Southwestern University
2001-2002 Catalog
Southwestern University: A Statement
The Academic Program
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MATHEMATICS AND COMPUTER SCIENCE DEPARTMENT
Division of Natural Sciences
Associate Professor Gary H. Richter,
PhD, Chair
Associate Professor Kendall C. Richards, PhD, Associate
Chair
Professor John B. Chapman, PhD
Professor Walter M. Potter, PhD
Associate Professor Richard T. Denman, PhD
Associate Professor Barbara
Boucher Owens, PhD
Associate Professor Therese N. Shelton, PhD
Assistant
Professor Suzanne Fox Buchele, PhD
Assistant Professor Cameron Cunningham
Sawyer, PhD
Assistant Professor Jayne Harder, PhD (part-time)
Assistant
Professor Michael J. McCarthy, PhD (part-time)
Assistant Professor Philip
Owens, PhD (part-time)
Assistant Professor Cuihua Zhang, MA
(part-time)
Mathematics and Computer Science courses help students
develop concise and logical patterns of thinking and encourage independent and
creative work. The Department seeks to develop in students an understanding of
mathematical models and a facility with problem-solving techniques.
The
Department offers the following three majors leading to either the Bachelor of
Science or the Bachelor of Arts degree: Mathematics, Computer Science, and
Computational Mathematics. The Department also offers a minor in Mathematics and
in Computer Science. Each student’s major program must be determined in
consultation with the student’s academic advisor; the program should
reflect the student’s personal needs and goals. All majors in the
department are required to successfully complete the designated senior seminar
in their respective majors or to carry out a Department-approved senior project
to satisfy the capstone-experience requirement. Note: A minimum grade of C- must
be earned in any course if it is to count as a prerequisite for a subsequent
Mathematics or Computer Science course.
The major in Mathematics requires 34
semester hours in Mathematics and must include 52-154, 52-253, 52-353, 52-673,
52-683, 52-753, 52-853, 52-893, and three additional mathematics courses at the
300-level or above, (including at least one from 52-693, 52-763, 52-863,
52-883). The major in Mathematics also requires at least one computer science
course at the 100-level or above, preferably to be completed no later than the
sophomore year. The minor in Mathematics must include 52-154, 52-253, 52-353,
52-673, and two Mathematics courses at the 300-level or above.
The major in
Computer Science requires 33 semester hours in Computer Science and must include
54-183, 54-283, 54-393, 54-453, 54-473, 54-483, 54-893, and four additional
Computer Science courses at the 300-level or above, (including at least one from
54-633, 54-653,54-683, 54-723). The major in Computer Science also requires
Mathematics 52-154, 52-253, and 52-673. The minor in Computer
Science requires 18 semester hours in Computer Science, of which 12 must be
at the 200 level or above.
The Computational Mathematics major is designed
to provide students with a foundational mastery of the interdependent
disciplines of Mathematics and Computer Science. The curriculum is a blend of
core courses intended to provide a broad knowledge base while maintaining depth
in both subject areas. The major in Computational Mathematics requires 48
semester hours and must include Computer Science 54-183, 54-283, 54-393, 54-453,
54-473, 54-483; Mathematics 52-154, 52-253, 52-353, 52-523, 52-673, 52-753; the
capstone (either 52-893 or 54-893); at least one course from 52-683, 52-853; and
at least one from 54-633, 54-653, 54-683, 54-723.
A teaching field in
Mathematics requires 24 semester hours at least 12 of which must be advanced.
The 24 hours must include 52-154, 52-213, 52-253, 52-403, 52-673, and 52-683.
The additional six hours would generally be selected from 52-353, 52-373,
52-573, 52-693, or 52-843. An elementary academic specialization in
Mathematics requires 18 semester hours with at least nine advanced. Required
courses are 52-154, 52-203, 52-213, and 52-673 with two courses from 52-123,
52-253, 52-373, 52-403, and 52-683 recommended as the additional six semester
hours. The 24 semester hour teaching field in Computer Science must include
54-143,
54-183, 54-283, 54-393, 54-453 and 54-473.
