Mathematics & Computer Science

Chair: Robert P. Feinerman (Gillet Hall, Room 211)

Department Faculty and Staff: Distinguished Professors: Adam Koranyi and Victor Pan; Professors: Charles Berger, Robert Feinerman, Melvin Fitting, Nancy Griffeth Michael Handel, Nicholas Hanges, Leon Karp, Linda Keen, Joseph Lewittes, Richard Mosak, Melvyn B. Nathanson, Esther Phillips, Robert Schneider, Zoltan Szabo; Associate Professors:Yves Jean Gwang Jung, Julian Laderman, Nikola Lakic, John C. Mineka, Christina Sormani Katherine St. John; Assistant Professors: Calin Diaconu, David Fisher, Yiannis Petridis, Rhys Rosholt; Instructors: Brian Murphy; Lecturers: David J. Rothchild; Director of Mathematics Laboratory & Computer Services: Robert Sutliff; Systems and Network Administrator: Etina Bueno

The Department of Mathematics and Computer Science offers undergraduates four different degree programs, as well as a major in the interdisciplinary area of computer graphics and imaging and the opportunity to select a minor in any of these fields. Students can pursue programs leading to the Bachelor of Arts degree in either mathematics or computer science and to the Bachelor of Science degree in either computer science or computer information systems. These programs prepare students both for graduate study and for careers in industry, education, government, and the non-profit sector.

COLLEGE REQUIREMENT IN MATHEMATICS

All Lehman College students are required to pass either:

1. a) a 3- or 4-credit MAT course numbered above 125
2. or
3. b) three MAT courses numbered between 180 and 199 (each 1 credit).

NOTE: Students should consult with an advisor from their (prospective) major or from the Department of Mathematics to determine the appropriate course(s) to take.

PROGRAMS

THE MATHEMATICS AND COMPUTER SCIENCE QUALIFYING EXAM

All students must pass a Departmental qualifying exam before being enrolled as a major in any of the Departmental majors (Mathematics B.A., Computer Science B.A. and B.S., Computer Information Systems B.S.)

DEPARTMENTAL HONORS IN MATHEMATICS OR COMPUTER SCIENCE

Students who wish to qualify for Departmental honors in any of the Department's majors must meet the requirements outlined under "Academic Honors" in the chapter on ":Academic Services and Policies" in this bulletin.

40-TO-44 CREDIT MAJOR IN MATHEMATICS, B.A.

1. There are eleven required courses:

Credits

12 MAT 175, MAT 176, & MAT 226

8 MAT 313 and MAT 314

4 MAT 320

4 CMP 230

12-16 Four additional courses chosen from among 200 level or higher MAT courses, not counting MAT 231, 300, 301, and 348. CMP 326 and CMP 332 may be chosen

2. A minor is also required.

NOTE: All students who wish to apply for certification as a Secondary School Teacher of Mathematics must take (as three of the four electives required for the Mathematics major): MAT 237, MAT 343, and either MAT 345 or MAT 346.

REQUIREMENTS FOR THE MINOR IN MATHEMATICS

A minor in Mathematics consists of 12 credits in MAT courses at the 200 or higher level, with 6 of these credits in courses at a 300 or higher level.

NOTE: (1) Students majoring in Computer Science who elect a minor in Mathematics must include MAT 320 and cannot include any courses used to satisfy the Computer Science major. (2) Students not majoring in Computer Science must include MAT 226 and 313 and 4 additional credits in courses at the 300 or higher level.

43-TO-44-CREDIT MAJOR IN COMPUTER SCIENCE, B.A

There are eleven required courses:

Notes:

1. A minor is also required.
2. All students, particularly those considering graduate work, are advised to take more upper level computer science courses. (The list above is only the minimum required for graduation.)
3. For departmental honors, see one of the advisors in the Department of Mathematics and Computer Science

56-60 CREDIT MAJOR IN COMPUTER SCIENCE, B.S.

There are fifteen required courses:

Three advanced (300 or 400 level) CMP courses, (PHY 305 Digital Electronics, 2 hours lecture, 2 hours lab, 3 credits, can be substituted for one of these courses). One advanced (300 or 400 level) MAT course, not including MAT 300, 301 or 348 (CMP 332 can be used for this course). A minor is not required.

REQUIREMENTS FOR THE MINOR IN COMPUTER SCIENCE

A minor in Computer Science consists of 12 credits in CMP courses at the 200 or higher level, with 6 of these credits in 300-level courses or courses at a higher level.

NOTE: (1) Students majoring in Mathematics who elect a minor in Computer Science must include CMP 332 or 338 and cannot include any courses used to satisfy the Mathematics major. (2) Students not majoring in mathematics must include CMP 334 and 338.

REQUIREMENTS FOR THE MINOR IN COMPUTER APPLICATIONS

The minor consists of CIS 211: Computer Information Systems (4 hours, 4 credits) and three other courses chosen from the 200 level (or higher) CIS courses.

56-TO-58-CREDIT MAJOR IN COMPUTER INFORMATION SYSTEMS, B.S.

Required Courses in Computer Science (17 credits):

CIS 166: Computer Programming for Information Processing (4 hours, 4 credits)

CIS 211: Computer Information Systems (4 hours, 4 credits)

CIS 212: Microcomputer Architecture (4 hours, 3 credits)

CIS 234: Introduction to Spreadsheet Analysis (4 hours, 3 credits)

CIS 244: Introduction to Database Management (4 hours, 3 credits)

Elective Courses in Computer Science (6 - 8 credits):

Two additional courses chosen from the 200 level (or higher) CIS courses or from CGI 221, CGI 321, CGI 421 and CMP 326.

