Mathematics (MATH)
Computer Science (CMPT)

Associate Professor John McCabe,

Chair of the Department

Associate Professor Harold F. Bailey,

Associate Chair

General Requirements: Courses must be taken in the order prescribed in the Summary of Course Requirements for the various Schools. Any course in which a failure is obtained must be repeated and passed before the student may proceed to more advanced work. The Department offers two majors: mathematics and computer science.

Requirements for a Major in Mathematics: A major program in mathematics is available in the School of Science within either the Liberal Arts Curriculum leading to a Bachelor of Arts degree or the Science Curriculum leading to a Bachelor of Science degree. Students may also pursue a major program in Mathematics in the School of Education.

Students must complete MATH 103, 104, 201, 203, 213, 215, 313, 315, 316, 325, 407, 420, 460, CMPT 101 and 102, plus at least six additional credits in approved Departmental offerings. Students who major in mathematics and are selected for the honors sequence must complete MATH 109, 110, and 209 in place of 103, 104, 201.

Students who are pursuing certification in secondary education and majoring in mathematics must complete MATH 103, 104, 201, 213, 215, 311, 313, 315, 420, 421, 460, 466, and CMPT 101, 102.

Students who are pursuing certification in elementary education must complete MATH 103, 104, 201, 213, 215, 311, 420, 421, 466, CMPT 114, and 101 plus 3 credits in approved Departmental offerings.

A minimum grade of C in each of the required courses is necessary for the major. Before taking any major course, the student must obtain a grade of C or better in any prerequisite course.

Requirements for a Major in Computer Science.

A major program in computer science is available in the School of Science within either the Liberal Arts curriculum leading to a Bachelor of Arts degree or the Science Curriculum leading to a Bachelor of Science degree. Students may also pursue a major program in Computer Science in the School of Education.

Requirements for the BS in Computer Science.

Students must complete MATH 103, 104, 216, and 420; ELEC 229, CMPT 101, 102, 231, 238, 312, 334, 341, 335, 353, 360 and 438, plus at least six additional credits in approved departmental electives. A minimum grade of C in each of the required courses is required for the major. Before taking any major course, the student must obtain a grade of C or better in any prerequisite course.

Requirements for the BA in Computer Science.

Students must complete MATH 103, 104, 216, and 420; ELEC 229, CMPT 101, 102, 231, 238, 312, 334, 335, 341, 353, and 360, plus at least nine additional credits in approved departmental electives. A minimum grade of C in each of the required courses is required for the major. Before taking any major course, the student must obtain a grade of C or better in any prerequisite course.

Requirements for a Minor in Mathematics: Five approved courses, including MATH 103, 104, 201. A minimum grade of C is required in all courses.

Requirements for a Minor in Computer Science: CMPT 101, 102, and 3 additional approved courses. A minimum grade of C is required in all courses.

Mathematics (MATH)

Note: The following courses in Mathematics do not carry credit for the major or minor in mathematics: 100, 102, 105, 111, 211, 221, 222, 307, 333.

100. Pre-Calculus Mathematics. Basic set theory, functions, and their graphs. Topics from algebra, theory of equations, trigonometry and analytic geometry. Intended to prepare students for a course in calculus. (Meets four times a week.) (Cr.3)

102. Modern Mathematics. The mathematics of voting: different voting methods and various criteria for fairness. Weighted voting systems. Mathematics of fair division. Mathematics of apportionment. Graph theory. Consumer mathematics. Probability. (Cr.3)

103-104. Calculus I-II. Limits, derivatives, continuity, differentiation and an introduction to the definite integral. Applications of the definite integral, transcendental functions, integration techniques and infinite series. (Meets four times per week). Prerequisite: A satisfactory score on the mathematics placement exam or a Math SAT score of 550 or better to enroll in MATH 103; a grade of C or better in MATH 103 strongly recommended for students enrolling in MATH 104. (Cr.3)

105. Linear Mathematical Analysis. Functions, simultaneous linear equations and inequalities, and matrix algebra. Introduction to probability. (Cr.3)

106. Calculus for Business Decisions. A one-semester course in the calculus of functions of one variable, intended for students in Business. Polynomial, rational, and exponential functions, and the logarithm. Limits, derivatives, techniques and applications of differentiation. Indefinite and definite integrals, applications of the integral. Prerequisite: MATH 105 or permission of the chair. (Cr.3)

109-110. Honors Calculus I-II. Rigorous development of differential and integral calculus. Restricted to select students who will take this course in lieu of MATH 103-104. (Cr.3, 3)

111. Pre-Calculus. (For students in the School of Business only.) Review of elementary algebra, introduction to analytic geometry, functions and their graphs, logarithmic and exponential functions, polynomial functions. (This course meets four times per week). (Cr.3)