Mathematics (MAT)
52-123 ELEMENTARY FUNCTION THEORY. Relations, functions, and general
properties of functions. Polynomial, exponential, logarithmic, and circular
functions, analytic geometry in the plane. May not be used for mathematics major
or minor. (Each semester)
52-154 CALCULUS I. Functions and graphs;
derivatives, applications of differentiation. Exponential and trigonometric
functions, integration, applications of integration. The course includes a
laboratory component designed to explore applications and to enhance
conceptualization. Prerequisite: Departmental approval. (Each semester)
52-203 MATHEMATICAL CONCEPTS. An introduction to some of the
important ideas in mathematics illustrating the scope and spirit of mathematics
and emphasizing the role that mathematics plays in society from a historical
point of view. Topics include number systems, Euclidean and non-Euclidean
geometry, set theory and cardinality, and modern algebra and the axiomatic
method. The course is suitable for a general audience with a broad spectrum of
backgrounds and abilities. May not be used for Mathematics major or minor. (Each
semester)
52-213 INTRODUCTION TO STATISTICS. A course designed to
provide students in the social and biological sciences with the skills necessary
to perform elementary statistical analysis. Descriptive measures, probability,
sampling theory, random variables, binomial and normal distributions, estimation
and hypothesis testing, analysis of variance, regression and correlation,
nonparametric methods. May not be used for Mathematics major or minor. (Each
semester)
52-253 CALCULUS II. Numerical integration, methods of
integration, applications of the definite integral, improper integrals,
sequences and series, Taylor’s Formula and approximation, polar
coordinates. Prerequisite: Mathematics 52-154. (Each semester)
52-353
CALCULUS III. A course in multivariable calculus. Vectors, vector
functions, and curves. Functions of several variables, partial differentiation,
multiple integration, applications of partial differentiation and of multiple
integrals. Vector calculus, line integrals, Green’s Theorem, surface
integrals. Prerequisite: Mathematics 52-253. (Each semester)
52-373
MATHEMATICAL MODELING. A course designed to introduce the application of
mathematics to the social and natural sciences. Topics may include linear and
non-linear difference equations and probabilistic models. The course is
project-driven and requires written reports of the mathematics interpreted
within the context of the particular project. Prerequisite: Mathematics 52-253
or consent of instructor. (Spring, even years)
52-403 GEOMETRY.
Topics to be selected from synthetic geometry, analytic geometry, projective
geometry, Euclidean and non-Euclidean geometry. Prerequisite: Consent of
instructor. (Spring)
52-523 INTRODUCTION TO NUMERICAL ANALYSIS.
Emphasizes the derivations and applications of numerical techniques most
frequently used by scientists: interpolation, approximation, numerical
differentiation and integration, zeroes of functions, and solution of linear
systems. Prerequisites: 52-253, 52-673, and 54-183. Also Computer Science
54-523. (Spring)
52-573 PROBABILITY. Random variables and
distributions, sequences of random variables, and stochastic processes.
Prerequisite: Mathematics 52-253. (Spring, odd years)
52-673 LINEAR
ALGEBRA. Linear equations and matrices, vector spaces, linear mappings,
determinants, quadratic forms, vector products, groups of symmetries.
Prerequisite: Mathematics 52-253 or consent of instructor. (Each semester)
52-683 ALGEBRAIC STRUCTURES I. Sets, relations, functions, group
theory, ring theory. Prerequisite: Mathematics 52-673 or consent of instructor.
(Fall)
52-693 ALGEBRAIC STRUCTURES II. Vector spaces, algebraic
field theory. Prerequisite: Mathematics 52-683. (Spring, odd years)
52-753 ELEMENTARY DIFFERENTIAL EQUATIONS. Topics include first order
differential equations, separable equations, exact equations, linear
differential equations of order n>1, homogeneous equations with constant
coefficients, non-homogeneous equations and the method of undetermined
coefficients, variation of parameters, power series solutions, and applications.
