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An Introduction to Wavelets Through Linear Algebra
Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.
Combinatorial and Computational Algebra
This volume presents articles based on the talks at the International Conference on Combinatorial and Computational Algebra held at the University of Hong Kong (China). The conference was part of the Algebra Program at the Institute of Mathematical Research and the Mathematics Department at the University of Hong Kong. Topics include recent developments in the following areas: combinatorial and computational aspects of group theory, combinatorial and computational aspects of associative and nonassociative algebras, automorphisms of polynomial algebras and the Jacobian conjecture, and combinatorics and coding theory. This volume can serve as a solid introductory guide for advanced graduate students, as well as a rich and up-to-date reference source for contemporary researchers in the field.
Une Degustation Topologique: Homotopy Theory in the Swiss Alps
The talks given at the Arolla Conference on Algebraic Topology covered a broad spectrum of current research in homotopy theory, offering participants the possibility to sample and relish selected morsels of homotopy theory, much as a participant in a wine tasting partakes of a variety of fine wines. True to the spirit of the conference, the proceedings included in this volume present a savory sampler of homotopical delicacies. Readers will find within these pages a compilation of articles describing current research in the area, including classical stable and unstable homotopy theory, configuration spaces, group cohomology, K-theory, localization, p-compact groups, and simplicial theory.
Singularities in Algebraic and Analytic Geometry
This volume contains the proceedings of an AMS special session held at the 1999 Joint Mathematics Meetings in San Antonio. The participants were an international group of researchers studying singularities from algebraic and analytic viewpoints. The contributed papers contain original results as well as some expository and historical material. This volume is dedicated to Oscar Zariski, on the one hundredth anniversary of his birth. Topics include the role of valuation theory in algebraic geometry with recent applications to the structure of morphisms; algorithmic approaches to resolution of equisingular surface singularities and locally toric varieties; weak subintegral closures of ideals an...
Inverse Problems
The present volume contains manuscripts of lectures or topics related to the lectures which were given at the conference on "Inverse Problems" at the mathematical Research Institute at Oberwolfach. The conference took place during the week of May 18-24, 1986, and was managed by the editors. Recalling Professor Joseph Keller's paper entitled Inverse Problems, American Mathematical Monthly, 83 (1976), we give two direct quotes. "We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well unders...
Radon Transforms and Tomography
One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major t...
Orbifolds in Mathematics and Physics
This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems...
Celestial Mechanics
This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results. Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the $n$-body problem which was started by Poincare and Painleve. Saari'ssolution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central configurations, his decompositions of configurational velocities, etc., are still much studied today and were...
Harmonic Analysis and Boundary Value Problems
This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ``two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.
Quantum Symmetries in Theoretical Physics and Mathematics
This volume presents articles from several lectures presented at the school on ``Quantum Symmetries in Theoretical Physics and Mathematics'' held in Bariloche, Argentina. The various lecturers provided significantly different points of view on several aspects of Hopf algebras, quantum group theory, and noncommutative differential geometry, ranging from analysis, geometry, and algebra to physical models, especially in connection with integrable systems and conformal field theories.Primary topics discussed in the text include subgroups of quantum $SU(N)$, quantum ADE classifications and generalized Coxeter systems, modular invariance, defects and boundaries in conformal field theory, finite dimensional Hopf algebras, Lie bialgebras and Belavin-Drinfeld triples, real forms ofquantum spaces, perturbative and non-perturbative Yang-Baxter operators, braided subfactors in operator algebras and conformal field theory, and generalized ($d$) cohomologies.