112-113. Calculus with Pre-Calculus. Limits, Derivatives, Curve sketching and applications, antiderivatives and the definite integral. Calculus topics are integrated with a review of pre-calculus topics in context. Completion of the sequence is equivalent to completion of MATH 103. (Meets four times per week.) (Cr.3)

201. Calculus III. Vectors, algebra and geometry, partial differentiation, multiple integrals. Prerequisite: MATH 103-104. (Cr.3)

203. Differential Equations. Solutions of equations of the first order. Numerical methods. Second order equations. Series solutions. Applications. Prerequisite: MATH 201 or 209. (Cr.3)

209. Honors Calculus III. Continuation of MATH 109-110. Fall. Prerequisite: MATH 110. (Cr.3)

211. Elementary Statistics. An introduction to statistical methods applicable in the social sciences; descriptive statistics, normal curve, tests of significance, regression and correlation. (Cr.3)

213. Foundations for Higher Mathematics. This course will serve as a bridge between introductory and advanced mathematics. The context of set theory and logic will be used to develop the skills of constructing and interpreting mathematical proofs. Fall. Prerequisite: MATH 104 or MATH 110, or permission of instructor. (Cr.3)

215. Linear Algebra. Linear equations and matrices, vector spaces, subspaces, linear independence, bases, dimension, inner product spaces, linear transformations, eigenvalues and eigenvectors, orthogonal matrices and diagonalization. Prerequisites: MATH 213, or permission of instructor. (Cr.3)

216. Discrete Mathematics for Computer Science. An introduction to the mathematical concepts and techniques most frequently needed in the study of computer science: logic, induction, sets and relations, matrix algebra, and recursion. Fall. Prerequisite: MATH 104, or permission of the chair. (Cr.3)

221, 222. Mathematics for the Elementary School Teachers I and II. Courses for prospective teachers in the elementary school who are not majoring in mathematics. The content and method will follow the current standards of the National Council of Teachers of Mathematics for the elementary level. Topics include tools for problem solving, numeration systems, number theory, geometry, and trigonometry. (Cr.3, 3)

305. Vector Calculus. Review of vector algebra. Vector-valued functions. Divergence and curl. Multiple integrals; different coordinate systems. Line integrals, Green’s Theorem, independence of path, conservative force fields. Surface integrals, Divergence Theorem. Stokes’ Theorem. Applications. Prerequisite: MATH 201 or 209. (Cr.3)

307. Fundamental Concepts. A course for prospective teachers of mathematics. There will be a strong concentration on the Topics of the New York State Regents Syllabus for secondary school mathematics. There will also be a computer component of the course which will include some work with current educational software. Mathematical topics will include sets, proofs, symbolic logic, analytic geometry and basic probability and statistics. Prerequisites: MATH 103, 104 or equiv., CMPT 114 or equiv. (Cr.3)

308. Partial Differential Equations. Classification of partial differential equations. Characteristics. Derivation of the classical linear second order equations. Fourier series. Separation of variables. Initial and boundary value problems. Cauchy, Dirichlet, and Neumann problems. Prerequisite: MATH 203. (Cr.3)

311. Introduction to Higher Geometry. (formerly 411). Selected topics from Euclidean and non-Euclidean geometries. Further topics in higher geometry, as time permits. Offered every other year. Spring. Prerequisites: MATH 213, 215. (Cr.3)

313. Analysis I. (formerly 413). A rigorous treatment of differential calculus of one variable: sequences, limits, continuity, the derivative. Fall. Prerequisites: MATH 201 and 213. (Cr.3)

314. Analysis II. A continuation of 313. Topology of the real numbers, uniform convergence, Riemann integral, infinite series, Taylor and Fourier series, metric spaces. Spring. Prerequisite: MATH 313. (Cr.3)

315. Algebra I. The first part of a two-semester sequence. An introduction to algebraic structures with an emphasis on groups, covering normal subgroups, cosets. Langrange’s theorem and the fundamental homomorphism theorems. Fall. Prerequisites: MATH 213, 215. (Cr.3)

316. Algebra II. The second part of a two-semester sequence. Further study of algebraic structures, such as rings, fields and integral domains. The homomorphism theorems and applications. Spring. Prerequisite: MATH 315. (Cr.3)

325. Linear Algebra II. A Continuation of the topics introduced in Linear Algebra, with emphasis on orthogonality, inner product spaces, eigenvalues and eigenvectors, diagonalization, quadratic forms and numerical linear algebra. Fall. Prerequisite: MATH 215. (Cr.3)