Required Courses in Mathematics (15 credits):

MAT 132: Basic Concepts of Probability and Statistics (4 hours, 4 credits)

MAT 174: Elements of Calculus (4 hours, 4 credits)

MAT 301: Applied Statistics and Computer Analysis (4 hours, 3 credits)

MAT 348: Mathematical Methods for Management (4 hours, 4 credits)

Required Courses in Economics (9 credits):

ECO 166: Fundamentals of Economics (3 hours, 3 credits)

ECO 167: Economic Analysis (3 hours, 3 credits)

ECO 185: Introduction to Accounting for Non-Accounting Majors (3 hours, 3 credits)

Additional Electives (9 credits):

Students must choose 3 courses from:

ECO 304: Principles of Organizational Management (3 hours, 3 credits)

ECO 405: Management Process and Systems (3 hours, 3 credits)

PHI 221: Ethical Issues in Computing and Technology (3 hours, 3 credits)

POL 299: Law, Computers and the Internet: The Politics of Information Technology (3 hours, 3 credits)

POL 305: Public Administration (3 hours, 3 credits)

GEP 205: Principles of Geographic Information Science (2 hours lecture, 2 hours lab, 3 credits)

One additional CIS course (3 credits)

NOTE: At least one of PHI 221 and POL 299 must be chosen.

NOTES:

1. No minor is required.
2. Students considering graduate work should take MAT 175 - 176 instead of MAT 174.
3. For Departmental honors, see one of the advisors in the Department of Mathematics and Computer Science.

52-TO-54 CREDIT MAJOR IN COMPUTER GRAPHICS AND IMAGING, B.S.

In CGI/ART (21 credits: may be taken as CGI or ART)

CGI/ART 221: Applied Imaging and Applications to the World Wide Web I. 4 hours (2 lecture, 2 lab), 3 credits.

CGI/ART 222: Applied Imaging and Applications to the World Wide Web II. 4 hours (2 lecture, 2 lab), 3 credits.

CGI/ART 321: Computer Modeling and Design I. 4 hours (2 lecture, 2 lab), 3 credits.

CGI/ART 322: Computer Modeling and Design II. 4 hours (2 lecture, 2 lab), 3 credits.

CGI/ART 421: Computer Animation I. 4 hours (2 lecture, 2 lab), 3 credits.

CGI/ART 422: Computer Animation II. 4 hours (2 lecture, 2 lab), 3 credits.

CGI/ART 480: Senior Project. 3 hours, 3 credits.

In Computer Science (11 credits):

CMP 230: Programming Methods I. 4 hours, 4 credits.

CMP 326: Programming Methods II. 4 hours, 4 credits.

CMP 342: Internet Programming. 4 hours (2 lecture, 2 lab), 3 credits.

In Mathematics (5 credits):

MAT 155: Calculus Laboratory (2 hours, 1 credit)

MAT 175: Calculus I (4 hours, 4 credits)

In Art (13 credits):

ART 100: Basic Drawing. 4 hours, 2 credits.

ART 106: Introduction to Sculpture. 4 hours, 2 credits.

ART 108: Introduction to Photography. 4 hours, 2 credits.

ART 201: Life Drawing. 4 hours, 2 credits.

ART 202: Design. 4 hours, 2 credits.

ARH 167: Tradition and Innovation in the Art of the West. 3 hours, 3 credits.

Or

ARH 141: Introduction to the History of Modern Art of the Nineteenth and Twentieth Centuries in Europe and the United States. 3 hours, 3 credits.

Elective (2-4 credits):

One additional course from CMP, MAT, ARH, ART, or CGI/ART courses with permission from an advisor (2-4 credits). No minor is required.

COMPUTER GRAPHICS AND IMAGING MINOR (12 CREDITS)

The minor consists of any 12 credits chosen from the CGI courses. CMP 342 can be substituted for one of these courses.

Introductory Mathematics Courses (MAT)

*MAT 050: Applications of Arithmetic and Algebraic Skills. 2 hours, 2 credits. PREREQ: Satisfaction of College mathematics requirements.

MAT 080: Elementary Algebra. 4 hours, 0 credits. Integers, polynomials, solution of linear equations and inequalities, absolute value, systems of linear equations, graphing, applications. Mathematics Laboratory attendance may be assigned at the discretion of the instructor. PRE-REQ: Placement by the Department of Mathematics and Computer Science.

MAT 090: Algebra and Geometry. 4 hours, 1 credit. Factoring, solving quadratic equations, rational and radical expressions, direct and inverse variation, topics from geometry, introduction to trigonometry, applications to the natural and social sciences. Mathematics Laboratory attendance may be assigned at the discretion of the instructor. PREREQ: MAT 080 or placement by the Department of Mathematics and Computer Science.

MAT 104: College Algebra. 4 hours, 3 credits. Rational expressions, integer and rational exponents, quadratic formula, complex numbers, exponential and logarithmic functions, conic sections, trigonometry, sequences and series. Mathematics Laboratory attendance may be assigned at the discretion of the instructor. PREREQ: MAT 090 or placement by the Department of Mathematics and Computer Science.

MAT 123: A Problem-Solving Approach to Mathematics. 4 hours, 4 credits. A problem-solving approach to fundamental ideas in mathematics: properties of counting numbers, integers, rationals and reals; elementary number theory; probability and statistics; geometry. PREREQ: MAT 104 or placement by the Department of Mathematics and Computer Science.

MAT 132: Introduction to Statistics. 4 hours, 4 credits. Collection, plotting, and comparison of data sets, histograms, descriptive statistics, the frequency definition of probability, random experiments, random sampling, binomial and normal variables, confidence intervals and tests of hypotheses for binomial and normal parameters. Additional topics chosen from tests for the difference of proportions or population means, the Chi Square test, and regression analysis. Introduction to a computer statistical package. PREREQ: MAT 104 or placement by the Department of Mathematics and Computer Science.

MAT 135: Concepts and Uses of Mathematics. 3 hours, 3 credits. A survey course for liberal arts students. Topics chosen from a wide range of concepts in mathematics such as: probability, statistics, game theory, number theory, set theory, linear programming, geometry and logic. PREREQ: MAT 104 or placement by the Department of Mathematics and Computer Science.

