100 Elementary Algebra
Fall
The algebra of fractions, roots, powers, and radicals; inequalities; the
linear function; the solution of systems of two or more linear equations;
quadratic equations; word problems. (Does not meet General Education Natural
and Mathematical Sciences requirement.)
103 The Nature of Mathematics
Fall, Spring
Intended for students with primary interests in the humanities and social
sciences. The course uses set theory, logic, and languages as a foundation
for studying a variety of topics central to the development of modern mathematics.
Emphasizing the central role of language in mathematics, the course shows
that mathematics is about communication of ideas. Topics will be explored
through experimentation with computers where appropriate using games, puzzles,
and group progjects as well as lectures and discussions. Additional topics
include optimal form in nature, laws of the physical universe, symmetry,
codes, and basic geometry, among others. The course will focus on the interplay
of different ideas and will emphasize writing. (Cross-listed as Freshman
Studies 103.)
104 Elementary Mathematics From An Advanced
Standpoint
Spring
This course presents an overview, for a sophisticated audience, of several
topics from elementary mathematics. The course stresses three themes: Mathematics
in the liberal arets, mathematics from a historical perspective, and mathematics
as a problem-solving activity. Topics to be covered include: Numeration
systems, non base-ten representations, elementary number theory: inlcuding
primes and factorizations, rationals as terminating and repeating decimals,
irrationals, simple probability, experiments, elementary set theory, and
mathematical reasoning. Prerequisite: Mathematics 103 or permission of instructor.
(Cross-listed as Education 104.)
105 Elementary Functions
Fall, Spring
Properties of functions with emphasis on polynomial, exponential, logarithmic,
and trigonometric functions. Analytic geometry. (Does not meet General Education
Natural and Mathematical Science requirement.)
110 Calculus I
Fall, Spring
The calculus of functions of one variable. Limits, continuity, differentiation,
and applications; a brief introduction to integration. Prerequisite: 3 1/2
years of high school mathematics or Mathematics 105.
111 Calculus II
Fall, Spring
The calculus of functions of one variable. Integration, applications of
integration, sequences and series. Prerequisite: Mathematics 110.
115 Honors Calculus I
Fall
Theory and applications of the calculus of functions of one variable. Limits,
continous functions, differentiable functions, the definite integral, and
applications. Prerequisite: Permission of instructor.
116 Honors Calculus II
Spring
Continuation of Mathematics 115. Integration and application, sequences,
infinite series. Prerequisite: Permission of instructor.
150 Introduction to Probability and Statistics
Fall, Spring
Designed for students in the social and life sciences. Discrete probability
theory, distributions, sampling, correlation, and regression, Chi square
and other tests of significance. Emphasis on the use of the computer as
a tool and on applications to a variety of disciplines. (Not open to students
who have taken Economics 130, which is a comparable course.)
160 Finite Mathematics with Applications
Fall, Spring
Mathematical topics as needed to build and solve mathematical modesl of
situations in the life, social, and managerial sciences. Basic probability
theory; vectors, matrices, and Markov chains, linear programming; game theory.
210 Multivariable Calculus
Fall
Partial differentiation, the algebra and calculus of vectors, curves and
their parametrization, multiple integration, Stokes' and Green's theorem,
and applications. Prerequisite: Mathematics 111.
211 Mathematics of Chaos
Spring
A study of nonlinear dynamical systems, including iteration of functions,
attracting and repelling periodic orbits, bifurcation, the period doubling
route to chaos, complex dynamics, fractals, Mandelbrot and Julia sets. Real-world
implications and applications of chaos. Can meet the requirements for a 300
level or above mathematics course upon completion of an additional project
approved by the instructor. Prerequisite: Mathematics 111.
214 Differential Equations
Differential equation models, analyic solution techniques, qualitative solution
concepts, and computer visualization for single equations and systems. Applications
of differential equations.
230 Introduction to Abstract and Discrete
Mathematics
Fall
Topics covered include logic and proofs, set theory, relations, cardinal
numbers, countable and uncountable sets, permutations and combinations,
graph theory, group theory. Prerequisite: Mathematics 110.
231 Linear Algebra
Spring
Vector spaces, linear independance, linear transformations, matrices, determinants,
applications to geometry. Prerequisite: Mathematics 230 or permission of
instructor.
