Mathematics
Math placement information is in the front of this catalog in the
Undergraduate: Applying for Admission section. No student will be
permitted to enroll in a course having prerequisites if a grade lower
than a C is received in the prerequisite course.
A $42 per semester fee for computer facilities will be assessed for one or
more CS, STAT and MATH 310, 460 and 660 courses. This fee is in addition to
any lab/materials fees.
Developmental Mathematics
DEVM 050 3 Credits
Pre-Algebra
Operations with whole numbers, fractions, decimals, percents
and ratios, signed numbers, evaluation of algebraic expressions and
evaluation of simple formula. Metric measurement system and geometric
figures. Also available via Independent Learning. (Prerequisites:
Appropriate placement test scores.) (3 + 0) Offered Fall,
Spring
DEVM 052 2 Credits
Alternative Approaches to Math: Basic College Math
Basic college mathematics: operations with percents, decimals,
fractions and signed numbers, translating word problems, introduction
to algebra and geometry, using alternative teaching styles. (Prerequisites:
Appropriate placement test scores.) (2 + 0) Offered Fall
DEVM 060 3 Credits
Elementary Algebra
First year high school algebra. Evaluating and simplifying algebraic
expressions, solving first degree equations and inequalities, integer
exponents, polynomials, factoring, rational expressions, equations
and graphs of lines. Also available via Independent Learning. (Prerequisite:
DEVM 050 or placement.) (3 + 0) Offered Fall, Spring
DEVM 061 1 Credit
Review of Elementary Algebra
Designed to assist students in reviewing material covered by
DEVM 060. Individuals who have not previously taken an elementary
algebra course are recommended to enroll in DEVM 060. Independent
Learning Only
DEVM 062 3 Credits
Alternative Approaches to Math: Elementary Algebra
Algebraic topics. Includes operations with polynomial expressions,
first- and second-degree equations, graphing, integral and relational
exponents, and radicals using alternative teaching styles. (Prerequisites:
DEVM 050/052 or appropriate placement test scores.) (3 + 0)
Offered Fall, Spring
DEVM 063 2 Credits
Applied Math I: Alternative Approaches to Elementary Algebra
Elementary algebra, using an alternative teaching style; how
skills are used in the work place; problem solving in a hands-on
environment; evaluations, factoring, graphing, simplifying, estimating,
solving first-degree equations, integer exponents and polynomials.
Applied Math I and II will prepare students for DEVM 105. (Prerequisites:
DEVM 050, appropriate placement test scores or permission of instructor.)
(1 + 3) Offered Fall
DEVM 064 2 Credits
Applied Math II: Alternative Approaches to Elementary Algebra
Elementary algebra, using an alternative teaching style; how
skills are used in the work place; problem solving in a hands-on
environment; evaluations, factoring, graphing, simplifying, estimating,
solving first-degree equations, integer exponents and polynomials.
Applied Math I and II will prepare students for DEVM 105. (Prerequisites:
DEVM 060, DEVM 063 or permission of instructor.) (1 + 3)
Offered Spring
DEVM 065 1–3 Credits
Mathematics Lab
Designed to assist students in reviewing and reinforcing course
concepts covered by DEVM 050, 060 and 105. Consists of instruction
which may include lab instruction, individual student work or group
work. Recommended for students who need more time and help to master
the material in Developmental Math courses. (Prerequisite: Placement.)
(0+3-9) Offered Fall, Spring
DEVM 071 1 Credit
Review of Intermediate Algebra
Course reviews material covered by DEVM 105. Individuals who
have not taken an intermediate algebra course on the high-school
level are recommended to enroll in DEVM 105. Independent Learning
Only
DEVM 081 1 Credit
Review of Basic Geometry
High school geometry without formal proofs. Topics include basic
definitions, measurement, parallel lines, triangles, polygons, circles,
area, solid figures and volume. (Prerequisite: DEVM 060.) Independent
Learning Only
DEVM 082 1 Credit
Hands-On Geometry
Basic concepts and uses of geometry. Emphasis on "hands-on” and
applied problems. (Prerequisite: A solid knowledge of arithmetic—no
algebra required.) (1 + 0) Offered Fall, Spring
DEVM 105 3 Credits
Intermediate Algebra
Second year high school algebra. Operations with rational expressions,
radicals, rational exponents, logarithms, inequalities, quadratic
equations, linear systems, functions, Cartesian coordinate system
and graphing. Also available via Independent Learning. (Prerequisite:
DEVM 060 or placement.) (3 + 0) Offered Fall, Spring
DEVM 106 3 Credits
Alternative Approaches to Math: Intermediate Algebra
Algebraic topics. Includes .exponents, radicals, graphing, systems
of equations, quadratic equations and inequalities, logarithms and
exponentials, and complex numbers using alternative teaching styles.