MAT 155: Calculus I Laboratory. 2 hours, 1 credit. Calculus computer software will be used to illustrate the ideas introduced in

MAT 156: Calculus II Laboratory. 2 hours, 1 credit. Calculus computer software will be used to illustrate the ideas introduced in MAT 176. Students will be asked to solve problems using the software and to submit lab reports. COREC: MAT 176

MAT 161: Computer/Calculator Usage. 1 hour, 1 credit (May be repeated, with change in topic and departmental approval, up to a maximum of three credits.) An introduction to the use of computers or scientific calculators to solve problems arising in science, business, and mathematics. PREREQ: Departmental approval.

MAT 171: Problem Solving for Management, Economics, and Life Sciences. 4 hours, 4 credits. The use of functions, graphs, and matrices to solve various applied problems. Geometry of linear, quadratic, logarithmic, and exponential functions. PREREQ: MAT 104 or placement by the Department of Mathematics and Computer Science. NOTES:

1) MAT 171 is a prerequisite for MAT 174. Students planning on taking MAT 175, should take MAT 172 instead of MAT 171.

2) Students may not receive credit for both MAT 171 and MAT 172.

MAT 172: Precalculus. 4 hours, 4 credits. Polynomial, rational, logarithmic, and trigonometric functions with applications to problems in mathematics and the sciences. PREREQ: MAT 104 or placement by the Department of Mathematics and Computer Science. NOTES:

1) Students may not receive credit for both MAT 171 and MAT 172.

2) MAT 172 is a prerequisite for MAT 175. Students who plan on taking MAT 174, should take MAT 171 instead of MAT 172.

Enrichment Topics (Minicourses)

MAT 180: Voting and Polling Problems. 1 hour, 1 credit. Different kinds of voting schemes in elections. Different kinds of "fairness" in voting. Sampling techniques in polling. PREREQ: Three years of Regents-level high school mathematics or MAT 104.

MAT 181: Number Systems. 1 hour, 1 credit. Different types of numbers and different schemes for representing them. The base in a number system. Computer representation. PREREQ: Three years of Regents-level high school mathematics or MAT 104.

MAT 184: Codes and Number Patterns. 1 hour, 1 credit. Prime and composite numbers. Different kinds of codes, code breaking. Security and error detection. PREREQ: Three years of Regents-level high school mathematics or MAT 104.

MAT 186: Geometry and the Real World. 1 hour, 1 credit. Geometric forms in the real world. Topics: symmetry, geometric solids, crystals and fractals. PREREQ: Three years of Regents-level high school mathematics or MAT 104.

MAT 189: Sets and Infinity. 1 hour, 1 credit. Finite and infinite sets. Different orders of infinity. Paradoxes. PREREQ: Three years of Regents level high school mathematics or MAT 104.

MAT 192: Statistical Inference. 1 hour, 1 credit. Understanding statistics and judging the accuracy and relevance of statistical results. PREREQ: Three years of Regents-level high school mathematics or MAT 104.

MAT 194: Games and Puzzles. 1 hour, 1 credit. The mathematical principles behind many games and puzzles. PREREQ: Three years of Regents- level high school mathematics or MAT 104.

MAT 195: Gambling and Games of Chance. 1 hour, 1 credit. A study of gambling situations. Casino games. Probability and expected value. PREREQ: Three years of Regents-level high school mathematics or MAT 104.

MAT 197: Trees, Networks, Paths, and Flows. 1 hour, 1 credit. Cycles, connectedness, the Koenigsberg bridge problem, minimum paths, and minimum spanning trees. PREREQ: Three years of Regents- level high school mathematics or MAT 104.

MAT 199: Topics in Elementary Mathematics. 1 hour, 1 credit. Various mathematical topics of current interest. PREREQ: Three years of Regents- level high school mathematics or MAT 104.

Courses in Mathematics (MAT)

MAT 174: Elements of Calculus. 4 hours, 4 credits. (Not open to students majoring in MAT.) Differentiation and integration of elementary functions with applications to business, to social sciences, and to life sciences. PREREQ: MAT 171 or placement by the Department of Mathematics and Computer Science. NOTES:

1) Students may not receive credit for both MAT 174 and MAT 175.

2) MAT 174 will not serve as a prerequisite for MAT 176.

MAT 175: Calculus I. 4 hours, 4 credits. Differentiation of functions of one variable; applications to motion problems, maximum-minimum problems, curve sketching, and mean-value theorems. PREREQ: MAT 172 or placement by the Department of Mathematics and Computer Science. COREQ: MAT 155. NOTES:

1) Students may not receive credit for both MAT 174 and MAT 175.

2) MAT 174 will not serve as a prerequisite for MAT 176.

MAT 176: Calculus II. 4 hours, 4 credits. Inverse functions; logarithmic and exponential functions; integration of functions; and applications of the definite integral, including area, volume, and arc length. PREREQ: A grade of C or better in MAT 175. COREQ: MAT 156.

MAT 226: Intermediate Calculus I. 4 hours, 4 credits. Vectors in two and three dimensions, equations of lines and planes, functions of several variables, partial differentiation, directional derivatives, and multiple integration; line integrals; and infinite series and power series in one variable. PREREQ: A grade of C or better in MAT 176.

MAT 227: Intermediate Calculus II. 4 hours, 4 credits. A continuation of MAT 226. Taylor expansion in several variables, maximum and minimum problems, line integrals, Green's theorem, and introduction to differential equations. PREREQ: MAT 226.

*MAT 231: Statistics for Biologists. 4 hours, 4 credits. (Limited to BIO Concentrators.) Basic probability theory, randomization, conditional probability and independence, binomial Poison and normal distributions, testing statistical hypotheses, confidence and fiducial intervals, analysis of variance, Chi-square test of fit, correlation and linear regression, and selected topics in bioassay. PREREQ: MAT 175 and BIO 166.

