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MATHEMATICS MINOR
To graduate with a minor in mathematics, a student must complete a program approved by the department chair consisting of at least five mathematics courses numbered 145 or higher. No course may be taken pass/fail.
Courses
MTH 007. Intermediate Algebra (0).
A non-credit, pre-college course in intermediate algebra stressing graphing and equation solving, algebraic manipulation, laws of exponents functions, and logarithms.
MTH 102. Mathematics for Elementary Teachers (3).
A problem-solving oriented course for prospective elementary school teachers. Topics will include some of the following: properties of number systems, place value and scales of notation, elementary number theory, geometry and measurement, statistics probability. Open only to students in the Elementary Education program. Prerequisite: Three units of high-school mathematics or MTH 007.
MTH 111. Introduction to Statistics I (4).
A data-oriented, applied introduction to statistics; includes a 2 hour per week lab. Topics include descriptive statistics, distributions, hypothesis testing, confidence intervals, and an introduction to multivariate statistics. Prerequisite: Three years of Regents level mathematics.
MTH 112. Introduction to Statistics II (4).
Tabular and graphical representations of data. Descriptive statistics. Random sampling. Basic probability theory and sampling distributions. Point and interval estimation. Tests of hypotheses using normal distribution and non-parametric methods. Additional topics from correlation and regression analysis, measures of association, analysis of variance and goodness of fit. Introduction to use of computer statistical packages. Primarily for students in the social sciences and education. Prerequisite: three units of high-school mathematics including intermediate algebra or MTH 007, Math 111 or its equivalent is a prerequisite for Math 112.
MTH 120. Mathematics for Business Majors (3).
This course includes the following topics: exponential functions and models, mathematics of finance, linear systems and matrices, linear programming derivatives. There is particular emphasis on applied problems. Prerequisite: three units of high-school mathematics or MTH 007.
MTH 122. Introduction to Optimization Methods II (3).
Elementary functions, exponential and logarithmic functions, continuity, derivatives, max-min methods and applications. Primarily for students in economics and accounting. Prerequisite: three units of high-school mathematics including intermediate algebra.
MTH 123. MATHEMATICS FOR ACCOUNTING MAJORS (3).
An introduction to various contemporary applications of mathematics drawn from the following topics: linear algebra, combinatorics, graph theory, probability, modern algebra. The emphasis is on the interplay between theory and application in mathematics. Prerequisite: Four years of high school mathematics.
MTH 145-146. Calculus I, II (4) and (4).
A study of differential and integral calculus of one and several variables and applications. Differential equations and their solutions. Prerequisite: four units of high-school mathematics or permission of department. Math 145 or its equivalent is a prerequisite for Math 146.
MTH 152-152. Calculus I, II for Mathematics and Physics Majors (4) and (4).
Standard topics of calculus (derivatives, integrals, sequences and series) taught with extensive use of computers (ISTEL, MAPLE software) and group work. The emphasis is on deep understanding of the basic concepts. Prerequisite: four units of high-school mathematics. MTH 151 is a prerequisite for MTH 152.
MTH 202. Introduction to Contemporary Mathematics (3).
An introduction to topics in contemporary mathematics emphasizing practicality as well as beauty. Topics include management science, statistics, social choice, geometry and topology.
MTH 245. Calculus III (4).
Sequences, series, power series. Multi-variate calculus with vectors. Line integrals and Green's theorem. Prerequisite: MTH 146 or MTH 152.
MTH 261. Linear Algebra (3).
Systems of linear equations, matrix algebra, vectors and vector spaces, linear transformations, inner product spaces, determinants, characteristic values and vectors. Prerequisites: MTH 145-146 or MTH 151-152.
MTH 303. Differential Equations (3).
Linear differential operators and equations. Existence and uniqueness of solutions: initial-value problems. The Wronskian, homogeneous equations and non homogeneous equations: variation of parameters, the method of undetermined coefficients. The Euler equation, the Laplace transform, normal systems, eigen values and eigenvectors. Series solutions. Prerequisite: MTH 245.
MTH 306. Topics in Number Theory (3).
Elementary properties of integers, divisibility and related concepts, methods of representing integers, functions of number theory, simple diophantine equations, special sequences and series. Prerequisite: three semesters of mathematics or permission of the department chair.
MTH 307. Combinatorial Mathematics and Graph Theory (3).
Some classical puzzles of recreational mathematics; enumeration techniques; combinatorial designs; graph theory and network flows. Prerequisite: three semesters of mathematics or permission of the department chair.