(Prerequisites: DEVM 060/062 or appropriate placement test scores.
This course satisfies elective credit only.) (3 + 0) Offered
Fall, Spring
Mathematics
MATH 107X 3 Credits
Functions for Calculus (m)
A study of algebraic, logarithmic and exponential functions,
together with selected topics from algebra. Note: No credit may be
earned for more than one of MATH 107X or 161X. Also available via
Independent Learning. (Prerequisites: DEVM 105 or 106; or two years
of high school algebra and MATH 107X placement or higher.) (3 + 0)
Offered Fall, Spring
MATH 108 2–3 Credits
Trigonometry (m)
A study of the trigonometric functions. Also available via Independent
Learning. (Prerequisite: MATH 107X or placement or concurrent enrollment
in MATH 107X.) (2–3 + 0) Offered Fall, Spring
MATH 131X 3 Credits
Concepts and Contemporary Applications of Mathematics (m)
Applications of mathematics in modern life including applications
of graph theory in management science; uses of probability and statistics
in industry, government and science; and applications of geometry
to engineering and astronomy. Problem solving emphasized. Also available
via Independent Learning. (Prerequisites: DEVM 105 or 106 or placement;
or high school geometry and algebra II.) (3 + 0) Offered
Fall, Spring
MATH 161X 3 Credits
Algebra for Business and Economics (m)
Functions of one and several variables with attention to linear,
polynomial, rational, logarithmic and exponential relationships.
Geometric progressions as applied to compound interest and present
value. Linear systems of equations and inequalities. Note: No credit
may be earned for more than one of MATH 107X or 161X. (Prerequisites:
DEVM 105 or 106; or two years of high school algebra and MATH 161X
placement or higher.) (3 + 0) Offered Fall, Spring
MATH 200X 4 Credits
MATH 201X 4 Credits
MATH 202X 4 Credits
Calculus (m)
Techniques and application of differential and integral calculus,
vector analysis, partial derivatives, multiple integrals and infinite
series. Note: No credit may be earned for more than one of MATH 200X,
262X or 272X. MATH 200X, 201X and 202X also available via Independent
Learning. (Prerequisites: MATH 107X and 108 or placement for MATH
200X; MATH 200X for MATH 201X; MATH 201X for MATH 202X.) (4 + 0)
All Offered Fall and Spring
MATH 205 3 Credits
Mathematics for Elementary School Teachers I (m)
Elementary set theory, numeration systems and algorithms of arithmetic,
divisors, multiples, integers, introduction to rational numbers.
Emphasis on classroom methods. Also available via Independent Learning.
(Prerequisite: MATH 107X or placement. Restricted to B.A.S. and B.A.
Elementary Education degree students; others by permission of instructor.)
(3 + 1) Offered Fall
MATH 206 3 Credits
Mathematics for Elementary School Teachers II (m)
A continuation of MATH 205. Real number systems and subsystems,
logic, informal geometry, metric system, probability and statistics.
Emphasis on classroom methods. Also available via Independent Learning.
