Mathematics (MATH)

**090 Fundamentals
of Mathematics (3)** Review of pre-algebra mathematics with an introduction to
basic algebra. Topics include: real numbers, with an emphasis on fractions and
decimals, percent notation, exponents, algebraic expressions, solving equations
and inequalities, polynomials, and an introduction to graphing linear equations.
Does not apply toward general education requirements or graduation requirements.
Students taking this course must earn a grade of at least C- before enrolling in
MATH 095. F08, S09, F09, S10

**095 Fundamentals
of Algebra (3) **Review of elementary algebra topics typically studied in high
school. Topics include: the real number system, linear equations and
inequalities and their graphs, systems of linear equations and inequalities,
polynomials, factoring polynomials, quadratic equations. Does not apply toward
general education requirements or graduation requirements. Prerequisite:
Acceptable score on the Mathematics Placement Test or completion of MATH 090
with a grade of at least C-. F08, S09, F09, S10

**102 Intermediate
Algebra (2)** Review of intermediate algebra topics typically studied in high
school. Topics include: rational expressions and equations, rational exponents,
radical expressions and equations, complex numbers, functions, quadratic
equations and functions, graphing techniques, conic sections, exponential and
logarithmic functions and equations. Prerequisite: Acceptable score on the
Mathematics Placement Test or completion of MATH 095 with a grade of at least
C-. F08, S09, F09, S10

**112 Introduction
to Contemporary Mathematics (3)** A liberal arts mathematics course presenting
mathematics as a tool used by a wide range of professionals in modern society.
Real-life examples are used to promote understanding of mathematics and its
relationship to other areas of study. Mathematical problem solving is shown to
influence everything from the success of savvy entrepreneurs to the fairness of
voting practices. Examples such as the Traveling Salesman Problem and Arrow's
Impossibility Theorem are taken from management science, statistics, social
science and computer science. Satisfies the Mathematics requirement for general
education. Students enrolling in MATH 112 should have an acceptable score on the
Mathematics Placement Test or have completed an appropriate remedial course.
MATH 095 is recommended. F08, S09, F09, S10

**115 Precalculus
(5)** Covers the algebra and trigonometry required for Calculus and Analytic
Geometry. Topics include review of intermediate algebra; composite and inverse
functions; polynomial and rational functions, exponential and logarithmic
functions, trigonometric functions, identities, and equations; the binomial
theorem; fundamentals of analytic geometry; and the conic sections. Satisfies
the Mathematics requirement for general education. Prerequisite: acceptable
score on the Mathematics Placement Test or completion of MATH 102 with a grade
of at least C-. F08, S09, F09, S10

**130 Elementary
Statistics (4)** Introductory course for students of all disciplines. Includes
descriptive statistics, the binomial and normal distributions, confidence
intervals, linear regression correlation, the t-distribution, the Chi-square
distribution, nonparametric tests of statistical inference, and understanding
statistics in many different fields. Problems are taken from various fields
dependent on statistical decision making. Satisfies the mathematics requirement
for general education. Prerequisite: acceptable score on the Mathematics
Placement Test or completion of MATH 095 with a grade of at least C-. F08, S09,
F09, S10

**150 Finite
Mathematics for Business (3)** Introduction to mathematics concepts and
problem-solving techniques especially applicable in business, economics,
biology, and the social sciences. Topics include: linear equations, linear
functions, and graphs; systems of linear equations and matrices; linear
inequalities, linear programming, and the simplex method sets and counting
techniques; and fundamentals of probability. Satisfies the mathematics
requirement for general education. Prerequisite: acceptable score on the
Mathematics Placement Test or completion of MATH 095 with a grade of at least
C-. F08, F09

**151 Calculus for
Business, Life, and Social Sciences (3)** A short course in calculus including
concepts and problem-solving techniques for students in business, economics,
biology and the social sciences. Topics include algebraic, exponential and
logarithmic functions, derivatives, and optimization problems, partial
derivatives and Lagrange multipliers (as time permits). Satisfies the
mathematics requirement for general education. Prerequisite: acceptable score on
the Mathematics Placement Test or completion of MATH 102 with a grade of at
least C-. F08, S09, F09, S10

**230 Foundations of
Mathematics for Elementary Education I (3) **A first course in mathematical
concepts and techniques designed to meet the mathematical needs of students in
the Elementary Education program. Topics include: logic, sets and counting,
numeration systems, natural numbers, integers, rational numbers, real numbers,
and the arithmetic for these various systems. Satisfies the Mathematics
requirement for general education. Prerequisite: acceptable score on the
Mathematics Placement Test or completion of MATH 102 with a grade of at least
C-. MATH 112 and/or MATH 130 do not fulfill the prerequisites for MATH 230. F08,
S09, F09, S10

