## The Undergraduate Courses

110. QUANTITATIVE REASONING. Statistical reasoning, logical statements
and arguments,

personal business applications, linear programming, estimations, and
approximation. (3)

115. ELEMENTARY STATISTICS. Descriptive statistics; probability distributions;
sampling

distributions; estimation; hypothesis testing; and linear regression.
(3)

121. COLLEGE ALGEBRA. College algebra. (3)

123. TRIGONOMETRY. College trigonometry. (3)

125. BASIC MATHEMATICS FOR SCIENCE AND ENGINEERING. A unified freshman
course

designed especially for those students requiring a review of both algebra
and trigonometry before

beginning the calculus sequence. (3)

245. MATHEMATICS FOR ELEMENTARY TEACHERS I. Introduction to sets; the
real number system

and its subsystems. For elementary and special education majors only.
(3)

246. MATHEMATICS FOR ELEMENTARY TEACHERS II. Informal geometry; measurement
and the

metric system; probability and statistics. For elementary and special
education majors only.

Prerequisite: Math 245 with minimum grade of C. (3)

261. UNIFIED CALCULUS AND ANALYTIC GEOMETRY I. Differential and integral
calculus;

analytic geometry introduced, covered in integrated plan where appropriate.
Four-term sequence

for engineering and science majors. (3)

262. UNIFIED CALCULUS AND ANALYTIC GEOMETRY II. Differential and integral
calculus;

analytic geometry introduced, covered in integrated plan where appropriate.
Four-term sequence

for engineering and science majors. Prerequisite: Math 261 with minimum
grade of C. (3)

263. UNIFIED CALCULUS AND ANALYTIC GEOMETRY III. Differential and integral
calculus;

analytic geometry introduced, covered in integrated plan where appropriate.
Four-term sequence

for engineering and science majors. Prerequisite: Math 262 with minimum
grade of C. (3)

264. UNIFIED CALCULUS AND ANALYTIC GEOMETRY IV. Differential and integral
calculus;

analytic geometry introduced, covered in integrated plan where appropriate.
Four-term sequence

for engineering and science majors. Prerequisite: Math 263 with minimum
grade of C. (3)

267. CALCULUS FOR BUSINESS, ECONOMICS, AND ACCOUNTANCY I. Differential
and integral

calculus with an emphasis on business applications. (3)

268. CALCULUS FOR BUSINESS, ECONOMICS, AND ACCOUNTANCY II. Differential
and

integral calculus with an emphasis on business applications. Prerequisite:
Math 267 with minimum

grade of C. (3)

269. INTRODUCTION TO LINEAR PROGRAMMING. Selected topics in quantitative
methods

with an emphasis on business applications. Topics include Gauss-Jordan
elimination, simplex

solutions for linear programming models and transportation and assignment
algorithms.

Prerequisite: Math 267 with minimum grade of C. (3)

271. CALCULUS OF DECISION MAKING I. Differential calculus with an emphasis
on its uses in

decision making. Topics will include techniques to analyze functions
of one variable and maximize

functions of several variables subject to constraints, using the Lagrange
method. Other topics may

include elementary encryption techniques. Students may not receive credit
for both Math 267 and

Math 271. (3)

272. CALCULUS OF DECISION MAKING II. Integral calculus with an emphasis
on its uses in

decision making. Other topics may include markets and auctions. Nash
equilibria and game theory

and discrete forms on optimization. Students may not receive credit
for both Math 268 and Math

272. Prerequisite: Math 271 with minimum grade of C. (3)

281. COMPUTER LABORATORY FOR CALCULUS I. Investigation of the techniques
in Calculus I

(Math 261) through the use of a computer. (1)

282. COMPUTER LABORATORY FOR CALCULUS II. Investigation of the techniques
in Calculus II

(Math 262) through the use of a computer. (1)

283. COMPUTER LABORATORY FOR CALCULUS III. Investigation of the techniques
in Calculus

III (Math 263) through the use of a computer. (1)

284. COMPUTER LABORATORY FOR CALCULUS IV. Investigation of the techniques
in Calculus

IV (Math 264) through the use of a computer. (1)

301. DISCRETE MATHEMATICS. Elementary counting principles; mathematical
induction;

inclusion- exclusion principles; and graphs. Prerequisite: Math 261
with minimum grade of C. (3)

302. APPLIED MODERN ALGEBRA. Languages, generating functions, recurrence
relations,

optimization, rings, groups, coding theory, and Polya theory. Prerequisite:
Math 301 with minimum

grade of C. (3)

305. FOUNDATIONS OF MATHEMATICS. Set theory with emphasis on functions,
techniques used

in mathematical problems, cardinal numbers. Prerequisite: Math 262 with
minimum grade of C. (3)

319. INTRODUCTION TO LINEAR ALGEBRA. Vectors, matrices, determinants,
linear

transformations, introduction to vector spaces. Prerequisite: Math 262
with minimum grade of C.