MAT 237: Applications of Discrete Mathematics. 4 hours, 4 credits. Concepts and applications of graph theory, recurrence relations, linear programming, game theory, difference equations, matrices, combinatorics, statistical inference, probability. Problem solving using mathematical modeling. PREREQ: MAT 176. NOTE: Primarily for students planning to teach mathematics in a secondary school.

MAT 300: Mathematical Models in the Social Sciences. 3 hours, 3 credits. This course is designed for students interested in the social sciences. Topics covered will be selected from elementary probability, theory of gambling, random walks, game theory and linear programming. Emphasis is placed on a descriptive treatment of mathematical material and its application to the social sciences. PREREQ: Either three years of high school math or MAT 172. NOTE: MAT 300 may not be counted toward the MAT major.

MAT (SOC) 301: Applied Statistics and Computer Analysis for Social Scientists. 4 hours (2 lecture, 2 lab), 3 credits. An elementary treatment of statistical concepts. Data analysis using standard statistical methods available in the Statistical Package for Social Scientists. Computations will be run on a computer. Interpretation and misinterpretation of computer output. PREREQ: MAT 132 and MAT 171. NOTES:

1) MAT (SOC) 301 may not be counted toward the Mathematics major.

2) An equivalent college-level statistics course may be substituted for MAT 132 as a prerequisite for this course.

MAT 305: Introduction to Topology. 3 hours 3 credits. Intuitive discussion of topological concepts and problems such as networks, map-coloring problems, one sided surfaces topological transformations, Jordan curve theorem winding numbers and zeros of polynomials, fixed point theorems, and dimension. PREREQ: MAT 226.

MAT 313: Elements of Linear Algebra. 4 hours, 4 credits. Vector spaces, systems of linear equations, determinants, linear transformations, and matrices. PREREQ: MAT 176. With Departmental permission, MAT 176 may be taken as a COREQ.

MAT 314: Algebra and Number Systems I. 4 hours, 4 credits. The syllabus of this course is continued in MAT 315. Algebraic structures such as groups, rings, and fields; their relations and applications to school and college mathematics, including the number systems of arithmetic and analysis. PREREQ: MAT 313.

MAT 315: Algebra and Number Systems-II. 3 hours, 3 credits. Continuation of MAT 314. Further study of algebraic structures; polynomials; topics chosen from theory of equations; Galois theory; and rules and compass constructions. PREREQ: MAT 314.

MAT 316: Theory of Numbers. 4 hours, 4 credits. Study of problems concerning numbers and the properties of numbers such as divisibility, continued fractions, and congruences. Fermat's and Euler's theorems, quadratic residues and reciprocity law, elementary diophantine analysis, and introduction to algebraic numbers. Computer applications involving testing for primality and topics from coding theory. PREREQ: MAT 226 or Departmental permission.

MAT 320: Analysis I. 4 hours, 4 credits. The syllabus of this course is continued in MAT 321. Introduction to real analysis, the real number system, limits, continuity, differentiation, the mean value and Taylor's theorems and applications. Riemann integration and improper integrals. PREREQ: Either MAT 226 or Departmental permission.

*MAT 321: Analysis II. 4 hours, 4 credits. Continuation of MAT 320. Infinite series and power series, pointwise and uniform convergence, ndimensional Euclidean space, metric spaces, functions from Rn to Rm, continuity, and the differential as a linear map: inverse and implicit function theorems. PREREQ: MAT 320.

MAT 323: Differential Equations. 4 hours, 4 credits. Exact and approximate solutions of ordinary differential equations, existence theorems, and applications to problems in the physical sciences. Series solutions; Laplace transforms and Fourier analysis. Computer applications. PREREQ: MAT 226.

MAT 327: Statistical Inference. 4 hours, 4 credits. Introduction to the ideas and methods of probability and statistical inference for students in mathematics and the sciences. Topics include confidence intervals, tests of significance, chi-square tests of goodness-of-fit and independence, regression analysis, and analysis of variance. Students will be introduced to a standard computer statistical package. PREREQ: MAT 176.

MAT 330: Probability and Statistics. 4 hours, 4 credits. Basic probability theory. Fundamental concepts of statistics. Combinatorial problems, distributions, expectation, generating functions, law of large numbers, and central limit theorem. Other topics from probability and statistics. PREREQ: MAT 176.

*MAT 335: Applied Mathematics I. 3 hours, 3 credits. The syllabus of this course is continued in MAT 336. Calculus of variations, Lagrange's and Hamilton's formulations for mechanics, wave and heat equations, boundary-value problems, and solutions by separation of variables and special functions. Fourier series and integrals. PREREQ: MAT 226.

*MAT 336: Applied Mathematics II. 3 hours, 3 credits. Continuation of MAT 335. Existence and uniqueness theorems for initial value problems in ordinary differential equations. Green's function, and eigenvalue problems; control theory. PREREQ: MAT 335.

MAT 340: Foundations of Mathematics. 3 hours, 3 credits. The nature of mathematical proof, basic logic, and set theory. A rigorous construction of the natural numbers within set theory, of the rational numbers, and of the real numbers via Dedekind cuts or their equivalent. PREREQ: MAT 226 or MAT 314.

MAT 341: Mathematical Logic I. 3 hours, 3 credits. The syllabus of this course is continued in MAT 342. Propositional logic and first-order logic; model theory and proof theory; Godel's completeness theorem and its consequences. PREREQ: MAT 314.

*MAT 342: Mathematical Logic II. 3 hours, 3 credits. Continuation of MAT 341. General formal systems, recursive functions, and incompleteness and undecidability results for arithmetic and set theory. PREREQ: MAT 341.

MAT 343: History of Mathematics. 4 hours, 4 credits. Study of the historical development of mathematics from ancient to modern times, including the contributions of underrepresented groups and diverse cultures. PREREQ: MAT 313.

