2010-2011 HBU Catalog - Houston Baptist University

A review of mathematical topics of special interest to students obtaining teacher certification in mathematics, including
material from algebra, geometry, probability, statistics, linear algebra, discrete math, and others. This course includes
instruction on technology used in teaching mathematics, both graphing calculators and computer software. Required
for the mathematical studies major but may not be counted as part of a mathematics major.
MATH 4301 Real Variables I
Prerequisites: MATH 2451 and MATH 3301
A rigorous introduction to mathematical analysis. Topics covered include the real and complex number systems, basic
topology, numerical sequences and series, continuity of functions, and differentiation.
MATH 4302 Real Variables II
Prerequisites: MATH 4301
A continuation of MATH 4301. Further study of mathematical analysis. Topics covered include Riemann integration,
sequences and series of functions, functions of several variables, and integration of differential forms.
MATH 4310 Advanced Discrete Mathematics and Combinatorics
Prerequisites: MATH 3311
Further study of enumerative techniques and discrete structures including generating functions, recurrence relations,
graph theory, spanning trees, optimization, and Boolean Algebras.
MATH 4311 Topology I
Prerequisites: MATH 3353
An introduction to topology and its applications. Topics include a review of basic abstract algebra; the definition of a
topological space; interior, closure, and boundary of sets; subspace, product, and quotient topologies; continuity and
homeomorphisms; metrics and metric spaces; connectedness; and compactness.
MATH 4312 Topology II
Prerequisites: MATH 4311
A continuation of MATH 4311. Topics include dynamical systems and chaos, homotopy and degree theory, fixed
point theorems, embeddings, knots, graphs, and manifolds.
MATH 4332 Dynamics and Bifurcations
Prerequisite: MATH 3301, and 2451
Introduction to the theory of equilibrium solutions of nonlinear equations. Presentation of the theory of bifurcations
includes the analysis of the nonlinear ordinary and algebraic equations that arise from the methods of reduction by
projections.
MATH 3371 Introduction to Complex Variables
Prerequisites: MATH 2323 and 2451, or consent of the instructor
A first course in the study of analytic functions. Topics include complex numbers, complex functions, derivatives,
differentials, integrals, analytic functions, power series expansions, Laurent series expansions, poles and zeros, and
conformal mapping.
MATH 4341 Mathematical Biology
Prerequisites: MATH 3333
Introduction to modeling in biology and genetics. Some of the models covered include population models, hostparasite
models, and gene spread models as described by difference equations, differential equations, and partial
differential equations. The emphasis of this course will be to familiarize students with the selection of models and
predictions based on the models chosen.
MATH 4353 Advanced Abstract Algebra
Prerequisites: MATH 3353
A continuation of MATH 3353. The focus of this course is on rings, domains, fields, polynomials, Galois theory,
Boolean algebra, and modules. Other topics may be covered if time permits.
MATH 4372 Advanced Complex Variables
Prerequisites: MATH 3371
Further study of differentiable complex-valued functions of a single complex variable. Topics include residue theory
and contour integrals, z-transforms, conformal mapping, harmonic functions and their applications, Fourier Series, and
Laplace transforms.
2010-2011 HBU Catalog www.hbu.edu/catalog Page 260