(Prerequisite: MATH 205.) (3 + 1) Offered Spring
MATH 215 2 Credits
Introduction to Mathematical Proofs (m)
Emphasis on proof techniques with topics including logic, sets,
relations, equivalence induction, number theory, graph theory and
congruence classes. In addition, a rigorous treatment of topics from
calculus could be given. (Prerequisites: MATH 200X, 201X or concurrent
with 201X or permission of instructor.) (2 + 0) Offered
Spring
MATH 262X 4 Credits
Calculus for Business and Economics (m)
Ordinary and partial derivatives. Maxima and minima problems,
including the use of Lagrange multipliers. Introduction to the integral
of a function of one variable. Applications include marginal cost,
productivity, revenue, point elasticity of demand, competitive/complementary
products, consumer’s surplus, etc. Note: No credit may be earned
for more than one of MATH 200X, 262X or 272X. (Prerequisite: MATH
161X.) (4 + 0) Offered Fall, Spring
MATH 272X 3 Credits
Calculus for Life Sciences (m)
Differentiation and integration with applications to the life
sciences. Note: No credit may be earned for more than one of MATH
200X, 262X or 272X. (Prerequisites: MATH 107X and 108.) (3 + 0)
Offered Fall
MATH 302 3 Credits
Differential Equations
Nature and origin of differential equations, first order equations
and solutions, linear differential equations with constant coefficients,
systems of equations, power series solutions, operational methods
and applications. (Prerequisite: MATH 202X.) (3 + 0) Offered
Fall, Spring
MATH 305 3 Credits
Geometry
Topics selected from such fields as Euclidean and non-Euclidean
plane geometry, affine geometry, projective geometry and topology.
(Prerequisite: MATH 202X or permission of instructor. Next offered:
2005-06.) (3 + 0) Offered Alternate Spring
MATH 306 3 Credits
Introduction to the History and Philosophy of Mathematics
Includes a detailed study of certain important periods of history
as examined by such thinkers as Plato, B. Russell, D. Hilbert, L.E.J.
Brouwer and K. Godel. For students of mathematics, science, history
and philosophy. (Prerequisite: MATH 202X or permission of instructor.
Next offered: 2004-05.) (3 + 0) Offered Alternate Spring
MATH 307 3 Credits
Discrete Mathematics
Logic, counting, sets and functions, recurrence relations graphs
and trees. Additional topics chosen from probability theory. (Prerequisite:
MATH 201X or permission of instructor.) (3 + 0) Offered
Fall, Spring
MATH 308 3 Credits
Abstract Algebra
Theory of groups, rings and fields. (Prerequisite: MATH 215 or
permission of instructor. Recommended: MATH 307 and/or MATH 314.)
(3 + 0) Offered Spring
MATH 310 3 Credits
Numerical Analysis
Direct and iterative solutions of systems of equations, interpolation,
numerical differentiation and integration, numerical solutions of
ordinary differential equations and error analysis. Material fee:
$42. (Prerequisite: MATH 302 or MATH 314 or permission of instructor.
A knowledge of programming is desirable.) (3 + 0) Offered
Fall
MATH 314 3 Credits
Linear Algebra
Linear equations, finite dimensional vector spaces, matrices,
determinants, linear transformations and characteristic values. Inner
product spaces. (Prerequisite: MATH 201X.) (3 + 0) Offered
Fall, Spring
MATH 371 3 Credits
Probability
Probability spaces, conditional probability, random variables,
continuous and discrete distributions, expectation, moments, moment
generating functions and characteristic functions. (Prerequisite:
MATH 202X. Next offered: 2004-05.) (3 + 0) Offered Alternate
Fall
MATH 401W 3 Credits
MATH 402 3 Credits
Advanced Calculus
A rigorous treatment of one and several dimensional calculus.
Includes mappings from n-space and their continuity, differentiability
and integrability properties as well as sequences and series. (Prerequisites:
ENGL 111X; ENGL 211X or ENGL 213X; or permission of instructor; MATH
215 and 202X for MATH 401; MATH 401 for MATH 402.) (3 + 0)
401W Offered Fall, 402 Offered Spring
MATH 404W 3 Credits
Topology
Introduction to topology, set theory, open sets, compactness,
connectedness, product spaces, metric spaces and continua. (Prerequisites:
ENGL 111X; ENGL 211X or ENGL 213X or permission of instructor; MATH
202X and 215. Recommended: MATH 314 and/or 308.) (3 + 0)
Offered As Demand Warrants
MATH 408 3 Credits
Mathematical Statistics
Distribution of random variables and functions of random variables,
interval estimation, point estimation, sufficient statistics, order
statistics and test of hypotheses including various criteria for
tests. (Prerequisites: MATH 371 and STAT 200. Next offered: 2004-05.)