MAT 345: Axiomatic Geometry. 4 hours, 4 credits. Geometric theory from an axiomatic viewpoint motivated by Euclidean geometries and additional non-Euclidean examples. Emphasis on the relationship between proof and intuition. PREREQ: MAT 314

MAT 346: Geometry. 4 hours, 4 credits. Euclidean and non-Euclidean geometries approached from the points of view of axiomatics and transformation groups. PREREQ: MAT 314.

MAT 347: Game Theory and Linear Programming. 3 hours, 3 credits. An introduction to the mathematical theory of games of strategy. Matrix games. Optimal strategies for zero-sum two-person games. Convex sets in Euclidean n-space, systems of linear inequalities, linear programming, and the simplex method. N-person games and non-zero-sum games. PREREQ: One course in linear algebra.

MAT 348: Mathematical Methods for Management. 4 hours, 4 credits. Conditions for optimization, classical inventory problems. Linear programming and its applications, including the transportation problem. Use of software packages for linear programming calculations. Probability, expectation, and risk. Portfolio selection. Stochastic processes and queues. Computer simulation of stochastic processes. PREREQ: MAT 174 (or 175), 301, and CIS 211. NOTE: Primarily for students in the Computing and Management major; not to be counted toward the Mathematics major.

MAT 349: Operations Research. 4 hours, 4 credits. Inventory theory, queuing theory, linear programming, integer linear programming, nonlinear programming, the transportation problem, network analysis, and applications to industrial models. Software packages for linear programming. PREREQ: MAT 313 and CMP 230.

MAT (CMP) 417: Cryptography. 4 hours, 4 credits. Methods for transforming information into cryptic messages and for deciphering secret code. Review of selected topics in elementary number theory. Construction of linear, quadratic, and exponential ciphers, as well as key exchange protocols. PREREQ: MAT 313.

MAT 423: Theory of Functions of a Complex Variable. 4 hours, 4 credits. Algebra and geometry of complex numbers, analytic functions, elementary functions and conformal mapping. Cauchy integral theorem and applications. Taylor and Laurent series, calculus of residues, and classification of functions by singularities. Computer applications, including conformal mapping. PREREQ: MAT 320.

MAT 424: Partial Differential Equations and Applications. 4 hours, 4 credits. Study of the wave equation, heat equation, and Laplace's equation with an emphasis on problems in one and two dimensions. Topics to include: harmonic functions and the Dirichlet problem, mixed boundary conditions and Fourier series, Fourier transform and convolution. Computer-based projects. PREREQ: MAT 226.

*MAT 432: Differential Geometry. 3 hours, 3 credits. Curves and surfaces in E3. Curvature, torsion, fundamental existence theorem for space curves, geometry on a surface, and two-dimensional Riemannian geometry. PREREQ: MAT 313 and MAT 320.

*MAT 433: Topology. 3 hours, 3 credits. Sets functions, metric spaces, topological spaces, neighborhoods, continuity, connectedness, homotopy, fundamental groups, and compactness. PREREQ: MAT 314 and MAT 320.

MAT 441: Fundamental Concepts of Modern Mathematics. 3 hours, 3 credits. A rigorous development of set theory, including relations, functions, cardinal and ordinal numbers, the axiom of choice, the well-ordering theorem, and Zorn's lemma. PREREQ: MAT 314 or MAT 320 or MAT 340 or Departmental permission.

*MAT 450: Seminar in Algebra. 3 hours, 3 credits. Selected topics from algebra and number theory. Students will be expected to make oral presentations and work with periodical literature. PREREQ: MAT 314.

*MAT 451: Seminar in Geometry. 3 hours, 3 credits. Selected advanced topics from Euclidean geometry. Students will be expected to make oral presentations and work with periodical literature. PREREQ: Either MAT 345 or MAT 346.

MAT 456: Topics in Mathematics. 4 hours, 4 credits (maximum 8 credits). Various sections on topics in mathematics. (For specific topics and sections, consult the Department.)

MAT 485: Independent Study. 3 hours, 3 credits (maximum 6 credits). Independent reading under faculty supervision. PREREQ: Departmental permission.

Courses in Computer Science (CMP)

CMP 230: Programming Methods I. 4 hours, 4 credits. Introduction to structured computer programming using a modern high level programming language. Programming constructs covered to include console I/O, data types, variables, control structures including iteration, arrays, function definitions and calls, parameter passing, functional decomposition, and an introduction to objects. Debugging techniques. PREREQ: MAT 104 or placement by the Department of Mathematics and Computer Science. NOTE: For students who intend to major in computer science, mathematics, computer graphics and imaging or the sciences. Some previous computer programming experience is highly recommended.

CMP 232: Elementary Discrete Structures & Applications to Computer Science. 4 hours, 4 credits. Sets, relations and functions; propositional calculus, Boolean algebras, and combinatorial circuits, counting methods; proof techniques; analysis of algorithms; graphs and trees, puzzles; finite machines, sequential circuits and recognizers. PREREQ: MAT 172 or placement by the Department of Mathematics and Computer Science or departmental permission. NOTE: Students who receive a grade below B- in MAT 172 are strongly urged to speak to an advisor in the Department of Mathematics and Computer Science prior to registering for CMP 232.

CMP 270: Computer Programming in Visual Basic. 2 hours, 2 credits. Intensive introduction to Visual Basic, for students who have successfully completed a two-semester sequence in another programming language. PREREQ: Two semesters of programming in another language, or Departmental permission. NOTE: Taught as a regular programming course or as a self-study course with reading and programming assignments and weekly conferences with the instructor.

CMP 273: Computer Programming in Fortran. 2 hours, 2 credits. Intensive introduction to Fortran for students who have successfully completed a two-semester sequence in another programming language. PREREQ: Two semesters of programming in another language or Departmental permission. NOTE: Taught as a regular programming course or as a self-study course with reading and programming assignments and weekly conferences with the instructor.

