University of Delaware
1995-1996 Undergraduate Catalog
1995-1996 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 179 Problem Solving Strategies I 1
Designed to study a multitude of problem solving strategies such as
working backwards, look for a pattern, etc. In particular, will
emphasize the use of these strategies with the content that secondary
mathematics teachers normally teach.
PREREQ: MATH241.
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 series.
PREREQ: MATH241.
RESTRICTIONS: Credit cannot be received for both MATH242 and MATH222.
MATH 243 Analytic Geometry and Calculus C 4
Vectors, partial derivatives, multiple integrals, line integrals and
Green's Theorem.
PREREQ: MATH242.
MATH 245 An Introduction to Proof 3
Basic set operations, relations, equivalence relations, functions,
inverse functions, cardinality, order properties of real numbers, least
upper bound, greatest lower bound, completeness axiom, topology of
reals, complex numbers.
PREREQ: MATH243.
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 401 Advanced Calculus 3
A rigorous treatment of one variable calculus. Topics will include
sequences of real numbers, limit theorems, monotone sequences, Cauchy
sequences, Bolzanno-Weierstrass Theorem, continuity, uniform continuity,
differentiability and Riemann integral.
PREREQ: MATH245.
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 451 Abstract Alegbra I 3
Basic properties of the integers and the rationals, fields of quotients,
polynomial rings, root-finding, introduction to groups and vector
spaces.
PREREQ: MATH349 and MATH260.
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 510 Modeling and Analysis of Environmental Systems 3
An elementary course to introduce basic analytical and numerical methods
for studying mathematical problems arising in environmental sciences.
PREREQ: MATH242 or equivalent.
RESTRICTIONS: Open to Environmental Science graduate students or by
consent of instructor.
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 Taylor's theorem, and the
analysis of sequences and series of functions.
PREREQ: MATH245.
MATH 602 Advanced Calculus - Introduction to Analysis II 3
Continuation of MATH600 OR MATH601.
PREREQ: MATH600.
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: One semester 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: One semester 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 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 Analysis 3
Investigation of topics chosen from function theory, functional
analysis, optimization, 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 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