1994-1995 Undergraduate Catalog
1994-1995 Courses
Mathematics
MATH 010 Intermediate Algebra 3 R
Establishes, or reestablishes, the background of those
who desire to take College Algebra. Experience indicates
that many persons who need college mathematics are not
able to proceed because of a deficient background.
MATH 012 Concepts of Intermediate Algebra 1-3 R
Reviews algebra concepts and skills needed for college
level mathematics courses. Topics (when three credits are
completed) include a review of sets, operations with
polynomial and rational expressions, solving various
types of equations and inequalities and an introduction
to coordinate plane and functions.
RESTRICTIONS: Requires arithmetic skills.
MATH 114 College Mathematics and Statistics 3
Basic algebra skills and concepts with a strong emphasis
on graphing and applications in the areas of management,
life and social sciences. Topics include exponential
functions, logarithms, statistics, linear programming and
arithmetic and geometric sequences.
PREREQ: MATH012 or MATH010.
RESTRICTIONS: Only three credits from any combination of
MATH114, MATH115, MATH170, MATH171 and MATH172 can count
toward graduation.
MATH 115 Pre-Calculus 3
Develops concepts required for calculus around the
unifying notions of a function and the graph of a
function (polynomial, algebraic, exponential,
logarithmic, and trigonometric functions).
RESTRICTIONS: Familiarity with central concepts of
algebra (factoring, solving equations, simplifying
algebraic expression and laws of exponents) recommended.
Only three credits from any combination of MATH114,
MATH115, MATH170, MATH171 and MATH172 can count toward
graduation.
MATH 170 Self-Paced College Mathematics and Statistics 1-3
Stresses algebra concepts and applications, elementary
and trigonometric functions and topics in statistics.
Variable credit allows the student to proceed at his/her
own pace.
RESTRICTIONS: Content same as MATH114 when all three
credits completed. Only three credits from any
combination of MATH114, MATH115, MATH170, MATH171 and
MATH172 can count toward graduation.
MATH 171 Self-Paced Pre-Calculus 1-3
Develops concepts required for calculus around the
concept of a function and its graph. Polynomial,
rational, exponential, logarithmic and trigonometric
functions stressed. Variable credit allows the student to
proceed at his/her own pace.
PREREQ: Intermediate Algebra.
RESTRICTIONS: Content is same as MATH115 when all three
credits completed. Only three credits from any
combination of MATH114, MATH115, MATH170, MATH171 and
MATH172 can count toward graduation.
MATH 172 Algebra and Precalculus 2
Mastery-based algebra review followed by concepts
required for MATH221 developed around functions and their
graphs (polynomial, rational, logarithmic and
exponential).
RESTRICTIONS: Does not satisfy general skills math
requirement. Only three credits from any combination of
MATH114, MATH115, MATH170, MATH171 and MATH172 can count
toward graduation.
MATH 210 Discrete Mathematics I 3
Sets, logic, induction, number systems, counting, finite
probability, introduction to graph theory, sequences and
formal power series.
PREREQ: MATH115.
RESTRICTIONS: Credit cannot be received for both MATH210
and MATH230.
MATH 221 Calculus I 3
Topics include functions, graphing functions, limits,
derivatives, sequences, series, exponential and
logarithmic functions, and integration.
RESTRICTIONS: Requires two years of high school algebra
and one year of geometry. Credit cannot be received for
both MATH221 and MATH241.
MATH 222 Calculus II 3
Topics include integration, Taylor polynomials, series,
multivariable calculus and trigonometric functions.
PREREQ: MATH221.
RESTRICTIONS: For students in the behavioral, management
and social sciences. Credit cannot be received for both
MATH222 and MATH242.
MATH 230 Finite Mathematics with Applications 3
Set theory, probability, optimization, linear programming
and an introduction to matrix methods.
PREREQ: MATH221.
RESTRICTIONS: For students in the behavioral, management
and social sciences. Credit cannot be received for both
MATH230 and MATH210.
MATH 241 Analytic Geometry and Calculus A 4
Functions, limits, continuity, derivatives and definite
integrals.
