Catalog 2008-2009

MATHEMATICS AND COMPUTER SCIENCE DEPARTMENT

Division of Natural Sciences

Professor Kendall C. Richards, PhD, Chair
Professor John B. Chapman, PhD
Professor Walter M. Potter, PhD
Associate Professor Suzanne Fox Buchele, PhD
Associate Professor Richard T. Denman, PhD
Associate Professor Barbara Boucher Owens, PhD
Associate Professor Gary H. Richter, PhD
Associate Professor Therese N. Shelton, PhD
Assistant Professor Barbara Anthony, PhD
Assistant Professor Fumiko Futamura, PhD
Assistant Professor Alison Marr, PhD
Assistant Professor Linda DiLullo, 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 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 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 adviser; 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.

Major in Mathematics (BA or BS): 34-36 semester hours, including Mathematics 52-154, 254, 353, 673, 683, 753, 853, 894 (Capstone); one from 52-693, 763, 863, 883; six additional hours of Mathematics at the 300-level or above.

Required supporting course in the Mathematics major: Computer Science 54-183, normally to be completed no later than the sophomore year. Note that this is a prerequisite for Mathematics 52-683. Those without programming experience should first take Computer Science 54-143.

Minor in Mathematics: Mathematics 52-154, 254, 353, 673; six additional hours of Mathematics above the introductory level.

Major in Computer Science (BA or BS): 34 semester hours, including Computer Science 54-183, 283, 383, 393, 453, 473, 533, 643, 894 (Capstone); six additional hours of Computer Science at the 300-level or above.

Required supporting courses in the Computer Science major: Mathematics 52-154, 254, 673.

Minor in Computer Science: 18 semester hours of Computer Science, 12 hours of which must be above the introductory level.

Major in Computational Mathematics (BA or BS): 48 semester hours, including Computer Science 54-183, 283, 383, 393, 453, 473, 643; Mathematics 52-154, 254, 353, 523, 673, 753; Mathematics 52-683 or 853; Mathematics 52-894 or Computer Science 54-894 (Capstone).

See the Education Department for information regarding teacher certification in mathematics and computer science.

Mathematics (MAT)

52-103MATHEMATICAL 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) (NS)
52-113INTRODUCTION 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) (NS)
52-123ELEMENTARY 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. (Fall) (NS)
52-154CALCULUS 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: Mastery of high school level precalculus (algebra, trigonometry, exponential and logarithmic functions). (Each semester) (NS)
52-254CALCULUS II. Numerical integration, methods of integration, applications of the definite integral, improper integrals, sequences and series, Taylor’s Formula and approximation, polar coordinates. The course includes a laboratory component designed to explore applications and to enhance conceptualization. Prerequisite: Mathematics 52-154. (Each semester) (NS)
52-353CALCULUS 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 52-254. (Each semester) (NS)
52-383DISCRETE MATHEMATICS. See Computer Science 54-383. (Fall)
52-403GEOMETRY. Topics to be selected from synthetic geometry, analytic geometry, projective geometry, Euclidean and non-Euclidean geometry. Prerequisite: Permission of instructor. (Spring, even years) (NS)
52-523INTRODUCTION 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: Mathematics 52-254, 673, and Computer Science 54-183. Also Computer Science 54-523. (Fall, odd years) (NS)
52-573PROBABILITY. Random variables and distributions, sequences of random variables and stochastic processes. Prerequisite: Mathematics 52-254. (Spring, odd years) (NS)
52-673LINEAR ALGEBRA. Linear equations and matrices, vector spaces, linear mappings, determinants, quadratic forms, vector products, groups of symmetries. Prerequisite: Mathematics 52-254 or permission of instructor. (Each semester) (NS)
52-683ALGEBRAIC STRUCTURES I. Sets, relations, functions, group theory, ring theory. Prerequisite: Computer Science 54-183 and Mathematics 52-673 or permission of instructor. (Fall) (NS)
52-693ALGEBRAIC STRUCTURES II. Vector spaces, algebraic field theory. Prerequisite: Mathematics 52-683. (Spring, odd years) (NS)
52-753ELEMENTARY DIFFERENTIAL EQUATIONS. Topics include first order differential equations, separable equations, exact equations, linear differential equations of order n>1, homogeneous equations with constant coefficients, nonhomogeneous equations, the method of undetermined coefficients, variation of parameters, power series solutions, and an introduction to the Laplace Transform. Prerequisite: Mathematics 52-353, or permission of instructor. (Fall) (NS)
52-763INTERMEDIATE DIFFERENTIAL EQUATIONS. Topics include the Laplace transform, linear systems, numerical solutions, nonlinear systems and an introduction to partial differential equations. Prerequisites: Mathematics 52-673 and 52-753 or permission of instructor. (Spring, even years) (NS)
52-843SEMINAR 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: nine hours at the 200 level or above and permission of instructor. (NS)
52-853INTRODUCTORY 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: Mathematics 52-353 or permission of instructor. (Spring) (NS)
52-863COMPLEX ANALYSIS. Algebra and geometry of complex numbers. Analytic and harmonic functions, series, contour integration, conformal maps and transformations. Prerequisite: Mathematics 52-353 or permission of instructor. (Fall, even years) (NS)
52-883TOPOLOGY. Topology of the line and plane, limit points, open sets, closed sets, connectedness, compactness. Continuous functions, homeomorphisms. Prerequisite: Mathematics 52-254. (Fall, odd years) (NS)
52-894SENIOR 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, three hours of Computer Science and permission of instructor. (Fall) (NS)
52-001, 002, 003, 004SELECTED TOPICS. May be repeated with change in topic.
52-301, 302, 303, 304SELECTED TOPICS. May be repeated with change in topic. Prerequisite: Permission of instructor.
52-901, 902, 903, 904TUTORIAL.
52-951, 952, 953, 954INDEPENDENT STUDY.
52-983HONORS. By invitation only.