MTH 311. Introduction to Probability theory (3).
Basic probability theory, combinatorial analysis, independence and dependence. Discrete and continuous distributions, random variables, random vectors, multivariate distributions. Expectations and moment generating functions. Binomial, normal, Poisson and related distributions. Sums and sequences of random variables. Central limit theorem. Prerequisites: MTH 245 and MTH 281 or permission of department.
MTH 312. Mathematical Statistics (3).
Distributions related to the normal. Estimation: consistency, unbiasedness, mean square error, sufficiency, method of moments, maximum likelihood estimates, confidence limits and intervals. Bayesian intervals. Tests of hypotheses: tests of simple hypotheses, Neyman-Pearson lemma, Bayes procedures, composite hypotheses, generalized likelihood ratio tests. Non-parametric procedures. Simple linear regression. Prerequisite: MTH 311.
MTH 313. Applied Statistics (3).
Linear models and analysis of variance. Least squares theory. Regression and correlation. Design of experiments. Some applications of regression analysis in practical research. Prerequisite: MTH 312.
MTH 332. Real Analysis (4).
An introduction to techniques of mathematical proof, with emphasis on the recognition and evaluation of problem structures common to all areas of mathematics. Application of these techniques to a detailed description of the Real Number system. Examination of the algebraic, set-theoretic and topological structures of the Real Number system (completeness, compactness, connectedness) and real sequences. Prerequisites: MTH 245, MTH 261.
MTH 341. Algebraic Structures I (3).
Fundamental structures of semigroups, groups, rings, integral domains and fields and their morphisms. Prerequisite: MTH 261 or permission of the department chair.
MTH 351. Linear and Mathematical Programming (3).
The general linear programming problem. The simplex algorithm: theoretical and computational aspects. Duality and relationships to sensitivity analysis. Specialized algorithms. Extensions to some nonlinear programming problems. Prerequisite: MTH 261.
MTH 361. Modern Geometry (3).
Topics from the foundations of geometry, non-Euclidean geometry, transformation theory, dissection theory, convexity. Prerequisite: three semesters of mathematics or permission of the department chair.
MTH 370. Intermediate Problem Solving (3).
A working introduction to general heuristic reasoning (including specialization, generalization, analogy and induction) useful in solving mathematical problems. Prerequisite: MTH 245 or permission of the department chair.
MTH 390-399. Independent Study.
A student who wishes to pursue an independent study project for academic credit must submit, prior to registration, a proposed plan of study that includes the topic to be studied and goal to be achieved, the methodology to be followed, schedule of supervision, end product, evaluation procedure and number of credits sought. The proposal must be approved by the supervising faculty member, the department chair and the assistant academic vice president. It will be kept on file in the assistant academic vice president's office.
MTH 421. Numerical Analysis (3).
The development of algorithms for and error analysis of: solutions of equations, interpolation and approximation, numerical differentiation and integration, numerical solutions of differential equations. Prerequisites: MTH 245; MTH 261 also, knowledge of a high level programming language or permission of the department chair.
MTH 431. Introduction to Complex Analysis (3).
The complex number system. Differenti-ability and the Cauchy-Riemann conditions. The exponential, trigonometric and logarithm functions. Complex integration; the Cauchy integral theorem and its implications. Consequences of the Cauchy integral formula. Taylor and Laurent series, singularities. Prerequisite: MTH 245 or permission of the department chair.
MTH 470-479. Topics in Mathematics (3).
These courses will vary in content and will be offered irregularly depending on student interest and faculty availability. The following titles apply for MTH 470-475:
MTH 470. HISTORY OF MATHEMATICS (3).
MTH 471. ADVANCED TOPICS IN ANALYSIS (3).
MTH 472. ADVANCED TOPICS IN ALGEBRA (3).
MTH 473. ADVANCED TOPICS IN STATISTICS (3).
MTH 474. PROBABILITY MODELS (3).
MTH 475. ADVANCED TOPICS IN LINEAR ALGEBRA (3).
MTH 481. Topology (3).
Topological spaces; separation and countability properties. Mappings and continuity. Compactness and connectedness of various types. Product and quotient spaces. Prerequisite: MTH 332 or permission of the department chair.
MTH 490. Internship (3).
A limited number of internships are available to students to provide them with practical experience in the applications of mathematics in business. Prerequisite: Senior standing in mathematics and prior consultation with department chair.
MTH 495. Senior Research Project (3).