(3 + 0) Offered Alternate Spring
MATH 412 3 Credits
Differential Geometry
Introduction to the differential geometry of curves, surfaces
and Riemannian manifolds. Basic concepts covered include the Frenet-Serret
apparatus, surfaces, first and second fundamental forms, geodesics,
Gauss curvature and the Gauss-Bonnet Theorem. Time permitting topics
such as minimal surfaces, theory of hypersurfaces and/or tensor analysis
may be included. (Prerequisites: MATH 314 and 401; or permission
of instructor. Next offered: 2004-05.) (3 + 0) Offered
Alternate Spring
MATH 421 4 Credits
Applied Analysis
Vector calculus, including gradient, divergence and curl in orthogonal
curvilinear coordinates, ordinary and partial differential equations
and boundary value problems, and Fourier series and integrals. (Prerequisite:
MATH 302.) (4 + 0) Offered Fall
MATH 422 3 Credits
Introduction to Complex Analysis
Complex functions, including series, integrals, residues, conformal
mapping and applications. May be taken independently of MATH 421.
(Prerequisite: MATH 302.) (3 + 0) Offered Spring
MATH 460W,O 3 Credits
Mathematical Modeling
Analysis, construction and interpretation of mathematical models.
Applications to the physical, biological and social sciences. Topics
selected from combinatorics, probability, statistics, perturbation,
numerical analysis and differential equations. Students develop a
modeling project. Material fee: $42. (Prerequisites: COMM 131X or
141X; ENGL 111X; ENGL 211X or ENGL 213X or permission of instructor;
MATH 201X. Recommended: One or more of MATH 302, 314, STAT 300, 401;
and some programming experience. Next offered: 2005-06.) (3 + 0)
Offered Alternate Fall
MATH 490O 1 Credit
Senior Seminar
Advanced topics selected from areas outside the usual undergraduate
offerings. A substantial level of mathematical maturity is assumed.
(Prerequisites: COMM 131X or 141X; MATH 308 or 401.) (1 + 0)
Offered Spring
MATH 600 1 Credit
Teaching Seminar
Fundamentals of teaching mathematics in a university setting.
Topics may include any aspect of teaching; university regulations,
class and lecture organization, testing, book selection, teaching
evaluations, etc. Specific topics will vary on the basis of student
and instructor interest. Individual classroom visits will also be
used for class discussion. May be repeated for credit. (Prerequisite:
Graduate standing.) (1 + 0) Offered Fall, Spring
MATH 608 3 Credits
Partial Differential Equations
First and second order differential equations, boundary value
problems, and existence and uniqueness theorems. Green’s functions
and principal equations of mathematical physics. (Prerequisite: MATH
422 or permission of instructor.) (3 + 0) Offered As Demand
Warrants
MATH 611 3 Credits
MATH 612 3 Credits
Mathematical Physics
(Cross-listed with PHYS 611 and PHYS 612)
Advanced consideration of such topics as transform methods, asymptotic methods,
Green’s function, Sturm-Liouville theory, conformal mapping and calculus
of variations with applications to problems arising in physics. (Prerequisite:
MATH 422 or permission of instructor.) (3 + 0) 611 Offered Fall,
612 Offered Spring
MATH 615 3 Credits
Applied Numerical Analysis
Review of numerical differentiation and integration, and the
numerical solution of ordinary differential equations. Main topics
to include the numerical solution of partial differential equations:
curve fitting, splines and the approximation of functions. Supplementary
topics such as the numerical method of lines, the fast Fourier transform
and finite elements may be included as time permits and interest
warrants. (Prerequisites: CS 201, MATH 310, 314, 421, 422 or permission
of instructor. Next offered: 2005-06.) (3 + 0) Offered
Alternate Spring
MATH 621 3 Credits
Advanced Applied Analysis
Topics covered may include conformal mapping, Fourier, Laplace
and Z transforms and impulse functions with applications to solving
differential equations which arise in science and engineering. Other
topics as time permits include asymptotic expansions, local analysis,
O.D.E.’s and special functions. (Prerequisites: MATH 421 and
422; or permission of instructor. Next offered: 2004-05.) (3 + 0)
Offered Alternate Fall
MATH 630 3 Credits
Advanced Linear Algebra
Vector spaces over arbitrary fields primary, rational and Jordan
canonical forms, invariant subspace decompositions and multilinear
algebra. (Prerequisites: MATH 308 and MATH 314.) (3 + 0)
Offered As Demand Warrants
MATH 631 4 Credits
Theory of Modern Algebra I
Rigorous development of groups, rings and fields. Introduction
to category theory, module theory, homological algebra and Galois
Theory. (Prerequisites: MATH 308 and graduate standing or permission
of instructor. Next offered: 2004-05.) (4 + 0) Offered
Alternate Fall
MATH 632 3 Credits
Theory of Modern Algebra II
Advanced topics taken from group theory, category theory, ring
theory, homological algebra and field theory. (Prerequisite: MATH
631.) Next offered: 2005-06. (3 + 0) Offered Alternate
Fall
MATH 641 4 Credits
Real Analysis I
General theory of Lebesgue measure and Lebesgue integration on
the real line. Convergence properties of the integral. Introduction
to the general theory of measures and integration. Differentiation,
the product measures and an introduction to LP spaces. (Prerequisites:
MATH 401-402 or permission of instructor.) Next offered: 2005-06.