**231 Foundations of
Mathematics for Elementary Education II (3) **Continuation of MATH 230. Topics
include: concepts of algebra, fundamentals of two- and three-dimensional
geometry, and an introduction to counting techniques, probability, and
statistics. Prerequisite: Completion of MATH 230 with a grade of at least C-.
F08, S09, F09, S10

**240 Calculus and
Analytic Geometry I (4)** A first course in the fundamentals of calculus. Topics
include: real numbers, functions, limits, continuity, derivatives, integrals,
and applications. Satisfies the Mathematics requirement for general education.
Prerequisite: acceptable score on the Mathematics Placement Test or completion
of MATH 115 with a grade of at least C-or equivalent. F08, S09, F09, S10

**241 Calculus and
Analytical Geometry II (4) **Continuation of MATH 240. Topics include: conic
sections, transcendental functions, techniques of integration, indeterminate
forms, improper integrals, and infinite series. Prerequisite: A grade of C- or
better in MATH 240. F08, S09, F09, S10

**242 Calculus and
Analytic Geometry III (4) **Continuation of MATH 241. Topics include:
three-dimensional analytic geometry, vectors, partial derivatives, multiple
integrals, line integrals, and surface integrals. Prerequisite: A grade of C- or
better in MATH 241. S09, S10

**310/510
Introduction to Abstract Mathematics (3)** Fundamentals of formal mathematics
emphasizing mathematical writing and types of formal proof. Includes significant
coverage of topics in logic, set theory and number theory. Prerequisite: MATH
115. F08, S09, F09, S10

**315 Linear Algebra
(3)** Introduction to the algebra and geometry of two- and three-dimensional space
and extension to n-dimensional space. Topics include: line and coordinate
vectors, systems of linear equations and their solution by reduction methods,
matrix algebra, determinants, fundamentals of abstract vector spaces, linear
independence, dimension theorems, linear transformations, eigenvalues and
eigenvectors, diagonal matrices, quadratic forms, inner products , and the
Gram-Schmidt orthogonalization. Prerequisite: MATH 310. S09, S10

**320/520 Discrete
Structures (4) **Continuation of MATH 310. Investigation of concepts of noncalculus mathematics used in computer science, operations research and other
areas of applied mathematics. Topics include: relations and functions,
recurrence relations, combinatorics, graph theory, and related algorithms.
Cross-listed as CSCI 320/520. Prerequisite: MATH 310. F08, F09

**339 Teaching
Mathematics and Computer Science in the Secondary School (3)** General principles
and problems of teaching mathematics in grades 5-12. Topics include: organizing
teaching activities, teaching materials and resources, and current methodology.
Student activities include classroom presentations, a formal paper, and 20-25
hours of laboratory experience. Prerequisite: Admission to the Teacher Education
program. F09

**344/544
Differential Equations (4)** Introduction to the theory of ordinary differential
equations including some coverage of series solutions, as time permits. Also
covers various classical applications, such as spring mass systems.
Prerequisite: MATH 241. S09

**362/562 Topics in
Geometry (3) **Modern treatment of topics from Euclidean geometry with an
introduction to other geometries. Appropriate for students in Elementary or
Secondary Education or Secondary school mathematics teachers. Prerequisite: MATH
310. S09, S10

**370/570
Probability (3) **A first course in probability theory intended for students in
mathematics, pre-engineering, and the sciences. Prerequisites: MATH 241 and MATH
310. S09

**371 Statistics (4)
**Calculus-based statistics emphasizing applications intended for students in
applied mathematics, economics and the sciences. Topics include: estimation and
prediction, hypothesis testing, linear and multiple regression, F and t tests,
analysis of variance, and non-parametric statistics. Prerequisite: MATH 241 and
MATH 310. MATH 242 and MATH 370 are recommended. F08

**372 Actuarial
Mathematics (4) **Introductory course in actuarial science. Topics may include
risk models, life tables, life insurance and annuities, and pension funding.
Prerequisite: MATH 370 or MATH 371. Offered as needed.

**380/580
Introduction to Mathematical Modeling (4)** Applied mathematics course emphasizing
probabilistic models. Topics include: discrete-and continuous-time Markov
chains, Monte Carlo estimates, queuing theory, reliability theory, Brownian
motion, and financial mathematics. Prerequisites: MATH 241 and one of MATH 370,
MATH 371. MATH 242 is recommended. Offered as needed.

