 # MATH MATHEMATICS

## MATH 099 INTRODUCTION TO ALGEBRA

An analysis of basic algebra topics in preparation for MATH 100. Topics to be covered at a review pace include basic operations of real numbers, linear equations, and inequalities, operations of polynomials, and factoring. This course is designed for non-traditional and transfer students who may be lacking the background necessary to enter MATH 100. May not be counted toward the general college mathematics requirement; may be taken for credit only as a general elective. 3 s.h.

## MATH 100 ALGEBRA FUNDAMENTALS

Prerequisite: one year of secondary school algebra. A review of the fundamentals of high school algebra designed for students who need a review in preparation for MATH 111 Analysis for Business and Economics I. May not be counted toward the general college mathematics requirement; may be taken for credit only as a general elective. 3 s.h.

## MATH 105 CONTEMPORARY MATHEMATICS I

A survey of some contemporary applications of mathematics. Two thirds of the course focuses on the use of graph theory in the area of management science. Topics include: Euler circuits, Hamilton circuits and the Traveling Salesman Problem, minimum network problems, and scheduling. There is an emphasis on using graph theory to model many real world problems and applying mathematical algorithms to solve them. The remainder of the course focuses on growth, symmetry, and the connections between mathematics and nature. Topics include: spiral growth, Fibonacci numbers, the golden ratio, symmetry of scale and fractals. 3 s.h.

## MATH 106 CONTEMPORARY MATHEMATICS II

A survey of some contemporary applications of mathematics. Two thirds of the course focuses on the mathematics of social choice. Topics include voting theory, weighted voting systems, fair division problems, and apportionment. The remainder of the course focuses on the study of probability and statistics. Topics include: graphical representations and numerical summaries of data, as well as the use of formal probability models to solve a variety of interesting problems. 3 s.h.

## MATH 109 PRE-CALCULUS MATHEMATICS

Prerequisites: two years of algebra and one year of geometry. An overview of the algebra and trigonometry needed for analytic geometry and calculus. Designed for students who need a review before taking calculus. Topics include basic algebra, functions and graphs, radicals and exponents, trigonometric functions, identities and equations. TI-83 Calculator is required. 3 s.h.

## MATH 111 ANALYSIS FOR BUSINESS AND ECONOMICS I

Prerequisite: MATH 100 or the equivalent within the last four years, or successful performance on the WNEC placement test. A course covering modeling with linear and quadratic functions in addition to a study of two optimization methods: linear programming and calculus. Topics include linear and quadratic functions with applications to supply, demand, cost, revenue, profit, break- even, and equilibrium analysis, in addition to systems of linear equalities and inequalities as they lead to linear programming. Modeling using the logarithmic and exponential functions, and the derivative as used in optimization are included. Emphasis is on the problem-solving approach with use throughout of the graphing calculator and a spreadsheet program. TI-83 Calculator is required. 3 s.h.

## MATH 112 ANALYSIS FOR BUSINESS II

Prerequisite: MATH 100 or the equivalent within the last four years, or successful performance on the WNEC placement test. A study of some areas of mathematics which are useful to business decision-makers. Generally, the topics covered are probability, statistics, and graph theory. The course includes basic counting principles, permutations and combinations, basic probability distributions, expectation, measures of central tendency and dispersion, the critical path method, Hamiltonian circuits, scheduling, and PERT. TI-83 Calculator is required. 3 s.h.

## MATH 123 CALCULUS I FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES

Prerequisite: Three years of secondary school mathematics, including two years of algebra. A study of functions, limits, continuity, the derivative, and applications of the derivative. Among the business related applied topics are supply and demand functions; marginal revenue, cost, and profit; elasticity of demand; inventory control; and compound interest. Other applied topics include looking at population trends; velocities and accelerations; depreciation of resources; and rates of change of medication in the blood stream. General applications include rates of change; curve sketching; and maximizing and minimizing functions. Credit for both this course and MATH 131 or MATH 133 is not permissible. TI- 83 Calculator is required. 3 s.h.

## MATH 124 CALCULUS II FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES

Prerequisite: MATH 123 or the equivalent. A study of exponential and logarithmic function, techniques and applications of integration, and multivariable calculus. Among the applied topics are models of growth and decay; continuous interest; payments on loans; consumers' and producers' surplus; and probability distributions. Credit for both this course and MATH 134 is not permissible. TI-83 Calculator is required. 3 s.h.

## MATH 131 CALCULUS IA (WITH PRE-CALCULUS REVIEW)

Prerequisite: 3 units of high school mathematics. An introduction to calculus designed for students needing a review of pre-calculus mathematics. Topics include algebra review, algebraic functions and graphs, limits of functions, the derivative, differentiation of algebraic functions, the chain rule, implicit differentiation, and related rates. Not open to students who have received credit for MATH 123 or MATH 133. TI-85 Calculator is required. 4 s.h.