(3)

353. ELEMENTARY DIFFERENTIAL EQUATIONS. Equations of first and second
order; linear

equations with constant coefficients; solution in series. (3)

368. INTRODUCTION TO OPERATIONS RESEARCH. An introduction to the mathematics

involved in optimal decision making and the modeling of deterministic
systems. Major topics to

include linear programming, the simplex method, transportation algorithms,
integer programming,

network theory, and CPM/PERT. Prerequisite: Math 319 with minimum grade
of C. (3)

375. INTRODUCTION TO STATISTICAL METHODS. Probability; distributions;
joint probability

distributions; conditional distributions; marginal distributions; independence;
probability

distributions; simple regression; simple correlation; and tests of significance;
introduction to the use

of statistical software packages. Prerequisite: Math 261 with minimum
grade of C. (3)

390. TECHNIQUES IN TEACHING SECONDARY LEVEL MATH. Teaching techniques
for algebra,

geometry, trigonometry, and calculus are presented and discussed. For
mathematics education

majors only. (3)

397. SPECIAL PROBLEMS. May be repeated twice for credit for a total
of 6 hours. Prerequisite:

Math 305 with minimum grade of C. (1-3)

401. COMBINATORICS. An introduction to the mathematics of finite sets,
Ramsey theory, Latin

squares, graph theory, matroid theory, and other related topics. Prerequisite:
Math 305 with

minimum grade of C, Math 301 with minimum grade of C. (3)

425. INTRODUCTION TO ABSTRACT ALGEBRA. Real number system, groups, rings,
integral

domains, fields. Prerequisite: Math 263 with minimum grade of C. (3)

454. INTERMEDIATE DIFFERENTIAL EQUATIONS. Certain special methods of
solution; systems of

equations; elementary partial differential equations; equations occurring
in physical sciences.

Prerequisite: Math 353 with minimum grade of C. (3)

459. INTRODUCTION TO COMPLEX ANALYSIS. Complex numbers, complex differentiation,
the

Cauchy-Riemann equations and applications; the Cauchy integral formula,
contour integration,

series. Prerequisite: Math 264 with minimum grade of C. (3)

461. NUMERICAL MATHEMATICAL ANALYSIS I. (3)

462. NUMERICAL MATHEMATICAL ANALYSIS II. (3)

475. INTRODUCTION TO MATHEMATICAL STATISTICS. Data analysis; moment
characteristics;

statistical distributions, including Bernoulli, Poisson, and Normal;
least squares, simple correlation,

and bivariate analysis; applications. Prerequisite: Math 375 with minimum
grade of C, Math 262

with minimum grade of C. (3)

480. INTRODUCTION TO ACTUARIAL SCIENCE. A course to develop knowledge
of the

fundamental probability tools for quantitatively assessing risk with
emphasis on the application of

these tools to problems encountered in actuarial science. Topics include
general probability

concepts, univariate distributions, multivariate distribution, and risk
management concepts.

Prerequisite: Math 475 with minimum grade of C. (3)

501. GENERAL TOPOLOGY I. Metric spaces, continuity, separation axioms,
connectedness,

compactness, and other related topics. Prerequisite: Math 555 with minimum
grade of C. (3)

502. GENERAL TOPOLOGY II. Introduction to algebraic topology. Prerequisite:
Math 501 with

minimum grade of C. (3)

513. THEORY OF NUMBERS I. Congruences; divisibility; properties of prime
numbers; arithmetical

functions; quadratic residues. Prerequisite: Math 305. (3)

514. THEORY OF NUMBERS II. Diophantine equations, distribution of prime
numbers, and an

introduction to algebraic number theory. Prerequisite: Math 513. (3)

519. MATRICES. Basic matrix theory, eigenvalues, eigenvectors, normal
and Hermitian matrices,

similarity, Sylvester’s Law of Inertia, normal forms, functions
of matrices. Prerequisite: Math 319

with minimum grade of C. (3)

520. LINEAR ALGEBRA. An introduction to vector spaces and linear transformations;
eigenvalues,

and the spectral theorem. (3)

525. MODERN ALGEBRA I. General properties of groups. (3)

526. MODERN ALGEBRA II. General properties of rings and fields. Prerequisite:
Math 525. (3)

533. TOPICS IN EUCLIDEAN GEOMETRY. A study of incidence geometry; distance
and

congruence; separation; angular measure, congruences between triangles;
inequalities; parallel

postulate; similarities between triangles; circles area. Prerequisite:
Math 305 with minimum grade

of C. (3)

537. NON-EUCLIDEAN GEOMETRY. Brief review of the foundation of Euclidean
plane geometry

with special emphasis given the Fifth Postulate; hyperbolic plane geometry;
elliptic plane geometry.