333. Statistics for Civil Engineers. Elements of probability theory: probability distributions; empirical determination of distribution models; sample size determination and statistical inference; linear and non-linear regression and correlation analysis; applications to civil engineering problems. Does not carry credit towards the mathematics major or minor. Prerequisite: MATH 201. (Cr.3)

407. Complex Analysis. The complex plane, functions, limits and continuity. Analytic functions, Cauchy-Riemann equations. Cauchy integral theorem and consequences. Power series, Taylor and Laurent series, classification of singularities. The Residue Theorem and its applications. Conformal mapping. Selected applications. Spring. Prerequisite: MATH 203 or permission of instructor, MATH 213 recommended. (Cr.3)

417. Topology. An Introduction to Topology. Beginning with a review of set theory and basic topological definitions, topological spaces are studied with metric spaces considered as examples. Compactness, connectedness, metrization theorems. An introduction to homotopy theory. Prerequisite: MATH 213 or permission of instructor. (Cr.3)

420. Probability. (formerly 323). Basic theorems in probability, random variables, distribution functions, expected values; binomial, Poisson and normal distributions. Fall. Prerequisite: MATH 104. (Cr.3)

421. Statistical Inference. (formerly 324). Sampling distributions, point estimation, interval estimation, testing statistical hypotheses, regression and correlation. Spring. Prerequisite: MATH 420. (Cr.3)

423. Advanced Mathematical Statistics I. Analysis of variance, regression analysis, nonparametric and sequential tests of hypotheses. Prerequisite: MATH 421. (Cr.3)

425. Operations Research. Optimization, linear programming, simplex method, duality theory. Transportation problems, scheduling problems, queuing theory. Prerequisite: MATH 215 or permission of instructor. (Cr.3)

460. Problem Seminar. A capstone course for senior mathematics majors. Problems will be chosen to integrate the themes of the major. Oral presentations and mathematical writing and proof will be emphasized. Spring. Prerequisites: MATH 313, 315, and senior status. (Cr.3)

461-462. Topics in Mathematics. Admission only by permission of the Chair of the Department. This course is offered when demand warrants. (Cr.3, 3)

465. Topics in Applied Mathematics. Topics covered include Fourier series, partial differential equations, the Laplace Transform. (Cr.3)

466. Seminar for Mathematics Education. Topics vary from year to year, but will be chosen by the instructor from the history of mathematics, mathematical modeling, number theory and algebra. (Offered in alternate years. Enrollment restricted to students in the School of Education.) Spring. Prerequisites: MATH 213 and 215. (Cr.3)

467. Mathematics Seminar. A course limited to students of superior ability who wish to study some advanced topic mutually agreed upon by them, the instructor and the Department Chair. (Cr.3)

469. Independent Study. Individual study and/or research under faculty supervision. (Cr.3)

Computer Science (CMPT)

Note: The following courses in Computer Science do not carry credit for the major or minor in computer science: 114, 115.

101. Computer Science I. An introduction to structured programming, problem solving, and algorithm development using the C++ programming language. (Cr.3)

102. Computer Science II. An introduction to classes, objects, and data structures including stacks, queues, linked lists, trees, searching and sorting. Prerequisite: A grade of C or better in CMPT 101. (Cr.3)

114. Computers and Their Uses. Introduction to computer systems, hardware and software including applications packages such as word processing, spreadsheet and database. (Cr.3)

115. Intermediate Computer Applications. This course is an alternative to CMPT 114, covering topics chosen at the discretion of the instructor. Permission required. (Cr.3)

231. Introduction to Computer Systems and Assembly Language. An overview of the computer’s internal structure. Representation of data. Assembly language instruction set and addressing modes. Common programming structures in assembly language. Macros. The stack; subroutines and procedures. Input/Output. A discussion of the assembly process. Fall. Prerequisites: CMPT 101, 102. (Cr.3)

238. Data Structures. Advanced data structures including hashing, trees, and heaps. Introduction of binary trees, binary search trees, and heaps as abstract data types. Implementation of these abstract data types and hashing using an object-oriented design. Discussion of the algorithms for searching, sorting, insertion and removal of values in various data structures. Prerequisite: CMPT 102; Corequisite: MATH 216 (Cr.3)

312. Operating Systems. File systems, CPU scheduling, memory management, virtual memory and machines, disk and drum scheduling, deadlocks and their prevention, concurrency, protection mechanisms, multiprocessors, distributed systems. A survey of the services provided by some of the more popular operating systems. Spring. Prerequisite: CMPT 353. (Cr.3)

334. Computer Organization. A detailed study of the internal structure of a computer. Historical evolution of computers. Computer systems organization: processors, memory, input/output. The digital logic level: gates, integrated circuits, memory, microprocessors. The microprogramming level: microarchitecture, microprograms. The conventional machine level; some examples of conventional machines. Prerequisite: ELEC 229 (Cr.3)

