Southwestern University
2004-2005 Catalog
Southwestern University: A Statement
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Mathematics and Computer Science Department
Division of Natural Sciences
Associate Professor Therese N. Shelton, PhD, Chair
Professor John B. Chapman, PhD
Professor Walter M. Potter, PhD
Professor Kendall C. Richards, PhD
Associate Professor Richard T. Denman, PhD
Associate Professor Barbara Boucher Owens, PhD
Associate Professor Gary H. Richter, PhD
Assistant Professor Suzanne Fox Buchele, PhD
Assistant Professor Cameron Cunningham Sawyer, PhD
Visiting Assistant Professor Anand Pardhanani, PhD
Instructor Andre Budinszky, MS (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 Calculus I, 52-253 Calculus II, 52-353 Calculus III, 52-673 Linear Algebra, 52-683 Algebraic Structures I, 52-753 Elementary Differential Equations, 52-853 Introductory Analysis, 52-893 Senior Seminar in Mathematical Modeling, 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 Calculus I, 52-253 Calculus II, 52-353 Calculus III, 52-673 Linear Algebra, and two Mathematics courses at the 200-level or above.
The major in Computer Science requires 33 semester hours in Computer Science and must include 54-183 Computer Science I, 54-283 Computer Science II, 54-383 Discrete Mathematics, 54-393 Computer Organization, 54-453 Algorithms, 54-473 Programming Languages, 54-643 Computer Systems, 54-893 Senior Seminar in Software Engineering, and three additional Computer Science courses at the 300-level or above. The major in Computer Science also requires 52-154 Calculus I, 52-253 Calculus II, and 52-673 Linear Algebra. The minor in Computer Science requires 18 semester hours in Computer Science, 12 of which 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 54-183 Computer Science I, 54-283 Computer Science II, 54-383 Discrete Mathematics, 54-393 Computer Organization, 54-453 Algorithms, 54-473 Programming Languages, 54-643 Computer Systems, 52-154 Calculus I, 52-253 Calculus II, 52-353 Calculus III, 52-523 Introduction to Numerical Analysis, 52-673 Linear Algebra, 52-753 Elementary Differential Equations; the capstone (either 52-893 Senior Seminar in Mathematical Modeling or 54-893 Senior Seminar in Software Engineering); and at least one course from 52-683 Algebraic Structures I, or 52-853 Introductory Analysis.
A teaching field in Mathematics requires 24 semester hours, at least 12 of which must be advanced. The 24 hours must include 52-113 Introduction to Statistics, 52-154 Calculus I, 52-253 Calculus II, 52-403 Geometry, 52-673 Linear Algebra, and 52-683 Algebraic Structures I. The additional six hours would generally be selected from 52-173 Mathematical Modeling, 52-353 Calculus III, 52-573 Probability, 52-693 Algebraic Structures II, or 52-843 Seminar in Special Topics. An elementary academic specialization in Mathematics requires 18 semester hours with at least nine advanced. Required courses are 52-103 Mathematical Concepts, 52-113 Introduction to Statistics, 52-154 Calculus I, and 52-673 Linear Algebra with two courses from 52-123 Elementary Function Theory, 52-173 Mathematical Modeling, 52-253 Calculus II, 52-403 Geometry, and 52-683 Algebraic Structures I recommended as the additional six semester hours. A teaching field in Computer Science requires 24 semester hours, at least 12 of which must be advanced. The 24 hours must include 54-143 Introduction to Programming, 54-183 Computer Science I, 54-283 Computer Science II, 54-393 Computer Organization, 54-453 Algorithms and 54-473 Programming Languages. Also see Education Department.