Prerequisite: Mathematics 52-673 or consent of instructor. (Fall)
52-763
INTERMEDIATE DIFFERENTIAL EQUATIONS. Topics include the Laplace transform,
linear systems, numerical solutions, and nonlinear systems. An introduction to
partial differential equations may also be included. Prerequisites: Mathematics
52-353 and 52-753. (Spring, even years)
52-843 SEMINAR IN SPECIAL
TOPICS. A limited enrollment seminar in a major area of mathematics not
generally covered in other courses. Topics may include but are not limited to
advanced analysis, combinatorics, logic, history of mathematics. May be repeated
for credit as topics vary. Prerequisite: 9 hours of 200 level or higher courses
and consent of instructor.
52-853 INTRODUCTORY ANALYSIS. Topics may
include completeness, topology of the reals, sequences, limits and continuity,
differentiation, integration, infinite series, and sequences and series of
functions. A rigorous approach to learning and writing proofs is emphasized.
Prerequisite: 52-353 or consent of instructor. (Spring)
52-863 COMPLEX
ANALYSIS. Algebra and geometry of complex numbers. Analytic functions,
integration, series, contour integration, analytic continuation, conformal maps,
boundary values, and transforms. Prerequisite: Mathematics 52-353 or consent of
instructor. (Fall, even years)
52-883 TOPOLOGY. Topology of the line
and plane, limit points, open sets, closed sets, connectedness, compactness.
Continuous functions, homeomorphisms. Prerequisite: Mathematics 52-253. (Fall,
odd years)
52-893 SENIOR SEMINAR IN MATHEMATICAL MODELING. This
course will fulfill the capstone requirement in mathematics. Since it serves as
a culmination of the student’s undergraduate mathematical experience, a
balance is sought between application and theory. Topics may include linear and
non-linear differential and difference equations and stochastic methods. Topics
may vary with the instructor. Applications will be taken from the social and
natural sciences. A major semester project is expected from each student, as
well as significant class participation and presentation. Prerequisites: 21
hours in the major at the 200-level or above, 3 hours of Computer Science at the
100-level or above, and consent of instructor. (Fall)
52-301, 302, 303 SELECTED TOPICS. May be repeated with change in topic. Prerequisite: Consent of instructor.
52-951, 952, 953 INDEPENDENT STUDY.
52-983 HONORS.
Computer Science (CSC)
54-143 INTRODUCTION TO PROGRAMMING. An introduction to computer
programming in an object-oriented style for practical application. Topics
include class definition, basic program constructs, basic data structures,
interactive user interfaces, and encapsulation. This course satisfies the
General Education Mathematics requirement. (Each semester)
54-183
COMPUTER SCIENCE I. Computer programming in an object-oriented style.
Topics include primitive types and operations, assignment, selection, iteration,
arrays, classes, methods, recursion, encapsulation, type extension, inheritance,
and reasoning about programs. Prerequisite: Previous programming with
Departmental approval, or 54-143. (Each semester)
54-191 SEMINAR IN
ELEMENTARY SOFTWARE ENGINEERING. Project-based (one credit hour) course
emphasizing current tools and methodologies. Students may work in groups on
projects chosen in conjunction with the instructor. Prerequisite: Consent of the
instructor. This course may be repeated for credit.
54-283 COMPUTER
SCIENCE II. A continuation of 54-183, with an emphasis on abstract data
objects such as lists, stacks, queues, trees, and graphs. Topics include
algorithms for searching, sorting, traversing, inserting, and deleting, and
reasoning about these algorithms. Prerequisite: Computer Science 54-183 or
consent of instructor. (Each semester)
54-393 COMPUTER ORGANIZATION.