## MATH 132 CALCULUS IB (WITH TRIGONOMETRY)

Prerequisite: MATH 131 or permission of instructor. A continuation of MATH 131. Topics include trigonometry review, derivatives of trigonometric functions, local extrema of functions, derivative tests for extrema, antiderivatives, the definite integral, the fundamental theorem of calculus, and change of variables in indefinite integrals. Credit for both this course and MATH 123 or MATH 133 is not permissible. TI-85 Calculator is required. 4 s.h.

## MATH 133 CALCULUS I

Prerequisite: MATH 109 or the equivalent. An introduction to the calculus of algebraic and trigonometric functions of one variable. Topics include limits, continuity, the derivative and applications of the derivative, the integral, and the Fundamental Theorem of Calculus. Credit for both this course and MATH 123 or MATH 132 is not permissible. TI-85 Calculator is required. 4 s.h.

## MATH 134 CALCULUS II

Prerequisite: MATH 132 or MATH 133. A study of the transcendental functions, using the methods developed in the Prerequisite course. Other topics include applications of integration, integration techniques, indeterminate forms, conic sections, parametric equations, polar coordinates, and infinite series. Credit for both this course and MATH 124 is not permissible. TI-85 Calculator is required. 4 s.h.

## MATH 190 SPECIAL TOPICS IN MATHEMATICS

Topics in mathematics which are not carried in the catalogue on a regular basis. The course may be repeated for credit if the topic varies. 1-3 s.h.

## MATH 207 INTRODUCTORY STATISTICS FOR THE ARTS AND SCIENCES

Prerequisite: MATH 105 or MATH 111 or permission. An introduction to the basic descriptive and inferential techniques for presenting, analyzing, and interpreting data that may arise in several fields. Topics include frequency distributions, measures of central tendency, probability, sampling, estimation, correlation and regression, hypothesis testing, and tests of significance. Emphasis is on understanding and interpreting, not on computations. A standard statistical software package is used throughout the course. The course is intended for general students, not for those whose major program requires PSY 207, QM 203, or ENGR 212. Credit for both this course and PSY 207 or QM 201 is not permissible. TI-83 Calculator is required. 3 s.h.

## MATH 235 CALCULUS III

Prerequisite: MATH 134 or MATH 124. An extension of the basic concepts of calculus to functions of several variables. Topics include three-dimensional analytic geometry, vectors and vector functions, partial differentiation, and multiple integration. TI-85 Calculator is required. 3 s.h.

## MATH 236 DIFFERENTIAL EQUATIONS

Prerequisite: MATH 134. A survey of the standard techniques for solving ordinary differential equations. Emphasis is on first and second order linear equations, with a focus on applications. The Laplace transform method and some "one-step" numerical methods of solution are included. TI-85 Calculator is required. 3 s.h.

## MATH 261 DISCRETE STRUCTURES I

Prerequisites: PH 104 and either MATH 124 or MATH 134; or permission. A first course in discrete mathematical structures with an emphasis on the foundations of higher mathematics. It is designed for students who need a transitional course to bridge the gap between the study of calculus and the study of a variety of upper division mathematics courses, where the ability to think like a mathematician is critical. Emphasis is on exploring, thinking, and thought processes as opposed to "how to do it" when solving problems. The topics include sets, sequences, relations, functions, the language of mathematics, proof and exploration, induction, cardinality, algorithms, and recursion. 3 s.h.

## MATH 262 DISCRETE STRUCTURES II

Prerequisite: MATH 261 or permission. A continuation of the study of discrete mathematical structures with an emphasis on the foundations of higher mathematics. The topics include combinatorics, graphs, and trees. Emphasis is on the exploration of mathematical ideas by working with examples, asking questions, making guesses, and testing conjectures. Applications of the topics are presented in several diverse fields. 3 s.h.

## MATH 272 PROBABILITY

Prerequisite: MATH 235. A calculus based course in the theory of probability. Topics include sample spaces, combinatorics, axioms and rules of probability, conditional probability and independence, discrete and continuous random variables, mathematical expectation, and the moment generating function. 3 s.h.

## MATH 290 SPECIAL TOPICS IN MATHEMATICS

Topics in mathematics which are not carried in the catalogue on a regular basis. The course may be repeated for credit if the topic varies. 1-3 s.h.

## MATH 306 LINEAR ALGEBRA

Prerequisite: MATH 124 or MATH 134. Topics include vectors and matrices, systems of linear equations, vector spaces, mappings, determinants, eigenvalues and eigenvectors, and transformations. Applications in many fields are discussed. The computer is used at the discretion of the instructor. TI-85 Calculator is required. 3 s.h.

## MATH 310 TOPICS IN ACTUARIAL SCIENCE

Prerequisites: MATH 235 and permission of the instructor. A course specifically designed to provide students with additional preparation for one or both of the first two actuarial examinations. Topics are selected from the areas of calculus, real analysis, and probability and statistics, depending upon the needs of the students. The course may be repeated for credit, subject to the permission of the instructor. Offered on demand. 1-3 s.h.