RESTRICTIONS: Requires two years of high school algebra,
one year of geometry and trigonometry. Credit cannot be
received for both MATH241 and MATH221.
MATH 242 Analytic Geometry and Calculus B 4
Exponential, log and trig functions; integration
techniques; polar coordinates; and vectors.
PREREQ: MATH241.
RESTRICTIONS: Credit cannot be received for both MATH242
and MATH222.
MATH 243 Analytic Geometry and Calculus C 4
Partial derivatives, multiple integrals, line integrals
and series.
PREREQ: MATH242.
MATH 251 Mathematics for the Elementary School I 3
Basic number concepts: numeration, whole numbers,
integers, rational numbers, real numbers and arithmetic
procedures.
MATH 252 Mathematics for the Elementary School II 3
Continuation of MATH251.
PREREQ: MATH251.
MATH 260 Basic Concepts of Analysis 3
The notion of limit, continuity, convergence, uniform
continuity, least upper bound, greatest lower bound,
compactness and connectedness.
PREREQ: MATH243.
MATH 280 Insights into Mathematics 3
A basic course. Mathematics presented as a human
endeavor. Topics include problem solving, reasoning and
modeling.
PREREQ: MATH114 or MATH115.
RESTRICTIONS: For liberal arts students not necessarily
planning further study in mathematics.
MATH 302 Ordinary Differential Equations 3
Solutions of ordinary differential equations of first and
second order; and applications, Laplace transforms,
Fourier series and power series solutions.
PREREQ: MATH243.
RESTRICTIONS: Credit not given for both MATH302 and
either MATH341 or MATH342.
MATH 303 Differential Equations Computing Lab 1
Provides computing experience in differential equations.
COREQ: MATH302.
MATH 305 Applied Mathematics for Chemical Engineering 3
A special applied mathematics course designed for
chemical engineering majors. Emphasis is given on the
interaction between mathematical theory and its
engineering applications.
PREREQ: MATH302.
RESTRICTIONS: For chemical engineering majors (Juniors
and Seniors) only.
MATH 315 Discrete Mathematics II 3
Algorithmic graph theory, correctness and complexity of
algorithms, recurrence relations, numerical algorithms,
algorithms for polynomials (such as Horner's method).
PREREQ: MATH210 and MATH241.
MATH 341 Differential Equations with Linear Algebra I 3
Topics include first and second order differential
equations, systems of algebraic equations, determinants,
vector spaces, eigenvalues and eigenvectors of matrices
and systems of differential equations. Emphasis on the
interaction between these topics and appropriate physical
systems.
PREREQ: MATH242.
RESTRICTIONS: Credit not given for both MATH302 and
MATH341, or both MATH349 and MATH341.
MATH 342 Differential Equations with Linear Algebra II 3
A continuation of MATH341. Topics include series
solutions, Laplace transform methods, boundary value
problems, orthogonality, higher order equations,
difference equations and numerical techniques. Continued
emphasis on the interaction between these topics and
physical systems.
PREREQ: MATH341.
RESTRICTIONS: Credit not given for both MATH349 and
MATH342, or both MATH302 and MATH342.
MATH 349 Elementary Linear Algebra 3
Systems of linear equations, determinants, vector spaces,
linear transformations, eigenvalues and eigenvectors.
PREREQ: MATH230 OR MATH242.
RESTRICTIONS: Credit not given for both MATH349 and
either MATH341 or MATH342.
MATH 366 Independent Study 1-6
MATH 379 Problem Solving Strategies 1
Studies a multitude of problem solving strategies such as
looking for a pattern, making a model, working backwards,
etc.
COREQ: MATH380.
RESTRICTIONS: Requires permission of the Committee on
Secondary School Mathematics. Not for major (B.A. or
B.S.) or minor credit in Mathematical Sciences.
MATH 380 Approaches to Teaching Math 3
Aims, course planning, instructional strategies,
evaluation and selection of materials for teaching
mathematics in secondary schools.
COREQ: MATH379.
