**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.
F06, S07, F07, S08

**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-. F06, S07, F07, S08

**102
Intermediate Algebra (2)** Review of intermediate algebra topics typically studied in
high school. Topics include: rational expressions and equations; rational
exponents; 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-. F06, S07, F07, S08

**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. MATH
112 is intended as a terminal course and cannot be used as a prerequisite for
other mathematics courses. F06, S07, F07, S08

**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 mathematical
requirement for general education. Prerequisite: acceptable score on the
Mathematics Placement Test or completion of MATH 102 with a grade of at least
C-. F06, S07, F07, S08

**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-. F06, S07,
F07, S08

**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; 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-. F06, F07

**151
Calculus for Business, Life, and Social Sciences (3)** 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. 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-. F06, S07, F07, S08

**230
Foundations of Mathematics 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. Prerequisite: acceptable
score on the Mathematics Placement Test or completion of MATH 102 with a grade
of at least C-. F06, S07, F07, S08

**231 Foundations of Mathematics 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-.
F06, S07, F07, S08

**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. Prerequisite: acceptable
score on the Mathematics Placement Test or completion of MATH 115 with a grade
of at least C- or equivalent. F06, S07, F07, S08

**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. F06, S07, F07, S08

**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. S07, S08

**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. F06, S07, F07, S08

**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. S07, S08

**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 with CSCI 320/520. Prerequisite: MATH
310. F06, F07

**339 Teaching Mathematics and Computer Science in
the Secondary School (3)** General principles and problems of teaching mathematics for
ages 10-21.
Topics include: organizing teaching activities; teaching materials and
resources; and current methodology. Student activities include classroom
presentations, a formal paper, and 20 hours of laboratory experience.
Prerequisite: Admission to the Teacher Education program. F06, S08

**344/544 Differential Equations (4)** Introduction to the
theory of ordinary differential equations including some coverage of series
solutions, as time permits. Various classical applications, such as spring
mass systems, also covered. Prerequisite: MATH 241. S07

**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. Prerequisite: MATH 310. S07, S08

**370/570
Probability (3)**
A first course in probability theory intended for students in mathematics,
pre-engineering, and the sciences. Topics include: axioms of probability;
combinatorial analysis; conditional probability; independence; discrete and
continuous random variables; probability distributions; expectation; variance;
Poisson processes; and limit theorems. Prerequisites: MATH 241 and MATH 310.
F07

**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 recommended. F06

**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.

**380/580
Introduction to Mathematical Modeling (4) **Applied mathematics course emphasizing
probabilistic models. Topics include: discrete-and continuous-time Markov
chains;

**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. Evaluation. Pass-Fail only.
Instructor consent required. Prerequisites: Preliminary project plan and an
independent study contract. Topics: Independent Study, Java Certification Part
2, C++, JAVA, On-Line Curriculum Development, DNA Microarrays.
F06, S07, F07, S08

**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. Independent study. F06,
S07, F07, S08

**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 instructor required. F06, F07

** **

**399
Mathematical Sciences Seminar (1)** Students 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 and consent of instructor. Cross-listed as CSCI 399. F06, S07, F07, S08

**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 investigation of mathematical
properties of these models as well as related cryptographic and system
implementations. Models include classical lattice-based models as well as
modern policy-based models usch as the Bell-LaPadula model; nointerference
models, hybrid models, integrity models, and miscellaneous formal verification
techniques. Prerequisite: MATH 310, CSCI 270. S08

**421/621 Theory of Computation (4) **Thorough introduction to
automata, formal languages and compatibility. 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 MATH 421/621.
Prerequisites: CSCI 320. F07

**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 MATH 425/625. Prerequisites: CSCI 320. CSCI
202 recommended. F06

**437/637 Cryptography (4)** Study of the theory of
cryptography and its use in computer security. Topics include:
discrete probability spaces, Shannon's theory of information, unicity distance, perfect secrecy, redundancy of a
language, classical cryptosystems, classical cryptanalysis (frequency analysis,
index of coincidence), authentication and key exchange, public key
cryptosystems, elementary number theory, primality
checking, the RSA cryptosystem. Prerequisite: CSCI 201, MATH 310. S07

** **

**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. F07

** **

**455/655 Abstract Algebra (4) **Introduction to
algebraic systems including groups, rings, integral domains and fields, homomorphisms and isomorphisms. Prerequisite: MATH 301.
F06

**471/671 Introduction to Complex Variables (4) **Introduction to the
study of analytic functions including series, residues, conformal mapping and
applications.
Prerequisite: MATH 242. S08

**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. Offered when sufficient demand exists. Cross-listed
as MATH 475/675. Prerequisite: MATH 242.

**481/681 Special Topics (1-4)** In-depth study of specialized
current topics in mathematical sciences. May be repeated when
topics are different. Topics: Introduction to Point Set Topology,
Cryptography