542 Algebra II.
4 Credits.
Group Theory continued: Sylow Theorems, finite Abelien groups.
Ring Theory, rings, domains, fields, fields of quotients, homomorphisms and
ideals, P.I.D.'s and U.F.D's, polynomial rings;
Field extensions: splitting fields, finite fields.
Text: Contemporary Abstract Algebra, Joseph A. Gallian,
D.C. Heath and Company, Lexington, Massachusetts, 1986.
Instructor: Daniel Frohardt
560 Introduction to Analysis I.
4 Credits.
Completeness, convergence, compactness and continuity in the context of
Euclidean spaces;
applications to differential and integral calculus.
Text: Methods of Real Analysis, 2nd Edition, Richard R. Goldberg,
John Wiley and Sons, New York, 1976.
Instructor: Leon Brown
561 Introduction to Analysis II.
3 Credits.
Point-wise and uniform convergence of sequences and series of functions;
power series;
introduction to analytic functions;
Fourier series; possible additional topics.
Text: Methods of Real Analysis, 2nd Edition, Richard R. Goldberg,
John Wiley and Sons, New York, 1976.
Instructor: Leon Brown
570 Probability and Stochastic Processes.
4 Credits.
Probability spaces, combinatorial analysis;
independence; discrete and continuous random variables; expectations;
normal Poisson and binomial distribution; joint, marginal and
conditional distribution functions; law of large numbers; central limit
theorems; random walks; Markov chains; Poisson processes.
Text:
Instructor: Lowell Hansen.
650 Topology I.
4 Credits.
Topological spaces and continuous functions;
connectedness;
compactness;
product and quotient spaces;
metric spaces;
Urysohn's lemma;
Tietze extension theorem;
homotopy;
covering spaces and path lifting;
the fundamental group and examples;
Brouwer fixed point theorem and applications.
Text:
Instructor: Choon Jai Rhee.
660 Complex Analysis.
4 Credits.
Complex differentiation;
elementary functions;
Cauchy's integral theorem;
power series;
Laurent expansions;
singularities;
residue theorem;
entire and meromorphic functions;
Riemann mapping theorem.
Text:
Instructor: Lawrence Brenton.
790 Directed Study.
1 Credit.
This project is intended to further the understanding of
tomographic reconstruction from diverging rays.
Reconstruction methods will be studied for sets of rays
whose angular distance varies differentiably with respect
to radial distance for each projection set.
Data collection schemes which give rise to these ray sets
comprise about half of the collection methods currently used.
The proposed study of these methods will provide a strong
theoretical background for further independent investigation
in this area.
Advisor: Robert Bruner.
799 Master's Essay.
3 Credits.
This project is intended to further the understanding of
a tomographic reconstruction problem,
in particular, the estimation of line integral values by knowing
only the nearby values.
To accomplish this goal, it will be nesassary to study the the
mathematical fundamentals of tomography and interpolation/estimation
of nonuniform points in a space that is not Euclidean.
This space consists of line integrals over a function defined on a disk.
In understanding this problem, insight will be gained in the application
of this theory to reconstruct objects when the object is not sampled
by uniformly spaced line integrals.
Advisor: Robert Bruner.