310 Complex Analysis
Fall
Study of functions of one complex variable. Analytic functions, complex
integrations, Cauchy's theorem, complex power series, and special functions.
Applications to other areas of mathematics and to mathematical physics.
Prerequisite: Mathematics 210 and 230 or permission of instructor.
311 Real Analysis
Spring
A rigorous one dimensional course covering the following introductory real
analysis topics: Axioms for the real numbers, boundedness, limits, monotone
functions, continuity, uniform continuity, Cauchy criterion for convergence,
cluster points, compactness, differentiability, integration, infinite series.
Prerequisite: Mathematics 210, 230.
314 Numerical Analysis
Spring
Linear and polynomial interpolation, finite differences, matrix methods.
Solution of equations and systems of equations. Numerical differentiation,
integration, and solutions of differential equations. Algorithms and computer
applications. Prerequisite: Mathematics 111, 231, and Computer Science 112.
(Cross-listed as Computer Science 314.)
320 Mathematical Methods
Practical techniques for solving the partial differential equations that
arise in the physical sciences. Special functions, series, solutions of
differential equations, orthogonal polynomials, boundary value problems
eigen systems, and asymptotic methods. Emphasis on examples with exact solutions
to illustrate principles and to develop intuition, followed by numerical
approaches to applications. Four lectures per week. Prerequisite: Physics
210, Mathematics 210 required; Mathematics 214, 231, and Computer Science
112 recommended.
329 Number Theory
Mathematical induction, divisibility properties of integers, prime numbers,
congruences. Prerequisite: Mathematics 230 or permission of instructor.
330 Modern Algebra I
Fall
A study of algebraic structures with emphasis on groups, rings and fields.
Prerequisite: Mathematics 230.
331 Modern Algebra II
Additional topics in modern or linear algebra such as field extensions,
group conjugacy, modules, eigenvalue theory, dual spaces, and unitary spaces.
Prerequisite: Mathematics 330 or permission of instructor.
350 Mathematical Probability
Fall
Discrete and continous probability. Distributions, the law of large numbers,
the central limit theorem, random vaiables, generating functions. Prerequisite:
Mathematics 210 or permission of instructor.
351 Mathematical Statistics
Spring
A mathematical study of such topics as estimation of parameters, confidence
intervals, and test of hyptheses, decision theory, regression, analysis
of variance and nonparametric methods. Prerequisite: Mathematics 350.
360 Mathematical Modeling and Computer Simulation
Introduction to the process and techniques of modeling actual situations
using mathematical methods and computer simulation. Topics may include optimization,
dynamical systems, axiom systems, queuing theory, and introduction of a
simulation language. Second half will include team projects and reports.
Prerequisite: Mathematics 111, Computer Science 112, and some additional
sophistication in at least one of the following: mathematics, computer
science, or applying mathematics in a field of interest. (Cross-listed as
Computer Science 360.)
375 Combinatorics and Graph Theory
Enumeration techniques with emphasis on permutations and combinations, generating
functions, recurrence relations, inclusion and exclusion and the pigeonhole
principle. Graph theory with emphasis on trees, circuits, cut sets, planar
graphs, chromatic numbers and transportation networks. Also included will
be designs with emphasis on Latin squares, finite projective and affine
geometries, block designs and design of experiments. Prerequisite: Mathematics
230. (Cross-listed as Computer Science 375.)
Mathematics Courses Offered Less Frequently
260 History of Mathematics
A survey of the important concepts of mathematics form the time of the Babylonians
to the present. Emphasis will be on the evolution of mathematical ideas
and the contributions of the most prominent individuals associated with
the development of mathematics. Prerequisite: Mathematics 111 or permission
of instructor.
340 Geometry
Selected topics from affine, Euclidian, non-Euclidian, projective and differential
geometry. Prerequisite: Mathematics 230 or permission of instructor.
410 Topology
Point set topology. Such topics as topological spaces, separation axioms,
covering properties, metrization, convergence and completeness and homotopy
theory. Prerequisite: Mathematics 230.
411 Topics in Modern Analysis
Introductory notions of functional analysis. Banach spaces, integration
and measure, Hilbert spaces, commutative Banach algebras.