Southwestern University
2000-2001 Catalog

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 Michael John McCarthy, PhD (part-time)
Instructor Vijay Kumar Chhipa, PhD (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 51-154, 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 54-493, 54-633, 54-653, 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 54-493, 54-633, 54-653, 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 54-043, 54-183, 54-283, 54-393, 54-453 and 54-473.

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. (Fall, odd years)

52-573 PROBABILITY. Random variables and distributions, sequences of random variables, and stochastic processes. Prerequisites: Mathematics 52-154 and consent of instructor. (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. (Spring)

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 presentation beyond the classroom of major work or of a semester project is expected from each student. Prerequisite: 21 semester hours in the major at the 200-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.

54-043 INTRODUCTION TO COMPUTING. This course emphasizes the use of the computer as a tool for problem solving and quantitative reasoning. It introduces the student to the discipline of computer science through its history, its various content areas, and its relationship to a liberal arts education. After a review of application programs such as word-processing, spreadsheet programs, presentation software and web-based tools, topics will include an introduction to interface design, programming in a web-based language, language translation, logic design, artificial intelligence, interpretation of data, and social issues involved with the use and misuse of computers. May not be used for Computer Science major or minor. (Spring)

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)

54-283 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 modelling 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)

54-493 FORMAL DERIVATION OF PROGRAMS (Formerly: Programming Methodology). Characterization of semantics by predicate transformers, the calculus of weakest preconditions, program design guided by proofs of correctness, design of guarded command sets, design of loops using loop invariants and variant functions. Prerequisite: Computer Science 54-283. (Spring, even years)

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. Emphasizes the derivations and applications of numerical techniques most frequently used by scientists: interpolation, approximation, numerical differentiation and integration, zeroes of functions; solution of linear systems. Prerequisites: Mathematics 52-253, 52-673 and Computer Science 54-183. Also 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). Prerequisite: 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 AUTOMATA THEORY. 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)

54-893 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.