# 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)

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)

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)

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)

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)

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)

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)

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)

(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)

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)

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)

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)

(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)

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.

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