linear programming, numerical analysis, stochastic calculus, non-parametric statistics, partial differential equations, or mathematical modeling. This course is intended to be a topic not in the current curriculum that is a logical extension and development of the student’s academic plan. Prerequisite: permission of instructor. MATH-4900 1–3 hours Independent Study in Mathematics –Fa, Sp Independent research in the various branches of mathematics and allied fields of application. Submission and approval of a research proposal must precede registration. Prerequisite: major in mathematics or permission of research advisor. Mathematics Education (MTED) MTED-3110 Clinical Teaching in Mathematics –Fa, Sp 1 hour Students are assigned to assist a college instructor in classroom and laboratory teaching, evaluation, and related responsibilities. The student must complete 40 clock hours of clinical involvement in each teaching field for which licensure is desired. Prerequisite: completion of Introduction to Education Block. MTED-3120 Teaching Mathematics –Fa 3 hours Designed to introduce prospective secondary school mathematics teachers to the curriculum, materials, and methods of classroom teaching. Prerequisite: admission to the Teacher Education Program. Physics: General Education (PHYS) Except where noted, general education courses are designed to meet the general education requirements for graduation. These courses will not count toward graduation requirements for majors found in the Department of Science and Mathematics unless they are specifically listed in the curriculum requirements for a major. A student majoring in science or mathematics may take these courses only as electives. However, any course listed for a science or mathematics major or minor may also count toward fulfilling general education requirements. PHYS-1010 College Physics I –Fa 4 hours Basic concepts of mechanics using algebra and trigonometry. This is the first of a two course sequence intended for students in the life sciences and pre-professional programs. Topics include kinematics, motion in two dimensions, force and motion, torque and rotation, work and energy, momentum, circular motion, gravitation, oscillation, waves and fluid. Three lectures and one two-hour laboratory per week. Prerequisite: high school trigonometry; or GMTH-1030 Precalculus or equivalent. (Fee: $75) PHYS-1020 College Physics II –Sp 4 hours Basic concepts of electricity, magnetism and modern physics using algebra and trigonometry. This is the second of a two course sequence intended for students in the life sciences and pre-professional programs. Topics include electricity, magnetism, circuits, and geometrical and physical optics, relativity theory, quantum theory and nuclear physics topics. Three lectures and one two-hour laboratory per week. Prerequisite: PHYS-1010 College Physics I or equivalent. (Fee: $75) Page 292 2017–18 Undergraduate Academic Catalog Course Descriptions MATH-3750 – PHYS-1020 SCIENCE AND MATHEMATICS