## MATH 311 NUMERICAL ANALYSIS

Prerequisite: MATH 124 or MATH 134. A study of various approximation techniques. Topics include error evaluation, numerical solution of non-linear equations, numerical solution of systems of equations, interpolating polynomials, numerical differentiation, numerical integration, and numerical solution of ordinary differential equations. Students use interactive computer programs throughout the course. Offered on demand. TI-85 Calculator is required. 3 s.h.

## MATH 333-334 INDEPENDENT STUDY IN MATHEMATICS

Prerequisite: senior standing. See "Independent Study" on page 29. 1-3 s.h.

## MATH 350 ENGINEERING ANALYSIS I

Prerequisite: MATH 236. Selected topics from linear algebra, vector calculus, line and surface integrals, Fourier series and integrals, and partial differential equations. The emphasis is on engineering applications and the use of the computer to illustrate techniques. 3 s.h.

## MATH 363 MATHEMATICAL FOUNDATIONS AND METHODS FOR COMPUTER SCIENCE

Prerequisite: MATH 262 and CS 283; or permission of the instructor. A study of the mathematical background and methods needed in computer science, especially in the specification, design, analysis, and verification of algorithms. Topics include predicate calculus, solution of recurrences, generating functions, finite state machines and formal languages, and introduction to computability and complexity. Offered in alternate years. 3 s.h.

## MATH 371 MODERN ASPECTS OF GEOMETRY

Prerequisite: MATH 261. An examination of various topics in geometry. Topics selected depend on the interests of the instructor and the needs of the students involved. Possible topics include finite geometries, Euclid's Elements (Book I), advanced topics in Euclidean geometry, Euclidean constructions and impossible constructions, transformations of the plane, non- Euclidean geometry, and projective geometry. Offered in alternate years. 3 s.h.

## MATH 373 MATHEMATICAL STATISTICS

Prerequisite: MATH 272. This course and the Prerequisite are intended to prepare students to take the actuarial exam on probability and statistics. Topics include sampling distributions of certain statistics, confidence intervals, tests of hypotheses, regression and correlation, goodness of fit tests, and Bayesian estimation. Offered in alternate years. 3 s.h.

## MATH 377 ELEMENTARY NUMBER THEORY

Prerequisite: MATH 261. The study of integers and their properties. The course provides a simple account of classical number theory as well as some of its historical background, including divisibility; gcd's; prime factorization; congruencies; theorems of Wilson, Fermat, and Euler; pseudoprimes; multiplicative functions; and primitive roots. Other topics include recent applications of the classical subject area in cryptology and computer science. Offered in alternate years. 3 s.h.

## MATH 390 SPECIAL TOPICS IN MATHEMATICS

Prerequisites: junior standing and permission of the instructor. Topics offered depend upon student interests as well as particular interests of instructors. The course is offered as often as faculty time and student interest permit. May be repeated for credit if topic differs. 1-3 s.h.

## MATH 412 INTRODUCTION TO TOPOLOGY

Prerequisite: MATH 261. Introductory topics in the general theory of topological spaces. Included are examinations of plane topology and topological properties of metric spaces. Offered on demand. 3 s.h.

## MATH 418 INTRODUCTION TO MODERN ALGEBRA

Prerequisite: MATH 261. An introduction to the abstract theory of groups, rings, and fields. Topics include homomorphisms and polynomials and their roots. The emphasis is on the axiomatic approach to algebra and the construction of proofs. Offered in alternate years. 3 s.h.

## MATH 420 MATHEMATICAL MODELING

Prerequisites: MATH 272; MATH 236 or MATH 311. An introduction to the construction and refinement of mathematical models. Applications include resource allocation, environmental planning, and decision theory. The mathematics involves difference equations, Markov chains, linear and dynamic programming, game theory, and queueing theory. 3 s.h.

## MATH 421 REAL ANALYSIS

Prerequisite: MATH 235. An introduction to the rigorous treatment of analysis. Topics covered include the real number system, sequences, limits of functions, continuity, differentiation, integration, infinite series, sequences and series of functions. Offered in alternate years. 3 s.h.

## MATH 427 COMPLEX ANALYSIS

Prerequisite: MATH 235. An introductory course in the theory of functions of a complex variable covering standard topics: the algebra and geometry of complex numbers, differentiation, integration, power series expansions, residues, and poles. Offered on demand. 3 s.h.

## MATH 480-81 INTERNSHIP IN MATHEMATICS

See "Internships" on page 30. MATH 490 SEMINAR Prerequisite: permission of the instructor. Topics discussed depend upon the interest of the students. Seniors or unusually well qualified juniors may be admitted to the course only by permission of the Department. Offered on demand. 3 s.h.

## MATH 501 ENGINEERING ANALYSIS II

Prerequisite: MATH 350. A study of selected topics from the theory of partial differential equations. Topics include vector spaces; linear algebra; systems of differential equations; Fourier transforms; and the theory of functions of a complex variable, including Taylor and Laurent series and residues and poles. Offered on demand. 3 s.h.