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Mathematics

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)