RESTRICTIONS: Requires permission of the Committee on
Secondary School Mathematics. Not for major (B.A. or
B.S.) or minor credit in Mathematical Sciences.
MATH 381 Practicum in Secondary Mathematics 1 PF
Teaching experience in a clinical setting, the Math
Center. Helps develop an enquiring attitude: to be a
perceptive observer of the learning behaviors of those
taught, one must develop hypotheses about the causes of
misconceptions, means of diagnosing them and methods of
treatment (including uses of technology).
COREQ: MATH243.
RESTRICTIONS: Requires permission of the Committee on
Secondary School Mathematics. Not for major (B.A. or
B.S.) or minor credit in Mathematical Sciences.
MATH 389 Graph Theory 3
Basic graph theory (paths and circuits, trees and
forests, connectivity and coloring theorems) and network
flow theory. Applications to areas such as economics,
engineering, chemistry and sociology.
PREREQ: MATH210.
MATH 426 Introduction to Numerical Analysis and Algorithmic
Computation 3
Direct and iterative methods for solution of algebraic
equations and systems of linear equations, matrix
inversion, pseudo-inverses, algebraic eigenvalue
problems, linear least-square problems and nonlinear
equations. Stresses both numerical analysis and
algorithmic aspects. May be cross-listed with CISC410.
PREREQ: MATH349 and CISC106.
RESTRICTIONS: Requires familiarity with computing (e.g.,
programming language).
MATH 428 Algorithmic and Numerical Solution of Differential
Equations 3
Algorithms for numerical integration and differentiation.
Initial value problems; boundary value problems in
ordinary differential equations; finite difference
(explicit and implicit) methods; polynomial and spline
approximation; finite elements and collocation; and
introduction to numerical methods for partial
differential equations. May be cross-listed with CISC411.
PREREQ: MATH426 or CISC410.
MATH 450 Abstract Algebra 3
Integers, modular arithmetic, euclidean algorithm and
chinese remainder theorem, polynomial rings, including
the fundamental theorem of algebra and lagrange
interpolation. Introduction to field theory, primitive
elements and simple extensions.
PREREQ: MATH349.
MATH 466 Independent Study 1-6
MATH 503 Advanced Calculus for Applications 3
Multivariable calculus, vector calculus, infinite series,
uniform convergence and Fourier analysis.
PREREQ: MATH302.
MATH 508 Introduction to Complex Variables and Applications 3
Introduction to analytic functions, contour integration,
power series, residues and conformal mapping.
PREREQ: MATH243.
MATH 514 Topics in Advanced Mathematics for Engineers 3
Basic methods of analysis: introduction to complex
variables; special functions including Bessel functions
and Legendre polynomials; Fourier series and integrals;
partial differential equations; and emphasis on
engineering applications.
PREREQ: MATH302.
RESTRICTIONS: For engineering students.
MATH 518 Mathematical Models and Applications 3
Illustration and analysis of mathematical models for
problems in the biological, physical and social sciences.
PREREQ: Either MATH230, or MATH349 and STAT370.
MATH 529 Linear Programming: Methods and Applications 3
Theory of linear programming (linear inequalities, convex
polyhedra, duality), related topics (games, integer
programming), main algorithms (simplex, dual) and
representative applications in agriculture, economics,
engineering, operations research and mathematics.
Familiarity with computer implementation of LP methods
acquired by individual (or small group) projects of
applying LP to the students' chosen areas.
PREREQ: MATH349.
MATH 540 Geometry 3
Axiomatic systems; transformations; Euclidean, projective
and hyperbolic geometry.
PREREQ: MATH349.
RESTRICTIONS: Graduate credit only for teachers.
MATH 555 Applied Calculus for Business and Economics 3
Accelerated version of the usual two-semester
undergraduate preparation in calculus.
RESTRICTIONS: Requires high school algebra. Designed for
students enrolling in M.B.A. program.
MATH 600 Fundamentals of Real Analysis 3
Rigorous introduction to classical real analysis. Brief
review of real numbers and a thorough discussion of the
basic topology of metric spaces. Covers in detail the
following topics: the analysis of sequences and series,
continuity, differentiation and Taylors theorem, and the
analysis of sequences and series of functions.