Computer Science (CSC)

54-143INTRODUCTION 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 does not fulfill the Area One Mathematics requirement. (NS)
54-183COMPUTER 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 Computer Science 54-143. (Each semester) (NS)
54-191SEMINAR 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: Permission of the instructor. This course may be repeated for credit. (NS)
54-283COMPUTER 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: Computer Science 54-183 or permission of instructor. (Spring) (NS)
54-291RAPID 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: Computer Science 54-183. (Fall) (NS)
54-383DISCRETE MATHEMATICS. Concepts for modeling discrete phenomena. Topics include: logic, set theory, order theory and lattices, graphs, induction and recurrence relations. Prerequisites: Mathematics 52-254 and Computer Science 54-283, or permission of instructor. Also Mathematics 52-383. (Fall) (NS)
54-393COMPUTER 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 permission of instructor. (Fall) (NS)
54-453ALGORITHMS. 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 permission of instructor. (Spring) (NS)
54-473PROGRAMMING LANGUAGES. Principles and practice in the design and implementation of imperative, functional and object-oriented programming languages. Prerequisite: Computer Science 54-393 or permission of instructor. (Fall) (NS)
54-513DATABASE 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 permission of instructor. (Fall, odd years) (NS)
54-523INTRODUCTION TO NUMERICAL ANALYSIS. See Mathematics 52-523. (Fall, odd years) (NS)
54-533FUNCTIONAL 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 permission of instructor. (Spring) (NS)
54-553COMPUTER 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, Computer Science 54-393 and 453, or permission of instructor. (Spring, even years) (NS)
54-573ARTIFICIAL 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 and 533, or permission of instructor. (Fall, even years) (NS)
54-643COMPUTER 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: Computer Science 54-393. (Spring) (NS)
54-683THEORY OF COMPUTATION. Finite state systems, finite automata, formal language theory. Context-free grammars, regular expressions, pushdown automata, Turing machines, decidability, switching theory. Prerequisite: Mathematics or Computer Science 52/54-383. (Fall, even years) (NS)
54-843SEMINAR IN SPECIAL TOPICS. A limited enrollment seminar not generally covered in other courses. May be repeated for credit as topics vary. Prerequisites: nine hours of 200-level courses or higher and permission of instructor. (NS)
54-894SENIOR 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 Computer Science 54-383, 453, 473, and permission of instructor. (Spring) (NS)
54-001, 002, 003, 004SELECTED TOPICS. May be repeated with change in topic.
54-301, 302, 303, 304SELECTED TOPICS. May be repeated with change in topic. Prerequisite: Permission of instructor.
54-901, 902, 903, 904TUTORIAL.
54-951, 952, 953, 954INDEPENDENT STUDY. May be repeated with change in content.
54-983HONORS. By invitation only.