This course, exclusively for senior mathematics majors, involves the completion and presentation of a research project in the student's area of concentration. Prior to registration for the course, a student must submit a proposal and have it approved by the department chair. Students may work in teams of two or three on projects; however, team projects will require commensurably greater scope than individual projects.
MTH 496-499. Research.
An upper-class student who wishes to undertake a research project for academic credit during a given semester must submit a research proposal prior to registration and a research report at the end of the semester. The proposal, indicating the number of credits sought, must be approved by the research director, the department chair and the academic dean. It will be kept on file in the academic dean's office.
COMPUTER SCIENCE
CSC 141. BASIC Programming (3).
This course is an introduction to programming and to interactive communication with the computer. It includes an in-depth study of a dialect of the BASIC programming language. The following topics are treated: problem analysis, algorithm construction, program development, control structures, modularization, arrays, elementary file-handling, an internal search algorithm and a simple internal sort algorithm. No prerequisites.
CSC 151. Introduction to Information Processing I (3).
An overview of past, present and future computing and its applications in the business setting. Topics include a brief history of modern computers and computer languages, an introduction to the hardware components of computer systems and their functions, information storage and organization, data communications and networks, and system and application software. Special features of microcomputer hardware and software will be considered. The course will include introductory concepts and applications of electronic spreadsheets, with practical experience in using standard spreadsheet software. No prerequisites.
CSC 171. Introduction to Programming Methodology (4).
After an introduction to the basic concepts of computer systems (hardware and software), this course deals with the general topic of problem solving and algorithm development, as implemented with the C programming language. The following aspects of programming are treated: data types (scalar and structured); program structures (control structures and subprograms, block structure of the language); introduction to program development (design, coding, testing, documentation). No prerequisites.
CSC 172. Data Structures and Program Development (4).
This course extends the study of programming methodology introduced in CSC 171 (specification, design, coding, verification). Concepts and implementations of standard data structures are studied: linear structures (lists, including stacks and queues) and nonlinear structures (trees, sets). Other topics include: recursion, the implementation and analysis of algorithms for internal searching and sorting, file merging as an external sort technique. Prerequisite: CSC 171.
CSC 203. COBOL Programming (3).
This course is a study of the COBOL programming language, with application of its features for table handling, sorting, sequential and random access file handling and modular programming. Prerequisite: prior experience with a high-level programming language.
CSC 206 (PHY 261). C/C++ Programming and Applications (3).
This course teaches the elements of C and C++ programming languages and applies those languages to topics in numerical problem solving relevant to science and engineering. Learning a subset of C and C++ is the dominant theme. In addition, the course applies those languages to problems from the following categories: elementary graphics programming, elementary concepts of numerical analysis, analysis of experimental data, simulation of physical systems, and representation and interpretation of quantitative information. Prerequisite: PHY 101 or permission of the instructor.
CSC 385. Consulting (1).
This course is a program of informal instruction in the total environment of the College's academic computer system hardware, operating system, system utilities, compilers, run-time systems, software packages and in the application of the student's consequent knowledge to assisting other students, as well as faculty members, in their use of this computer system. To be taken on a pass/fail basis only. Prerequisites: sophomore standing and permission of the department chair.
CSC 390-399. Independent Study.
A student who wishes to pursue an independent study project for academic credit must submit, prior to registration, a proposed plan of study that includes the topic to be studied and goal to be achieved, the methodology to be followed, schedule of supervision, end product, evaluation procedure and number of credits sought. The proposal must be approved by the supervising faculty member, the department chair and the academic dean. The proposal will be kept on file in the academic dean's office.
CSC 471. Automata and Computability (3).
A theoretical course dealing with ideas that underlie computing; the finite state automaton, pushdown automata, alphabets and strings, formal languages and grammars, Turing machines, the halting problem. Some of the following special topics may be introduced: fixed-point semantics, lambda calculus, combinators. Prerequisites: CSC 171.
CSC 481. Analysis of Algorithms (3).
This course deals with the design, implementation and validation of algorithms, along with the analysis of their time and space requirements. The course will consider several types of algorithms (recursion, divide-and-conquer, approximations) from various areas of computing (searching and sorting, graphs, matrix multiplication, combinatorics, pattern-matching, NP-complete problems). Prerequisites: CSC 172.
CSC 490. Internship in Computer Science.
Participation in a field learning experience in some area of computer science. The student intern reports as required to a supervising faculty member, who will evaluate the internship and its relation to the student's academic program. Prerequisites: a minimum of four computer science courses; junior or senior standing; and approval of the department. May be taken pass/fail only.
