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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)
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.
Page
272
2015–16 Undergraduate Academic Catalog
Course Descriptions
MATH-3240 – MATH-4880