2018-19 Undergraduate Academic Catalog

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-4130 Mathematical Statistics –Fa 3 hours Topics include random variables, normal sampling theory, likelihood-based and Bayesian approaches to point estimation, confidence intervals, tests of hypotheses, and an introduction to regression and the analysis of variance. Prerequisites: MATH-2210 Logic and Methods of Proof; MATH-2710 Calculus III; MATH-3110 Probability and Statistics or MATH-3120 Theory of Probability; MATH-3610 Linear Algebra. (odd years) 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. (odd 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) Physics: Major (PHYS) PHYS-2110 General Physics I –Fa, Sp 4 hours Basic concepts of mechanics using calculus. This is the first of a three-course sequence intended for students in the physical sciences and engineering programs. Topics include linear and rotational motion in three dimensions, oscillatory motion, gravitation, fluid mechanics, and basic concepts of wave motion. Three lectures and one two-hour laboratory per week. Prerequisites: MATH-1710 Calculus I; Corequisite: MATH-1720 Calculus II. (Fee: $100) PHYS-2120 General Physics II –Fa, Sp 4 hours Basic concepts of electricity and magnetism, light, and optics using calculus. This is the second of a three-course sequence intended for students in the physical sciences and engineering programs. Topics include electricity, magnetism, Maxwell’s equations, DC and AC circuits, geometrical and physical optics. Three lectures and one two-hour laboratory per week. Prerequisites: MATH-1720 Calculus II; PHYS-2110 General Physics I. (Fee: $100) PHYS-2130 General Physics III –Fa 2 hours Basic concepts of thermodynamics and modern physics using calculus. This is the third of a three-course sequence intended for students in the physical sciences programs. Topics include heat and thermodynamics, relativity theory, quantum theory, atomic and nuclear physics. Prerequisites: MATH-1720 Calculus II; PHYS- 2120 General Physics II; PHYS-2120 may be co-enrolled with permission of instructor. PHYS-3110 Intermediate Physics Laboratory –Fa 2 hours Designed to reinforce concepts of the advanced physics courses and develop critical research and analysis skills. This course provides laboratory experience in such topics as oscillatory motion and waves, mechanics, electricity and magnetism, thermodynamics, and quantum mechanics. During this semester the student will develop their prospectus for their advanced laboratory project. Laboratory skills for planning, setup, documentation, and analysis using the scientific method will be emphasized. Prerequisite: 3 hours of a 3000- or 4000-level physics course. (Fee: $100) PHYS-3310 Theoretical Mechanics –Sp 3 hours Derivation of the motion of a point object through three- dimensional space. Topics include an advanced treatment of Newtonian mechanics in three dimensions, oscillatory motion, accelerated frames of reference, central forces, and an introduction to Lagrangian mechanics. Prerequisites: PHYS-2120 General Physics II; MATH-2740 Differential Equations; MATH-2740 may be co-enrolled with permission of instructor. (even years) PHYS-3330 Acoustics –Fa 3 hours This course will study the generation, transmission and reception of sound. Topics include wave propagation through the air, resonance conditions for strings, bars, membranes and air cavities, acoustic filters, measurement and human perception of sound. Applications will be made to musical instruments, room acoustics, microphones, and speakers. Prerequisites: MATH-2710 Differential Equations; PHYS-2110 General Physics I. (even years) PHYS-3350 Thermal Physics –Sp 3 hours Study of the relationship between energy and matter through the use of thermodynamics and statistical mechanics. Topics include the laws of thermodynamics, heat, work, entropy, phase transformations, statistical distributions, and kinetic theory. Prerequisite: PHYS-2130 General Physics III. (odd years) PHYS-3410 Electromagnetic Theory –Fa 3 hours Electricity and magnetism from an advanced viewpoint using the methods of vector calculus. Includes electrostatics, Gauss’ Law, Poisson’s equation, Laplace’s equation, dielectric media, electric currents, and magnetostatics. Prerequisites: PHYS-2120 General Physics II; MATH-2710 Calculus III. (odd years) PHYS-3510 Modern Physics –Sp 3 hours Introduction to relativity theory, quantum theory, including Schrodinger’s Equation, and its basic applications, and atomic structure. Prerequisite: PHYS-2130 General Physics III. PHYS-3800 Research Methods in Physics –Sp 1 hour Reinforces concepts of the advanced physics courses and develops critical research and analysis skills. This course will focus on basic library, research, and laboratory skills for planning, setup, documentation, and analysis using the scientific method. Selected software will be introduced and used to collect data, analyze results, and document findings. There will be several laboratory sessions with experiments selected from oscillatory motion and waves, intermediate mechanics, intermediate electricity, intermediate magnetism, thermodynamics, or quantum mechanics. Prerequisite: PHYS-2130 General Physics III. (Fee: $50) Page 298 2018–19 Undergraduate Academic Catalog 2018–19 Undergraduate Academic Catalog Page 299 Course Descriptions Course Descriptions MATH-3500 – MATH-4900 MTED-3110 – PHYS-3800 SCIENCE AND MATHEMATICS SCIENCE AND MATHEMATICS