Mathematics (MAT)
| 52-103 | 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, algebra, geometry, and measurement. This course is designed for those seeking EC-4 or 4-8 teacher certification, however 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) |
| 52-113 | INTRODUCTION TO STATISTICS. 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) |
| 52-123 | ELEMENTARY FUNCTION THEORY. Relations, functions, and general properties of functions. Some of the elementary functions considered are polynomials, rational functions, exponentials, logarithms, and trigonometric functions. An objective of this course is to prepare students for Calculus I. May not be used for mathematics major or minor. (Each semester) |
| 52-154 | CALCULUS I. Functions and graphs; derivatives, applications of differentiation. Exponential, logarithmic 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) |
| 52-173 | 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: Consent of instructor. (Spring, even years) |
| 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: 52-154 Calculus I. (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: 52-253 Calculus II. (Each semester) |
| 52-383 | DISCRETE MATHEMATICS. See Computer Science 54-383. (Fall) |
| 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 Calculus II, 52-673 Linear Algebra, and either 54-143 Introduction to Programming or 54-183 Computer Science I. Also 54-523. (Fall, odd years) |
| 52-573 | PROBABILITY. Random variables and distributions, sequences of random variables, and stochastic processes. Prerequisite: 52-253 Calculus II. (Spring, odd years) |
| 52-673 | LINEAR ALGEBRA. Linear equations and matrices, vector spaces, linear mappings, determinants, quadratic forms, vector products, groups of symmetries. Prerequisite: 52-253 Calculus II or consent of instructor. (Each semester) |
| 52-683 | ALGEBRAIC STRUCTURES I. Sets, relations, functions, group theory, ring theory. Prerequisite: 52-673 Linear Algebra or consent of instructor. (Fall) |
| 52-693 | ALGEBRAIC STRUCTURES II. Vector spaces, algebraic field theory. Prerequisite: 52-683 Algebraic Structures I. (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: 52-673 Linear Algebra, as well as co-requisite or prerequisite of 52-353 Calculus III, 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: 52-353 Calculus III and 52-753 Elementary Differential Equations, or consent of instructor. (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 at the 200 level or above 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 Calculus III or consent of instructor. (Spring) |
| 52-863 | COMPLEX ANALYSIS. Algebra and geometry of complex numbers. Analytic and harmonic functions, series, contour integration, conformal maps, and transforms. Prerequisite: 52-353 Calculus III 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: 52-253 Calculus II. (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) |
| 52-001, 002, 003, 004 | SELECTED TOPICS. May be repeated with change in topic. |
| 52-301, 302, 303, 304 | SELECTED TOPICS. May be
repeated with change in topic. Prerequisite
Consent of instructor. |
| 52-951, 952, 953, 954 | INDEPENDENT STUDY. |
| 52-983 | HONORS. By invitation only. |
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. |
| 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 Introduction to Programming. (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 Computer Science I, 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: 54-183 Computer Science I, or consent of instructor. (Each semester) |
| 54-291 | RAPID APPLICATION DEVELOPMENT. This course will develop skills needed for the rapid development of programming solutions to problem specifications. This course (or, prior enrollment in this course) is required for students wishing to attend the South Central Programming Contest. This course may be repeated for credit. May not be counted toward the major or minor. Prerequisite: 54-183 Computer Science I. (Fall) |
| 54-383 | DISCRETE MATHEMATICS. Concepts for modeling discrete phenomena. Topics include: logic, set theory, order theory and lattices, graphs, induction, and recurrence relations. Prerequisites: 52-253 Calculus II and 54-283 Computer Science II, or consent of instructor. Also 52-383. (Fall) |
| 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: 54-283 Computer Science II 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: 54-283 Computer Science II or consent of instructor. (Spring) |
| 54-473 | PROGRAMMING LANGUAGES. Principles and practice in the design and implementation of imperative, functional, and object-oriented programming languages. Prerequisite: 54-393 Computer Organization or consent of instructor. (Fall) |
| 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: 54-283 Computer Science II or consent of instructor. (Fall, odd years) |
| 54-523 | INTRODUCTION TO NUMERICAL ANALYSIS. See 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: 54-283 Computer Science II or consent of instructor. (Spring) |
| 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: 52-673 Linear Algebra, 54-393 Computer Organization and 54-453 Algorithms, or consent of instructor. (Spring) |
| 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: 54-283 Computer Science II, 54-533 Functional Programming, or consent of instructor. (Fall, even 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: 52/54-383 Discrete Mathematics and 54-393 Computer Organization, or consent of instructor. (Fall, even years) |
| 54-643 | COMPUTER SYSTEMS. Introduction to operating systems and computer networks. Process control and scheduling, threads, concurrency, memory management and virtual memory, network protocol layers, packets and routing, and network security. Prerequisite: 54-393 Computer Organization. (Spring) |
| 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: 52/54-383 Discrete Mathematics. (Fall, even years) |
| 54-843 | SEMINAR IN SPECIAL TOPICS. A limited enrollment seminar 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 54-383, 54-453, 54-473, and consent of instructor. (Spring) |
| 54-001, 002, 003, 004 | SELECTED TOPICS. May be repeated with change in topic. |
| 54-301, 302, 303, 304 | SELECTED TOPICS. May be repeated with change in topic. |
| Prerequisite: Consent of instructor. | |
| 54-951, 952, 953, 954 | INDEPENDENT STUDY. May be repeated with change in content. |
| 54-983 | HONORS. By invitation only. |