CMP 274: Computer Programming in C++ . 2 hours, 2 credits. Intensive introduction to C++, for students who have successfully completed a two-semester sequence in another programming language. PREREQ: Two semesters of programming in another language, or Departmental permission. NOTE: Taught as a regular programming course or as a self-study course with reading and programming assignments and weekly conferences with the instructor.

CMP 279: Topics in Computer Programming. 2 hours, 2 credits. (May be repeated, with change of language and departmental permission.) Intensive introduction to a programming language, for students who have successfully completed a two-semester sequence in another programming language. PREREQ: Two semesters of programming in another language, and Departmental permission. NOTE: Taught as a regular programming course or as a self-study course with reading and programming assignments and weekly conferences with the instructor.

CMP 326: Programming Methods II. 4 hours, 4 credits. Continuation of parameter passing with a focus on devising function definitions and tracing recursive calls. Sorting and searching algorithms and a comparison of their performance. GUI programming. Threads, Exceptions and Exception Handling. Object-Oriented Programming techniques. PREREQ: A grade of B- or better in CMP 230 or departmental permission.

CMP 332: Numerical Methods. 4 hours, 4 credits. Computer methods of approximate calculation. Topics chosen from polynomial approximation and interpolation, orthogonal polynomials, finite difference methods, splines and least square approximations; numerical differentiation and integration; numerical solutions of equations by iterative methods and matrix inversion; eigenvalue computations; sparse matrix methods. PREREQ: CMP 326 and MAT 226 and MAT 313.

CMP 334: Computer Organization. 4 hours, 4 credits. Introduction to digital logic-expressions, gates, flip-flops, adders. busses, multiplexers Introduction to assembly language and assembly level organization-data representation, instruction formats, addressing modes, interrupts. Memory systems-caches (mapping and management policies) and memory hierarchies, latency and bandwidth, virtual memory (pagetables, TLB). Input/Output- busses, channels and DMA. Performance considerations- pipelining, RISC architecture, branch prediction, introduction to instruction level parallelism. PREREQ: CMP 230 and CMP 232 or departmental permission

CMP 335: Computer Organization Laboratory. 2 hours, 1 credit. A practical course applying principles taught in CMP 334. Construction and operation of the separate hardware components; system software installation. Pre- or co-requisite: CMP 334. NOTE: Not allowed as one of the electives in the Computer Science B.S. or B.A. degrees.

CMP 338: Data Structures and Algorithms I. 4 hours, 4 credits. Abstract characterizations of data structures such as arrays, stacks, queues, trees and graphs will be studied along with algorithms that make use of such structures, including algorithms for sorting, searching, and memory management. Implementation issues will be considered, and students will write programs that embody these structures and algorithms. PREREQ: CMP 232 and CMP 326.

CMP 339: Programming Languages. 4 hours, 4 credits. Design, evaluation, and implementation of programming languages. Syntax and semantics of language constraints. Control structures, including branching, selection, iteration, procedure calls and recursion; data types and data structures, and operations on them; name structures, binding, environments, dynamic and static scoping; parameter passing. PREREQ: CMP 334 and CMP 338.

CMP 342: Internet Programming. 4 hours, 4 credits. Programming using languages for the Internet, such as Java or Visual Basic. Web server management, including administrative software tools. PREREQ: CMP 326.

CMP 346: Object Oriented Techniques. 4 hours, 4 credits. Study of design patterns and a virtual machine. Class file structure, the virtual machine computer architecture and instruction set, Just-In-Time compilation, different forms of garbage collectors and their merits, and performance enhancements. PREREQ: CMP 326

CMP 405: Introduction to Networks. 4 hours, 4 credits. Introduction to the organizational principles of data communication and their implementation in particular networks. Examination of the way operating networks approach and solve communication problems. Examination of user utilities from a computer scientist's point of view. PREREQ: CMP 334 and CMP 338.

CMP 406: Network Systems Lab. 4 hours, 2 credits. Introduction to installation and configuration of networking equipment, and network monitoring and trouble-shooting, and network management. Use of typical networking equipment. Some programming in Java or C will be required. PREREQ: CMP 338. CO-REQ or PREREQ: CMP 405. Note: Not allowed as one of the electives in the Computer Science B.S. or B.A. degrees.

CMP 407: Compiler Construction. 4 hours, 4 credits. Compilation of simple expressions and statements. Organization of a compiler, including compile-time and run-time symbol tables, lexical scan, object code generation, error diagnostics, object-code optimization techniques such as register allocation via graph coloring, and method in-lining. Use of compiler writing languages and bootstrapping. NOTE: Students will work on a compiler for a small language. PREREQ: CMP 339

CMP 408: Software Engineering. 4 hours, 4 credits. Classical and object oriented software engineering. System life cycle, structured coding techniques, modularity, data encapsulation and generic facilities. Verification, validation and testing techniques: static analysis, input-output assertions, structured induction, and symbolic execution. PREREQ: CMP 338.

CMP 410: Data Structures and Algorithms II. 4 hours, 4 credits. Design and analysis of algorithms: Worst and average case behavior. Design strategies, such as divide and conquer, the greedy principle, dynamic programming, and backtracking, are illustrated by examples chosen from sorting and searching, applications of graph theory, scheduling, pattern matching, matrix multiplication, and other topics. NP-complete problems. Parallel processing and algorithms. PREREQ: CMP 338. PRE- OR COREQ: MAT 313.

CMP 412: Computer Graphics. 4 hours, 4 credits. Techniques of producing graphical displays. Two-dimensional transformations. World vs. Screen coordinates. Line drawing algorithms. Clipping. Motion. Use of devices such as light pens, graphics tablets, and mouses. PREREQ: CMP 326. PRE- or COREQ: MAT 313.