RESTRICTIONS: Credit not given for both MATH600 and
MATH601.
MATH 601 Advanced Calculus - Introduction to Analysis I 3
Limits, continuity, sequences and series, theory of
differentiation and integration, and several variable
calculus.
PREREQ: MATH260.
RESTRICTIONS: Credit not given for both MATH600 and
MATH601.
MATH 602 Advanced Calculus - Introduction to Analysis II 3
Continuation of MATH600 OR MATH601.
PREREQ: MATH600 or MATH601.
MATH 605 Applied Functional Analysis 3
Introduction to formulation and solution of problems of
engineering and science by means of functional analytic
methods in Hilbert and Banach spaces. Includes boundary
and initial value problems in ordinary and partial
differential equations as well as integral equations.
Emphasis on constructive techniques: variational methods,
approximate solutions, bounds for eigenvalues, etc.
PREREQ: MATH514, PHYS608, MEEG864 or advanced calculus.
MATH 609 Intermediate Ordinary Differential Equations with
Applications 3
Theory and applications of ordinary differential
equations; existence theorems of linear and nonlinear
systems, oscillation theorems, stability theory, and
Sturm-Liouville theory.
PREREQ: MATH302, MATH349 and one semester of advanced
calculus.
MATH 610 Introduction to Partial Differential Equations
with Applications 3
Introduction to partial differential equations: equations
of mathematical physics and their classical theories
emphasizing boundary and initial value problems and their
interpretations.
PREREQ: Two semesters of advanced calculus.
MATH 611 Introduction to Numerical Analysis and Scientific
Computing I 3
Introduction to numerical computing, analysis and
solution of systems of linear equations, linear least-
squares, eigenvalue problems, methods for unconstrained
optimization, solution of systems of nonlinear equations.
Experience with standard computer packages, code
development and simulations of applied problems.
PREREQ: MATH503 or MEEG863 or PHYS207.
MATH 612 Introduction to Numerical Analysis and Scientific
Computing II 3
Approximation, interpolation, data fitting and smoothing,
numerical methods for ordinary differential equations.
Additional topic selected at discretion of instructor.
Experience with standard computer packages, code
development and simulations of applied problems.
PREREQ: MATH503 or MEEG863 or PHYS207.
MATH 613 Applied Symbolic Computation 3
See CISC623 for course description.
MATH 616 Introduction to Applied Mathematics I 3
Introduction to formulation of mathematical problems for
systems of interest outside mathematics, particularly
those from engineering and physics; systems studied vary;
emphasis on interplay between system and mathematical
model.
PREREQ: Two semesters of advanced calculus and PHYS208.
MATH 617 Introduction to Applied Mathematics II 3
Methods of attack on mathematical problems for systems of
interest outside mathematics; calculus of variations
techniques; and interpretation of solutions to problems
in terms of systems.
PREREQ: MATH616.
RESTRICTIONS: Familiarity with systems treated acceptable
in lieu of Prereq.
MATH 630 Probability Theory and Applications 3
Introduction to probability theory as background for
further work in statistics or stochastic processes.
Sample spaces and axioms of probability; discrete sample
spaces having equally likely events; conditional
probability and independence; random variables, classical
discrete and continuous random variables; mathematical
expectation and moments of a distribution; Chebyshev's
inequality; and law of large numbers and central limit
theorem. May be cross-listed with STAT601.
MATH 631 Introduction to Stochastic Processes 3
Classical stochastic processes with emphasis on their
properties, which do not involve measure theory. Course
contents: Markov chains in discrete and in continuous
time with examples from random walk, birth and death
processes, branching processes and queueing theory.
Renewal and Markov renewal processes. Basic notions of
Brownian motion and second-order processes.
PREREQ: MATH630.
MATH 632 Topics in Applied Probability 3
The application of probability theory or stochastic
processes in a specific area of science. May include
treatment of probabilistic methods not ordinarily covered
in other courses. Possible topics are the theory of
queues, dams and inventories, replacement and
reliability, probability models in population growth and
biomathematics, Monte Carlo simulation, algorithmic
methods in probability and operational methods.