(4 + 0) Offered Alternate Fall
MATH 642 3 Credits
Real Analysis II
Theory of abstract measures and integration. Signed and vector-valued
measures. The fundamental theorems of functional analysis: open mapping,
closed graph, Hahn-Banach, uniform boundedness, Banach-Alaoglu, etc.
Lebesgue-Stieljies integration. Probability spaces and distributions.
Applications and special topics to be selected on the basis of instructor
and student interest. (Prerequisite: MATH 641. Next offered: 2004-05.)
(3 + 0) Offered Alternate Fall
MATH 645 4 Credits
Complex Analysis
Analytic functions, power series, Cauchy integral theory, Residue
Theorem. Basic topology of the complex plane and the structure theory
of analytic functions. The Riemann mapping theorem. Infinite products.
(Prerequisite: Math 641 or permission of instructor. Next offered:
2005-06.) (4 + 0) Offered Alternate Spring
MATH 651 4 Credits
Topology
Treatment of the fundamental topics of point-set topology. Separation
axioms, product and quotient spaces, convergence via nets and filters,
compactness and compactifications, paracompactness, metrization theorems,
countability properties and connectedness. Set theory as needed for
examples and proof techniques. (Prerequisites: MATH 401-402 or MATH
404 or permission of instructor. Next offered: 2004-05.) (4 + 0)
Offered Alternate Spring
MATH 655 3 Credits
Algebraic Topology
Fundamentals of algebraic topology with applications to topology
and geometry. The fundamental group, covering spaces, axiomatic homology
and singular homology. (Prerequisites: MATH 308 and MATH 401-402
and MATH 404 or permission of instructor.) Next offered: 2005-06.
(3 + 0) Offered Alternate Fall
MATH 660 3 Credits
Advanced Mathematical Modeling
Examination of models and procedures reflecting problems arising
in the physical and social sciences. Derivation of model equations
and methods for solution. Heat conduction problems, random walk processes,
simplification of equations, dimensional analysis and scaling, perturbation
theory and a discussion of self-contained modules that will illustrate
the principal modeling ideas. Students will develop a modeling project
as part of the course requirements. Material fee: $42. (Prerequisite:
Permission of instructor. Next offered: 2004-05.) (3 + 0)
Offered Alternate Spring
MATH 661 3 Credits
Optimization
(Cross-listed with CS 661)
Linear and nonlinear programming, simplex method, duality and dual simplex
method, post-optimal analysis, constrained and unconstrained nonlinear programming,
Kuhn-Tucker conditions. Applications to management, physical and life sciences.
Computational work with the computer. (Prerequisites: Knowledge of calculus,
linear algebra and computer programming. Next offered: 2004-05.) (3 + 0)
Offered Alternate Fall
MATH 663 3 Credits
Applied Combinatorics and Graph Theory
A study of combinatorial and graphical techniques for complexity
analysis including generating functions, recurrence relations, theory
of counting, planar directed and undirected graphs, and applications
to NP complete problems. (Prerequisites: MATH 307 and 314. Next offered:
2005-06.) (3 + 0) Offered Alternate Spring