CMP 414: Artificial Intelligence. 4 hours, 4 credits. Survey of artificial intelligence with an introduction to LISP programming. Graph-searching algorithms applied to problem solving. Selected topics from pattern recognition, natural language processing, and expert systems. PREREQ: CMP 338.

CMP 416: Computability Theory. 4 hours, 4 credits. Mathematical formulation of computability theory and abstract machine theory. Finite-state machines and Turing machines; Church-Turing Thesis; recursive functions and recursively enumerable sets; unsolvability and the Halting Problem. PREREQ: CMP 232 and CMP 326.

CMP (MAT) 417: Cryptography. 4 hours, 4 credits. Methods for transforming information into cryptic messages and for deciphering secret code. Review of selected topics in elementary number theory. Construction of linear, quadratic, and exponential ciphers, as well as key exchange protocols. PREREQ: MAT 313.

CMP 418: Systems Analysis and Design. 4 hours, 4 credits. Development of many systems will be studied using a structured approach to system design. Feasibility study, project cost estimation, top down design, Hierarchy/ Input/Process/Output (HIPO), data flow diagrams, data dictionaries, backup, security, maintenance and testing system. PREREQ: CMP 326.

CMP 420: Database Systems. 4 hours, 4 credits. Introduction to theory of database systems and database management: theory of relational, hierarchical, and network database organization, with emphasis on the first; views of data, data organization, data dependency and redundancy, normal forms, and query language. A database language will be taught and a project assigned in that language. PREREQ: CMP 338.

CMP 425: System Programming Languages. 4 hours, 4 credits. Assembly language for one machine language. Projects to illustrate programming techniques in assembly language including, loops, procedure and subroutine call and return, parameter passing, call stacks, data structures. Introduction to the C language,, including the C reprocessor, macros, and syntax. Data types, structures, pointers and pointers to functions. PREREQ: CMP 326 and CMP 334.

CMP 426: Operating Systems. 4 hours, 4 credits. Operating systems and their role in various types of computer systems; the principles of multiprogramming; algorithms for resource allocation; multiple-computer systems. PREREQ: CMP 338 and CMP 334.

CMP 464: Topics in Computer Science. 4 hours, 4 credits (maximum 8 credits). Various sections on topics in computer science. (For specific topics and sections, consult the Department.)

CMP 485: Independent Study. 3 hours, 3 credits (maximum 6 credits). Independent study on a specific topic under faculty supervision. PREREQ: Departmental permission.

CMP 487: Internship in Computer Science. One semester, 3 credits (maximum 6 credits). On-the-job training in a public or private institution. PREREQ: Prior approval of department chair. NOTE: Not allowed for credit toward the B.A. in Computer Science.

Courses in Computer Applications (CIS)

CIS 106: Computer Literacy. 4 hours (2, lecture; 2, lab), 3 credits. Use of software packages for word processing, database manipulation, and spreadsheet calculation. Introduction to the Internet and the World Wide Web.

CIS 166: Computer Programming for Information Processing I. 4 hours, 4 credits. Computers, algorithms, and programs. Data representation; processing of quantitative and character data. Control structures, multidimensional arrays. Introduction to formatted input/output procedures. Programming applications drawn from business information processing. PREREQ: MAT 104 or placement by the Department of Mathematics and Computer Science. NOTE: Intended for students in accounting or Computer Information Systems. Not intended for students in Mathematics or Computer Science.

CIS 211: Computer Information Systems. 4 hours, 4 credits. Survey of the technology and applications of computer-based information systems in business. PREREQ: three years of Regents-level mathematics or MAT 104.

CIS 212: Microcomputer Architecture. 4 hours (2 lecture, 2 lab), 3 credits. Architecture of microcomputer systems and its supporting system software. Various microprocessor systems, expansion bus design, memory design and management, secondary storage technologies and management, peripherals, and telecommunication technologies. PREREQ: CIS 211.

CIS 228: The Internet. 4 hours (2 lecture, 2 lab), 3 credits. Technical aspects of the Internet including: hardware needed to connect to the Internet, software requirements and service providers, Internet addressing, Mail, the World Wide Web (WWW) including home page creation with HTML, Web Site planning and implementation, FTP, search engines as well as security aspects. PREREQ: CIS 211 and CIS 166.

CIS 234: Introduction to Spreadsheet Analysis. 4 hours (2, lecture; 2, lab), 3 credits. Use of spreadsheet software for elementary data analysis, simple modeling and forecasting. Worksheets, files, graphs, and formatted output and screen presentation. Macro programming. PREREQ: MAT 171 and a grade of B- (or better) in CIS 166.

CIS 241: Computer Graphics in Business. 4 hours (2 lecture, 2 lab), 3 credits. Applications of graphics in business as a reporting and analysis tool: presentation packages, project management packages, desktop publishing, CAD/CAM. Overview of the methods (software and hardware) used for generating graphics, including algorithmic image manipulation, interactive processing, input tools and display tools. PREREQ: MAT 171.

CIS 242: Introduction to Systems Analysis and Design. 4 hours, 4 credits. Study of a computer system life cycle via a structured approach: problem definition, feasibility study, cost estimation, analysis, design, implementation, testing and maintenance. Hardware and software organization. Several case studies will be considered. PREREQ: CIS 211.

CIS 243: Introduction to Operating Systems. 4 hours (2 lecture, 2 lab), 3 credits. Overview of operating systems (OS) from the point of view of the OS user and the system manager: process management and multitasking, memory management, resource management, file management, I/O management, command interpreter/shell, shell scripts. Some time will also be spent on network OS. PREREQ: CIS 211, CIS 212, and CIS 166.

CIS 244: Introduction to Database Management. 4 hours (2 lecture, 2 lab), 3 credits. Fundamental concepts of database organization: fields, records, tables, indexes, queries, forms, reports. Use of a relational database system for loading, modifying and querying a data base. Programming in a database language. PREREQ: A grade of B- (or better) in CIS 166.

