Course Descriptions for Mathematics

MATH 128. Applied Complex
Analysis (3)
Prerequisite: MATH 77. Analytic functions
of a complex variable , contour integration,
series, singularities of analytic functions,
the residue theorems, conformal mappings;
emphasis on engineering and physics applications.
F

MATH 133. Number Theory
for Liberal Studies (3)
Prerequisite: MATH 10B or permission
of instructor. The historical development
of the concept of number and arithmetic
algorithms. The magnitude of numbers.
Basic number theory. Special numbers
and sequences. Number patterns. Modular
arithmetic. F

MATH 134. Geometry for
Liberal Studies (3)
Prerequisite: MATH 10B or permission of
instructor. The use of computer technology
to study and explore concepts in Euclidean
geometry. Topics include, but are not restricted
to, properties of polygons, tilings,
and polyhedra. S

MATH 137. Exploring Statistics (3)
Prerequisite: MATH 10B or permission
of instructor. Descriptive and inferential
statistics with a focus on applications to
mathematics education . Use of technology
and activities for student discovery and understanding
of data organization, collection,
analysis, and inference. F

MATH 138. Exploring Algebra (3)
Prerequisite: MATH 10B or permission of
instructor. Designed for prospective school
teachers who wish to develop a deeper conceptual
understanding of algebraic themes
and ideas needed to become competent and
effective mathematics teachers. S

MATH 143. History of Mathematics (4)
Prerequisite: MATH 75 or 75A and B.
History of the development of mathematical
concepts in algebra, geometry, number
theory, analytical geometry, and calculus
from ancient times through modern times.
Theorems with historical significance will
be studied as they relate to the development
of modern mathematics. S

MATH 145. Problem Solving (3)
Prerequisites: MATH 111; EHD 50 (may
be enrolled concurrently). A study of formulation
of problems into mathematical
form; analysis of methods of attack such
as specialization, generalization, analogy,
induction, recursion, etc. applied to a variety
of non-routine problems. Topics will be
handled through student presentation. F

MATH 149. Capstone Mathematics for
Teachers (4)
Prerequisites: MATH 151, 161, and 171.
(MATH 161 and MATH 171 may be
taken concurrently.) Secondary school
mathematics from an advanced viewpoint.
Builds on students’ work in upper- division
mathematics to deepen their understanding
of the mathematics taught in secondary
school. Students will actively explore
topics in number theory, algebra, analysis,
geometry.

MATH 151. Principles of Algebra (4)
Prerequisite: MATH 111. Equivalence
relations; groups, cyclic groups , normal
sub-groups, and factor groups ; rings, ideals,
and factor rings; integral domains and
polynomial rings ; fields and field extensions.
FS

MATH 152. Linear Algebra (4)
Prerequisite: MATH 77. Vector spaces, linear
transformations, matrices, determinants,
eigenvalues and eigenvectors, linear functions,
inner- product spaces , bilinear forms,
quadratic forms , orthogonal and unitary
transformations, selected applications. FS

MATH 161. Principles of Geometry (3)
Prerequisite: MATH 111. The classical elliptic,
parabolic, and hyperbolic geometries
developed on a framework of incidence,
order and separation , congruence; coordinatization.
Theory of parallels for parabolic
and hyperbolic geometries. Selected
topics of modern Euclidean geometry. S

MATH 165. Differential Geometry (3)
Prerequisite: MATH 111 or permission of
instructor. Study of geometry in Euclidean
space by means of calculus, including theory
of curves and surfaces , curvature, theory of
surfaces, and intrinsic geometry on a surface.
F

MATH 171. Intermediate
Mathematical Analysis I (4)
Prerequisite: MATH 111. Natural and rational
numbers, real numbers as a complete
ordered field, its usual topology, sequences
and series of real numbers, functions of a real
variable, limits, continuity, uniform continuity,
differentiability, generalized mean value
theorem, Riemann integrals, and power
series. FS

MATH 172. Intermediate
Mathematical Analysis II (4)
Prerequisite: MATH 77 and 171. Pointwise
and uniform convergence of sequences
and series of functions, convergence of
sequences in higher dimensions, continuity
and differentiability of functions of several
variables. Inverse and implicit function
theorems; topics in integration theory in
higher dimensions. S

MATH 181. Differential Equations (3)
Prerequisite: MATH 81 or 123. Definition
and classification of differential equations;
general, particular, and singular solutions;
existence theorems; theory and technique of
solving certain differential equations: phase
plane analysis, elementary stability theory;
applications. F

MATH 182. Partial Differential
Equations (3)
Prerequisites: MATH 81 or 123. Classical
methods for solving partial differential
equations including separation of variables,
Green’s functions, the Riemann-Volterra
method and Cauchy’s problem for elliptic,
parabolic, and hyperbolic equations; applications
to theoretical physics. S even

MATH 190. Independent Study
(1-3; max total 6)
See Academic Placement — Independent
Study. Approved for RP grading.