MATH 650 Abstract Algebra 3
Modular arithmetic, Chinese remainder theorem, rings
(including polynomial rings), ideals and quotient rings,
groups and homomorphism theorems, unique factorization
and principal ideal domains, field extensions.
PREREQ: MATH349.
MATH 672 Vector Spaces 3
Vector spaces, linear transformations, decomposition
theorems and bilinear forms.
PREREQ: MATH349.
MATH 688 Combinatorics and Graph Theory with Applications I 3
Permutations and combinations, generating functions and
other enumeration techniques, recurrence relations, basic
graph theory, partially ordered sets, combinatorial
optimization and time complexity.
PREREQ: An undergraduate course in linear algebra.
MATH 689 Combinatorics and Graph Theory with Applications II 3
Selected topics from graph theory, combinatorial designs,
finite geometries, extremal and probabilistic
combinatorics. Applications to combinatorial
optimization, experimental design and analysis of
algorithms.
PREREQ: MATH688.
COREQ: MATH650.
MATH 694 Methods of Optimization 3
Review of linear programming, unconstrained and
constrained non-linear programs, numerical methods, Kuhn-
Tucker theory, duality and Lagrange multipliers.
MATH 698 Thematic Seminar 2 PF
Problems oriented class, topics vary from year to year.
Aim is to give students research experience in
mathematics and to show how mathematics is used to solve
problems.
MATH 801 Calculus of Variations 3
Comprehensive introduction to variational principles and
methods in science and engineering; classical calculus of
variations with applications to mechanics; problems of
optimal control; direct methods including the method of
Faedo-Gelerkin. Emphasis on applications.
RESTRICTIONS: Requires familiarity with concepts of
advanced calculus.
MATH 804 Topics in Optimization 3
Selected topics from the following: variational
inequalities theory of optimal control, complex analysis
and nonsmooth optimization, game theory, and optimization
algorithms.
MATH 805 Analysis I 3
Topics include Lebesgue measure and integration, absolute
continuity and functions of bounded variations, Lp spaces
and Fubini's theorem.
PREREQ: MATH602.
MATH 806 Analysis II 3
Fundamental structures of modern analysis with special
emphasis on the theory of Hilbert space, spectral
theorems and application to integral and differential
equations.
PREREQ: MATH805.
MATH 807 Complex Analysis 3
Complex numbers; analytic functions; geometry of
elementary functions; integrals; power series; residues
and poles.
PREREQ: MATH602.
MATH 808 Complex Analysis 3
Conformal mapping with applications; analytic
continuation; Riemann surfaces; elliptic functions; and
infinite products.
PREREQ: MATH807.
MATH 811 Topics in Classical Analysis 3
Investigation of topics chosen from function theory such
as geometric function theory, Riemann surfaces,
meromorphic and entire functions, etc.
RESTRICTIONS: Requires permission of instructor.
MATH 815 Functional Analysis 3
Topological vector spaces with short introductory review
of Banach spaces.
PREREQ: MATH806.
MATH 818 Theory of Ordinary Differential Equations 3
Linear systems with isolated singularities and systems
with periodic coefficients; boundary value problems;
Poincare-Bendixson theory.
PREREQ: MATH609 and MATH805.
MATH 819 Theory of Ordinary Differential Equations 3
Singular Sturm-Liouville theory; asymptotic behavior of
linear and nonlinear systems; and topics of current
research.
PREREQ: MATH818.
MATH 822 Integral Equations 3
Fredholm and Hilbert-Schmidt theories of Fredholm
integral equations of the second kind. Equations of the
first kind. Volterra equations. Nonlinear eigenvalue
problems. Applications to physics and engineering.
RESTRICTIONS: Requires permission of instructor.
MATH 823 Integral Equations 3
Singular integral equations (Carleman and Wiener-Hopf
equations). Nonlinear integral equations (Volterra and
Hammerstein equations). Nonlinear singular integral
equations. Applications to physics and engineering (the
nonlinear oscillator, the airfoil equation, the Tricomi
Problem in partial differential equations, etc.).