335. Discrete Structures. Further study of those mathematical structures most frequently encountered in computer science; graphs, trees, search algorithms, recurrence relations and coding theory. Prerequisite: MATH 216 or 203 or 213. (Cr.3)

336. Simulation and Modeling. Probability distributions, mathematical models, simulation of queuing systems, Markov chains. Prerequisite: MATH 420 and CMPT 360. (Cr.3)

339. Scientific Computing. Selected topics in computation, such as: solution of non-linear equations, Monte Carlo simulation, polynomial approximation, Least Squares curve fitting, numerical integration and differentiation, and numerical solution of ordinary differential equations. Prerequisites: CMPT 101, MATH 104. (Cr.4)

341. Programming Languages. Organization of programming languages, study of language specification and analysis, control structures and data flow. Prerequisites: CMPT 335, and either 238 or 360. (Cr.3)

353. Systems Programming with Unix. Review of C programming language. Introduction to the UNIX operating system and shell programming. Design and implementation of selected systems software in the UNIX environment including concurrency control mechanisms. Fall. Prerequisite: CMPT 238 or 360 or permission of instructor. (Cr.3)

360. Object Oriented Design with Java. Topics include the concepts of abstract data types, encapsulation, inheritance and polymorphism, as implemented in Java. Particular emphasis on modularity, derived classes, user interfaces, and class design using Java. Such topics as stacks, queues, binary trees and implementation packages such as Java-Util will be discussed. Prerequisite: CMPT 102. (Cr.4)

415. Computer Graphics. Printer Graphics, Graphics Primitives, Two and Three-Dimensional Transforms, Clip-ping, Hardware, Projections, User interface, Raster methods, Hidden Line algorithms, color and shading. Fall. Prerequisites: CMPT 238 or 360, MATH 104. (Cr.3)

420. Artificial Intelligence. Introduction to LISP as a programming language for artificial intelligence. Simulation of intelligence by machines in the areas of natural language processing, automated reasoning, computer vision, and robotics. Searching strategies and use of heuristic functions. Introduction to expert systems and the use of PROLOG. Spring. Prerequisite: CMPT 238 or 360. (Cr.3)

431. Multimedia. An introduction to the production of multimedia products using Macromedia Director. Elements of animation using vector shapes and bitmaps. Shockwave movies, projectors. Adding audio: WAV and Shockwave file formats. Digital video: using QuickTime and AVI file formats, Interactivity and the scripting language Lingo. Prerequisite: CMPT 238 or 360. (Cr.3)

438. Algorithms. Intermediate and advanced material will be selected from topics as the master method, greedy algorithms, basic graph algorithms, minimum spanning tree, shortest paths, Strassen’s algorithm, polynomials and FFT, shared secrets, public key cryptography, primality testing, string matching, NP-completeness, and approximation algorithms. Prerequisites: CMPT 335, and either 238 or 360. (Cr. 3)

439. Numerical Computation. Selected topics in computation. Prerequisite: CMPT 102, MATH 104. (Cr.3)

441. Web Programming. An introduction to programming for the web, using HTML and other scripting languages. Prerequisite: CMPT 102 or permission of the instructor. (Cr.3)

443. Computability Theory. Turing-computable functions, and their relationship to recursive functions. Formal languages, regularity, finite and pushdown automata and their simulation. Universality of programs and Turing machines. Unsolvability and an introduction to the theory of computational complexity. Fall. Prerequisite: CMPT 335 or MATH 213. (Cr.3)

454. Compiler Design. Introduction to automata and context-free grammars. Basic techniques of parsing and derivations. Generators, symbol tables, syntax-directed translation. Error detection, optimization, and data-flow analysis. Spring. Prerequisite: CMPT 341. (Cr.3)

456. Software Engineering. A study of the principles and methods advocated for the development of large and complex software systems. Each student will be required to participate in a team project devoted to the specification, design and implementation of a sizable software system. Prerequisite: CMPT 238 or 360 or permission of instructor. (Cr.3)

458. Database Systems. An introduction to database system concepts; the design and implementation of computer databases; entity-relationship and relational database models; data organization and management; data integrity and security. Prerequisite: CMPT 102. (Cr.3)

463-464. Topics in Computer Science. Admission only by permission of the Chair of the Department. This course is offered when demand warrants. (Cr.3)

467-468. Topics in Computer Science. Admission only by permission of the Chair of the Department. This course is offered when demand warrants. (Cr.3, 3)

469. Independent Study. Individual study and/or research under faculty supervision. (Cr.3)