MATH 191T. Proseminar
(1-3; max total 9)
Prerequisite: permission of instructor. Presentation
of advanced topics in mathematics
in the field of the student’s interest.

MATH 198. Senior Project (3)
Prerequisites: senior standing or permission
of instructor; MATH 151, 171, and 152.
Independent investigation and presentation
of an advanced topic in mathematics.
Satisfies the senior major requirement for
the B.A. in Mathematics.

GRADUATE COURSES
(See Catalog Numbering System.)
Mathematics (MATH)

MATH 202. Fundamental
Concepts of Mathematics (3)
Prerequisites: MATH 151, 161, and 171.
Fundamental notions regarding number
theory, number systems, algebra of number
fields; functions.

MATH 216T. Topics in Number
Theory (3; max total 6)
Prerequisite: MATH 116. An investigation
of topics having either historical or current
research interest in the field of number
theory

MATH 223. Principles and Techniques
of Applied Mathematics (3)
Prerequisite: graduate standing or permission
of instructor. Linear spaces and spectral
theory of operators .

MATH 228. Functions of
a Complex Variable (3)
Prerequisite: MATH 128. Representation
theorems of Weierstrass and Mittag-Leffler,
normal families, conformal mapping
and Riemann mapping theorem, analytic
continuation, Dirichlet problem.

MATH 232. Mathematical Models
with Technology (3)
Prerequisite: graduate standing in mathematics
or permission of instructor. A
technology-assisted study of the mathematics
used to model phenomena in statistics,
natural science, and engineering.

MATH 250. Perspectives in Algebra (3)
Prerequisite: graduate standing in mathematics
or permission of instructor. Study
of advanced topics in algebra, providing a
higher perspective to concepts in the high
school curriculum. Topics selected from,
but not limited to, groups, rings, fields,
and vector spaces.

MATH 251. Abstract Algebra I (3)
Prerequisite: undergraduate abstract algebra.
Groups, rings, integral domains, and
fields.

MATH 252. Abstract Algebra II (3)
Prerequisite: MATH 251. Rings and ideals,
modules, linear and multilinear algebras,
representations.

MATH 260. Perspectives in Geometry (3)
Prerequisite: graduate standing in mathematics
or permission of instructor. Geometry
from a transformations point of view. Euclidean
and noneuclidean geometries in two
and three dimensions. Problem solving and
proofs using transformations. Topics chosen
to be relevant to geometrical concepts in the
high school curriculum.

MATH 263. Point Set Topology (3)
Prerequisite: MATH 172. Basic concepts of
point set topology, set theory, topological
spaces, continuous functions; connectivity,
compactness and separation properties of
spaces. Topics selected from function spaces,
metrization, dimension theory.

MATH 270. Perspectives in Analysis (3)
Prerequisite: graduate standing in mathematics
or permission of instructor. An overview
of the development of mathematical analysis,
both real and complex. Emphasizes interrelation
of the various areas of study, the use of
technology, and relevance to the high school
mathematics curriculum.

MATH 271. Real Variables (3)
Prerequisite: MATH 172. Theory of sets;
cardinals; ordinals; function spaces, linear
spaces; measure theory; modern theory of
integration and differentiation.

MATH 290. Independent Study
(1-3; max total 6)
See Academic Placement — Independent
Study. Approved for RP grading.

MATH 291T. Seminar
(1-3; max total 6)
Prerequisite: graduate standing. Seminar
covering special topics in an area of mathematical
research. (Formerly MATH 291)

MATH 298. Research Project
in Mathematics (3)
Prerequisite: graduate standing. Independent
investigation of advanced character as
the culminating requirement for the master’s
degree. Approved for RP grading.

IN-SERVICE COURSE
(See Catalog Numbering System.)
Mathematics (MATH)

MATH 302. Topics in Mathematics for
Teachers (1-3; max total 6 if topic not
repeated)
Prerequisite: permission of instructor. Topics
in modern mathematics with special
emphasis for teachers.