PREREQ: MATH822.
MATH 824 Topics in Applied Mathematics 3
Topics chosen from asymptotic analysis, elasticity,
electromagnetic theory, fluid dynamics, optimal control
theory and other areas.
RESTRICTIONS: Requires permission of instructor.
MATH 825 Topics in Applied Mathematics 3
Topics chosen from asymptotic analysis, elasticity,
electromagnetic theory, fluid dynamics, optimal control
theory and other areas.
RESTRICTIONS: Requires permission of instructor.
MATH 827 General Topology I 3
Generation and properties of topological spaces.
Continuity, separation and countability properties; and
convergence of nets and filters.
MATH 828 General Topology II 3
Compactness and connectedness, metrization, uniform
spaces and basic homotopy theory.
PREREQ: MATH827.
MATH 835 Partial Differential Equations I 3
First order differential equations and systems. Existence
and uniqueness for elliptic, parabolic and hyperbolic
equations. Boundary and initial value problems for
equations of hyperbolic and parabolic type in two
independent variables. Classical approaches employed.
PREREQ: MATH610.
MATH 836 Partial Differential Equations II 3
Cauchy's problem and initial boundary value problems for
hyperbolic and parabolic equations and systems. Boundary
value problems for elliptic equations and systems.
Equations of mixed type. Emphasis on modern approaches.
PREREQ: MATH835 and MATH805.
MATH 838 Numerical Methods for Partial Differential
Equations 3
Introduces concepts of consistency, stability and
convergence of numerical schemes. Emphasis on various
finite difference schemes and their applications to
fundamental partial differential equations.
PREREQ: MATH610.
MATH 839 Numerical Methods for Partial Differential
Equations 3
Emphasis on finite element method and its applications to
physical problems.
PREREQ: MATH838.
MATH 845 Group Theory with Applications 3
Groups acting on sets, the class equation, Sylow's
theorems, free groups, classical groups, Polya
enumeration theory, groups and graphs, Frieze groups and
crystallographic groups, and the group Knapsack problem.
PREREQ: MATH650.
MATH 846 Field Theory with Applications 3
Field extensions, structure of finite fields, and basics
of Galois theory. Applications of finite fields to block
designs and finite geometries. Additional applications
may include impulse response sequences, pseudorandom
sequences, algebraic coding theory (BCH and Goppa codes)
and cryptosystems.
PREREQ: MATH650, MATH672, and MATH845.
MATH 850 Foundation of Probability Theory 3
Mathematically rigorous treatment of the foundations of
probability theory. Families of sets, semi-ring and sigma
algebras, axioms of probability, and extension theorem.
Random variables, probability distributions, and modes of
convergence for sequences of random variables. Product
measure and independence and conditional expectation. The
weak and strong laws of large numbers, the central limit
theorem and the law of the iterated logarithm.
PREREQ: MATH630 and MATH805.
MATH 851 Stochastic Processes 3
Mathematically rigorous treatment of stochastic
processes. Course content: general definitions,
separability, Kolmogorov consistency condition. Markov
processes and Brownian motion. In-depth discussion of
topics such as weak convergence of processes, martingale
theory, diffusion processes or second order processes, as
announced by instructor.
PREREQ: MATH850.
MATH 868 Research 1-6
MATH 869 Master's Thesis 1-6
MATH 870 Reading in Mathematics 1-6
MATH 887 Mathematical Methods of Physics and Engineering 3
Green's function and eigenfunction expansions for
boundary value problems, theory of distributions, weak
solution, metric spaces, contractions, integral equations
and Hilbert spaces.
PREREQ: MATH503, MATH508 or MEEG863, MEEG864 or PHYS607,
and PHYS608.
MATH 964 Pre-Candidacy Study 3-12 PF
Research and readings in preparation of dissertation
topic and/or qualifying examinations for doctoral
students before admission to candidacy but after
completion of all required course work.
RESTRICTIONS: Not open to students who have been admitted
to candidacy.
MATH 969 Doctoral Dissertation 1-12 PF