**381 Special
Projects (1-4) **Various individual and small-group projects carried out under the
supervision of one or more instructors. Requires weekly progress reports plus a
final report and/or a final exam. May be repeated, but no more than a total of
four credits may be earned from both MATH 381 and CSCI 381. Pass-Fail only.
Prerequisites: Preliminary project plan and an independent study contract.
Offered as needed.

**390 Mathematical
Sciences Internship (1-4) **Work in an approved position to gain experience in
solving real problems using computer science, mathematics, and statistics.
Interns may receive salaried appointments with cooperating companies. Credits do
not apply to any major or minor in Mathematics and Computer Sciences.
Evaluation: Pass-Fail only. Offered as needed.

**391 Putnam
Mathematical Competition (1) **Preparation for the national Putnam Mathematics
Contest. Includes review of previous examination problems and lectures on
selected topics. May be repeated for a total of three credits. Pass-Fail only.
Consent of the instructor required. F08, F09

**399 Mathematical
Sciences Seminar (1) S**tudents will carry out individual investigations in
current literature and present their findings to the entire department. Taken
during senior year. Pass-Fail only. Prerequisite: Independent study contract.
F08, S09, F09, S10

**401/601 Formal
Models for Computer Security (4) **Survey of formal mathematical models for
computer security with in-depth examination of important features and
characteristics. Includes an investigation of mathematical properties of these
models as well as related cryptographic and system implementations. The models
include classical lattice-based models as well as modern policy-based models
such as the Bell-LaPadula model, no interference models, hybrid models,
integrity models, and miscellaneous formal verification techniques.
Prerequisite: MATH 310, CSCI 270. Offered as needed.

**421/621 Theory of
Computation (4)** Thorough introduction to automata, formal languages and
computability. Topics include: models of computation, regular and context-free
languages, finite and pushdown automata, Turing machines, unsolvable decision
problems, and fundamentals of computational complexity. Cross-listed as CSCI
421/621. Prerequisites: CSCI 320. F09

**425/625 Algorithm
Design and Analysis (4) **Study of the design and analysis of algorithms that are
based on elementary data structures such as queues, stacks and trees. Some graph
and network algorithms (shortest paths, connectivity, coloring, flows, matchings),
geometric algorithms (convex hulls, range search, nearest neighbors),
NP-complexity, approximation algorithms (vertex cover, traveling salesman,
scheduling), and introduction to randomized algorithms. Introduction to
algorithm design techniques, including greedy algorithms, divide-and-conquer,
and dynamic programming. Lower and upper bounds of program complexity are
analyzed. Introduction to algorithms used in the area of information security.
Cross-listed as CSCI 425/625. Prerequisites: CSCI 320. CSCI 202 recommended. F08

**437/637
Cryptography (4)** Study of the theory of cryptography together with applied
programming projects. Topics include: discrete probability spaces; Shannon's
theory of information and perfect secrecy; classical cryptosystems and
cryptanalysis; authentication and key exchange; public key cryptosystems;
elementary number theory, primality checking, and the RSA cryptosystem; and
Advanced Encryption Standard (AES). Cross-listed as CSCI 437. Prerequisite: CSCI
201, MATH 310. S09

**440/640 Real
Analysis (4)** Fundamental concepts of limit, continuity, differentiability, and integrability of functions of one variable; convergence and uniform convergence
of infinite series, and improper integrals. Prerequisites: MATH 242, MATH 301.
F09

**455 Abstract
Algebra (4)** Introduction to algebraic systems including groups, rings, integral
domains and fields, homomorphisms and isomorphisms. Prerequisite: MATH 301. F08

**471/671
Introduction to Complex Variables (4)** Introduction to the study of analytic
functions including series, residues, conformal mapping and applications.
Prerequisite: MATH 242. S10

**475/675 Numerical
Analysis (4)** Study of theory and applications of computational techniques for
mathematical solutions emphasizing rapid approximation and error analysis.
Topics include: solution to equations in one variable, polynomial approximations
to functions, error analysis, numerical solutions to ordinary differential
equations, boundary value problems. Cross-listed as CSCI 475/675. Prerequisite:
MATH 242. Offered as needed.

**481/681 Special
Topics (1-4) **In-depth study of specialized current topics in mathematical
sciences. May be repeated when topics are different. Offered as needed.

**550 Elementary
Number Theory (3) **Study of the system of integers including the division
algorithm, greatest common divisor, fundamental theorem of arithmetic, congruences, diophantine equations, and arithmetic functions. Prerequisite: MATH
240 or consent of instructor. Offered as needed.