# MATH MATHEMATICS

## School of Arts and Sciences

## 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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

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.
*

This page is maintained by Linda M. Chojnicki,

Western New England College's Academic Schedule Controller