CIS 247: Practical UNIX: Programming and System Administration. 4 hours (2 lecture, 2 lab), 3 credits. Topics chosen from the following: text editors, file system, utility programs, pipe and filter paradigms, shell language programming; tools for maintenance of normal system operation, security, hardware and software configuration management and network connections. PREREQ: CIS 211 and CIS 166.

CIS 249: Introduction to Local Area Networks (LAN's). 4 hours (2 lecture, 2 lab), 3 credits. An overview of LAN's from the point of view of a network administrator as well as a hands-on introduction to a popular network operating system. General topics will include LAN media, topologies, protocols, multi-platform connectivity, remote access, and rudimentary internetworking. PREREQ: CIS 211 and CIS 212.

CIS 252: Topics in Computer Applications. 4 hours (2 lecture, 2 lab), 3 credits. (May be repeated for credit as the topic changes up to a maximum of 6 credits.) Various sections on topics in Computer Applications (for specific topics, see the Department.) PREREQ: See the Department.

CIS 266: Computer Programming for Information Processing II. 4 hours, 4 credits. Techniques of business information processing using object-oriented programming. Random access files, data management and control, variable arrays, object variables. Introduction to advanced techniques. PREREQ: A grade of C or better in CIS 166.

CIS 324: Spreadsheet Design and Programming. 4 hours (2 lecture, 2 lab), 3 credits. Advanced features of spreadsheets, including graphics, database manipulation, built-in functions, and macros, applied to a variety of business-oriented problems. PREREQ: CIS 234.

CIS 344: Database Design and Programming. 4 hours (2, lecture, 2, lab), 3 credits. Programming in a database language. Emphasis on programming ideas and techniques and user interfaces in a modern database system. Review of elementary relational database concepts, with emphasis on programming rather than theory. PREREQ: CIS 244 and CIS 166.

CIS 349: Introduction to Data Communications and Distributed Networks. 4 hours, 4 credits. Data communications: standard models, system operations, major components, digital transmission (including some current schemes such as SONET, ISDN and ATM), distributed network architectures, local area network architectures, and the client/server model. PREREQ: CIS 211.

CIS 356: Intermediate-Level Topics in Computer Applications. 4 hours, 4 credits. (May be repeated for credit as the topic changes up to a maximum of 8 credits.) Various sections on topics in Computer Applications at the intermediate level (for specific topics, see the Department). PREREQ: See the Department.

CIS 488: Internship in Computer Information Systems. 12 hours per week, 3 credits (maximum 6 credits). On-the-job training in a public or private institution.

Courses in Computer Graphics & Imaging (CGI)

CGI (ART) 221: Applied Imaging and Applications to the World Wide Web I. 4 hours (2 lecture, 2 lab), 3 credits. Concepts and techniques underlying the World Wide Web. Image processing and two-dimensional graphics as methods to produce material for the World Wide Web. Emphasis on the artistic, mathematical, and computer science underpinnings of these topics. PREREQ: An introductory hands-on microcomputer course. COREQ: ART 108. NOTE: May be substituted for a CIS elective in the Computing and Management major.

CGI (ART) 222: Applied Imaging and Applications to the World Wide Web II. 4 hours (2 lecture, 2 lab), 3 credits. Advanced methods of two dimensional graphics, image processing, and World Wide Web design leading to team projects in the fields of science and art. PREREQ: CGI (ART) 221.

CGI (ART) 321: Computer Modeling and Design I. 4 hours (2 lecture, 2 lab), 3 credits. An introduction to the theory and practice of two- and three-dimensional modeling and rendering. Exploration of mathematical and design concepts in the lecture room, on the computer, and in the studio. Topics to include primitive objects, transformations, curve creation and manipulation, symmetries, surface creation and modification, basic rendering. PREREQ: CGI (ART) 221 or MAT 172, together with any hands-on Microcomputer course. NOTE: May be substituted for a CIS elective in the Computing and Management major.

CGI (ART) 322: Computer Modeling and Design II. 4 hours (2 lecture, 2 lab), 3 credits. Advanced surface modeling with consideration of continuity of surfaces and their tangents and curvature. Evaluation techniques, construction planes, modeling workflow. Creation of computer models from two-dimensional views and three-dimensional models. Projects from industrial design and scientific visualization. World Wide Web applications. PREREQ: CGI (ART) 321.

CGI (ART) 325: Digital Multimedia. 4 hours (2 lecture, 2 lab), 3 credits. Web and disk based multimedia projects in the digital realm including digital audio, digital video and interactivity. PREREQ: CGI (ART) 221 or CGI (ART) 321.

CGI (ART) 421: Computer Animation I. 4 hours (2, lecture; 2, lab), 3 credits. Introduction to computer animation. Frames, keyframes, hierarchical animation, morphing, expressions, and character animation with skeletons. PREREQ: CGI (ART) 321 and either MAT 175 or MAT 174. NOTE: May be substituted for a CIS elective in the Computing and Management major.

CGI (ART) 422: Computer Animation II. 4 hours (2 lecture, 2 lab), 3 credits. Advanced animation. Inverse kinematics, constraints and particle systems, manipulation of graphs to control animation. Applications to scientific visualization, film, multimedia, and TV. PREREQ: CGI (ART) 421.

CGI (ART) 451: Topics in Computer Imaging. 4 hours (2 lecture, 2 lab), 3 credits (maximum 6 credits). For specific topics and sections, consult the Department.

CGI (ART) 480: Senior Project. 3 hours, 3 credits. Advanced projects in the field of computer imaging under faculty guidance. PREREQ: Departmental permission.

CGI (ART) 481: Independent Study in Computer Imaging. 3 hours, 3 credits. Independent study on a specific topic under faculty supervision. PREREQ: Departmental permission.

*Not expected to be offered in 2005-2007