Computer architecture, internal representation of data, assembly language
programming, subroutines and parameter passing, design of machine language
instruction sets, bus structure, datapath and command interpreter. Prerequisite:
Computer Science 54-283 or consent of instructor. (Fall)
54-453
ALGORITHMS (Formerly: Data Structures). Algorithms for finding paths and
spanning trees in graphs, analysis of algorithms for sorting, searching, and
merging files, complexity of algorithms, hashing methods. Prerequisite: Computer
Science 54-283 or consent of instructor. (Fall)
54-473 PROGRAMMING
LANGUAGES. Principles and practice in the design and implementation of
imperative, functional, and object-oriented programming languages. Prerequisite:
Computer Science 54-393 or consent of instructor. (Spring)
54-483
DISCRETE MATHEMATICS. Concepts for modeling discrete phenomena. Topics
include: logic, set theory, order theory and lattices, graphs, induction, and
recurrence relations. Prerequisites: Mathematics 52-253 and Computer Science
54-283, or consent of instructor. (Spring)
54-513 DATABASE
MANAGEMENT. Logical and physical organization of data in conventional
database systems. Topics include: functional dependencies and normal form;
relational and other data models; indexing; and concurrency control.
Prerequisite: Computer Science 54-283 or consent of instructor. (Fall, even
years)
54-523 INTRODUCTION TO NUMERICAL ANALYSIS. See Mathematics
52-523. (Fall, odd years)
54-533 FUNCTIONAL PROGRAMMING.
Introduction to functional programming. Topics include functions, lists, types,
induction and recursion, pattern matching, infinite lists and trees. A
functional programming language such as Lisp, ML or Gofer will be used in the
course. There will be a large number of programming projects. Prerequisite:
Computer Science 54-183 or consent of instructor. (Spring, even years)
54-553 COMPUTER GRAPHICS. Introduction to 2D and 3D graphics. Topics
include: display hardware, graphics primitives and data structures, geometric
transformations and modeling, 2D display algorithms, 3D viewing, clipping,
hidden line and surface removal, illumination, and shading. Prerequisite:
Mathematics 52-673, and Computer Science 54-393 and 54-453, or consent of
instructor. (Fall, odd years)
54-573 ARTIFICIAL INTELLIGENCE.
Introduction to a functional programming language; study of tree and graph
searching, heuristics, knowledge representation schemes, predicate logic,
resolution theory, natural language and vision processing, and expert systems.
Prerequisite: Computer Science 54-283 or consent of instructor. (Spring, odd
years)
54-633 COMPUTER ARCHITECTURE. Introduction to computer
architecture and analysis of the performance of computer systems, especially
with respect to architectural and organizational issues. Topics include memory
instruction set architecture, pipelining, and memory hierarchy (including cache
and virtual memory). Prerequisites: Computer Science 54-393 and 54-483, or
consent of instructor. (Fall, even years)
54-653 COMPILER DESIGN. A
study of the theoretical aspects of parsing context-free languages, translation
specifications, and code optimization. Topics include context-free grammars,
lexical scanning, symbol tables, and parsing by the method of recursive descent.
Prerequisites: Computer Science 54-473 and 54-483 or consent of instructor.
(Spring, odd years)
54-683 THEORY OF COMPUTATION. Finite state
systems, finite automata, formal language theory. Context-free grammars, regular
expressions, pushdown automata, Turing machines, decidability, switching theory.
Prerequisite: Computer Science 54-483. (Fall, even years)
54-723 OPERATING SYSTEMS. Procedure activation and deactivation,
system structure, management of both memory and processes, and recovery
procedures. Prerequisite: Computer Science 54-393 or consent of instructor.
(Fall, odd years)
54-843 SEMINAR IN SPECIAL TOPICS. A limited
enrollment seminar in a major area of computer science not generally covered in
other courses. May be repeated for credit as topics vary. Prerequisites: 9 hours
of 200-level courses or higher and consent of instructor.
54-893 SENIOR
SEMINAR IN SOFTWARE ENGINEERING. Introduction to techniques and theories for
the development of large software systems. This course will fulfill the capstone
requirement in Computer Science. Topics include: software design and quality,
ethics, professional issues, and the study of current software engineering
trends, theory, and practice. A major semester project is expected from each
student, as well as significant class participation and presentation.
Prerequisite: 21 semester hours in the major at the 200-level or above including
54-453, 54-473, 54-483, and consent of instructor. (Spring)
54-301, 302, 303 SELECTED TOPICS. May be repeated with change in topic. Prerequisite: Consent of instructor.
54-951, 952, 953 INDEPENDENT STUDY. May be repeated with change in
content.
54-983 HONORS.