(3)

540. HISTORY OF MATHEMATICS. Development of mathematics, especially
algebra, geometry,

and analysis; lives and works of Euclid, Pythagoras, Cardan, Descartes,
Newton, Fuler, and Gauss.

Prerequisite requirements for this course may also be satisfied by consent
of instructor. Prerequisite:

Math 305 with minimum grade of C. (3)

545. SELECTED TOPICS IN MATHEMATICS FOR SECONDARY SCHOOL TEACHERS. High-school
subjects from an advanced point of view and their relation to the more
advanced subjects. (3)

555. ADVANCED CALCULUS I. Limits, continuity, power series, partial
differentiation; multiple,

definite, improper, and line integrals; applications. Prerequisite requirements
for this course may

also be satisfied by consent of instructor. Prerequisite: Math 305 with
minimum grade of C. (3)

556. ADVANCED CALCULUS II. Limits, continuity, power series, partial
differentiation; multiple,

definite, improper, and line integrals; applications. Prerequisite:
Math 555 with minimum grade of

C. (3)

567. INTRODUCTION TO FUNCTIONAL ANALYSIS I. Metric spaces, Normed linear
spaces and

linear operators. Prerequisite requirements for this course may also
be satisfied by consent of

instructor. Prerequisite: Math 556 with minimum grade of C. (3)

568. INTRODUCTION TO FUNCTIONAL ANALYSIS II. Metric spaces, Normed linear
spaces and

linear operators. Prerequisite: Math 567 with minimum grade of C. (3)

572. INTRODUCTION TO PROBABILITY AND STATISTICS. Emphasis on standard
statistical

methods and the application of probability to statistical problems.
Prerequisite: Math 261 with

minimum grade of C, Math 262 with minimum grade of C, Math 263 with
minimum grade of C,

Math 264 with minimum grade of C. (3)

573. APPLIED PROBABILITY. Emphasis on understanding the theory of probability
and knowing

how to apply it. Proofs are given only when they are simple and illuminating.
Among topics

covered are joint, marginal, and conditional distributions, conditional
and unconditional moments,

independence, the weak law of large numbers, Tchebycheff’s inequality,
Central Limit Theorem.

Prerequisite: Math 261 with minimum grade of C, Math 262 with minimum
grade of C, Math 263

with minimum grade of C, Math 264 with minimum grade of C. (3)

574. PROBABILITY. Topics introduced in Math 573 will be covered at a
more sophisticated

mathematical level. Additional topics will include the Borel-Cantelli
Lemma, the Strong Law of

Large Numbers, characteristic functions, fourier transforms. Prerequisite:
Math 573 with minimum

grade of C. (3)

575. MATHEMATICAL STATISTICS I. Mathematical treatment of statistical
and moment

characteristics; frequency distribution; least squares; correlation;
sampling theory. Prerequisite:

Math 262 with minimum grade of C. (3)

576. MATHEMATICAL STATISTICS II. Mathematical treatment of statistical
and moment

characteristics; frequency distribution; least squares; correlation;
sampling theory. Prerequisite:

Math 575 with minimum grade of C. (3)

577. APPLIED STOCHASTIC PROCESSES. Emphasis on the application of the
theory of stochastic

processes to problems in engineering, physics, and economics. Discrete
and continuous time

Markov processes, Brownian Motion, Ergodic theory for stationary processes.
Prerequisite

requirements for this course may also be satisfied by consent of instructor.
Prerequisite: Math 573

with minimum grade of C. (3)

578. STOCHASTIC PROCESSES. Topics will include general diffusions, Martingales,
and Stochastic

differential equations. (3)

590. TECHNIQUES IN TEACHING COLLEGE MATHEMATICS. Directed studies of
methods in the

presentation of college mathematics topics, teaching and testing techniques.
This course is required

of all teaching assistants, each semester, and may not be used for credit
toward a degree. (1-3)

597. SPECIAL PROBLEMS I. (1-3)

598. SPECIAL PROBLEMS II. (1-3)

599. SPECIAL PROBLEMS III. (1-3)