Auburn University

Topology Proceedings Volume 29 Number 1 (2005)

Mohammad Abry, Jan J. Dijkstra and Jan van Mill
Sums of almost zero-dimensional spaces

Liljana Babinkostova
Selective screenability game and covering dimension

David P. Bellamy
Certain analytic preimages of pseudocircles are pseudocircles

J. Bustamante, Samuel G. Moreno and J. M. Quesada
Best approximation and wrappings

Janusz J. Charatonik and W?odzimierz J. Charatonik
Connectedness properties of Whitney levels

Janusz J. Charatonik and Hector Mendez-Lango
Periodic-recurrent property for a class of l-dendroids

Debora Di Caprio and Stephen Watson
Continuous selections and purely topological convex structures

Alan Dow
Efimov spaces and the splitting number

Benjamin Espinoza
Whitney preserving maps onto decomposition spaces

Paul Fabel
Homeomorphisms of ? ~ R and rotation number

Ying Ge
Mappings in Ponomarev-systems

Fernando Hernandez-Hernandez and Michael Hru?ak
Q-sets and normality of Y-spaces

Yasushi Hirata and Nobuyuki Kemoto
The hereditarily collectionwise Hausdorff property in products of w1

W. T. Ingram
Two-pass maps and indecomposability of inverse limits of graphs

Francis Jordan
When are local connectivity functions connectivity?

Kenneth Kunen
Small locally compact linearly Lindelof spaces

Shou Lin
Covering properties of k-semistratifiable spaces

Chuan Liu
Notes on g-metrizable spaces

T. B. M. McMaster and C. R. Turner
Realizable repetition patterns in constrained total negation

Andres Millan
A crowded Q-point under CPAprismgame

Arnold W. Miller
On squares of spaces and Fs-sets

Takahisa Miyata and Tadashi Watanabe
Approximate sequences and Hausdorff dimension

Sam B. Nadler, Jr.
Absolute cones

Akio Noguchi
A functional equation for the Lefschetz zeta functions of infinite cyclic coverings with an application to knot theory

Kevin M. Pilgrim
Julia sets as Gromov boundaries following V. Nekrashevych

Kim Ruane
CAT(0) boundaries of truncated hyperbolic space

Carl Seaquist, Kasia Binam, Rob Street and Galen E. Turner, III
Orientable one-circuit double covers

Jon W. Short
Dense arc components in weakened topological groups

Yoshio Tanaka
Products of weak topologies

H. Murat Tuncali, E. D. Tymchatyn and Vesko Valov
Extensional dimension and completion of maps

Vladimir Uspenskij
A short proof of a theorem of Morton Brown on chains of cells

Kaori Yamazaki
Some theorems on base-normality

Douglas E. Cameron and Andre Duhoux
P. S. Urysohn: new aspects on his death

A. Lelek
Dilemma in topology (and in Science): bizarre vs. common

Edited by: Titu Andreescu, Zuming Feng, and Po-Shen Loh

USA and International Mathematical Olympiads 2004

The Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually by the MAA American Mathematics Competition since 1976.

The IMO is the world mathematics championship for high school students. It takes place every year in a different country. The IMO competitions help to discover, challenge, and encourage mathematically gifted young people all over the world.

The USAMO and the Team Selection Test (TST) are the last two stages of the selection process leading to selection of the US team in the IMO. The preceding examinations are the AMC 10 or AMC 12 and the American Invitational Mathematics Examination (AIME). Participation in the AIME, USAMO, and the TST is by invitation only, based on performance in the preceding exams of the sequence.

In addition to presenting their carefully written solutions to the problems presented here, the editors have provided remarkable solutions developed by the examination committees, contestants, and experts, during or after the contests. They also provide a comprehensive guide to other materials on advanced problem solving.

This collection of excellent problems and beautiful solutions is a valuable companion for students who wish to develop their interest in mathematics outside the school curriculum and to deepen their knowledge of mathematics.

ISBN: 0-88385-819-3
100 pp., Paperbound, 2005
Series:Problem Books

Andreescu, Titu, Andrica, Dorin

Complex Numbers from A to ...Z

2005, XI, 321 p., Softcover
ISBN: 0-8176-4326-5

About this textbook

It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.

The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.

The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented.

The book reflects the unique experience of the authors. It distills a vast mathematical literature, most of which is unknown to the western public, and captures the essence of an abundant problem culture. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W. L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics.

Table of contents

Preface.- Complex Numbers in Algebraic Form.- Complex Numbers in Trigonometric Form.- Complex Numbers and Geometry.- More on Complex Numbers and Geometry.- Olympiad-Caliber Problems.- Answers, Hints and Solutions to Proposed Problems.- Symbol Index.- Glossary.- Subject Index.- Index of Problems' Authors.- References.


Muller, Jean-Michel

Elementary Functions, 2nd ed.
Algorithms and Implementation

2006, XXII, 266 p. 36 illus., Hardcover
ISBN: 3-7643-4372-9

About this textbook

"An important topic, which is on the boundary between numerical analysis and computer sciencec. I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find. Moreover, there are very few books on these topics and they are not recent."

This unique book provides concepts and background necessary to understand and build algorithms for computing the elementary functions?sine, cosine, tangent, exponentials, and logarithms. The author presents and structures the algorithms, hardware-oriented as well as software-oriented, and also discusses issues related to accurate floating-point implementation. The purpose is not to give "cookbook recipes" that allow one to implement a given function, but rather to provide the reader with tools necessary to build or adapt algorithms for their specific computing environment.

This expanded second edition contains a number of revisions and additions, which incorporate numerous new results obtained during the last few years. New algorithms invented since 1997?such as Matulafs bipartite method, another table-based method due to Ercegovac, Lang, Tisserand, and Muller?as well as new chapters on multiple-precision arithmetic and examples of implementation have been added. In addition, the section on correct rounding of elementary functions has been fully reworked, also in the context of new results. Finally, the introductory presentation of floating-point arithmetic has been expanded, with more emphasis given to the use of the fused multiply-accumulate instruction.

The book is an up-to-date presentation of information needed to understand and accurately use mathematical functions and algorithms in computational work and design. Graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find the book a useful reference and resource.

Table of contents

List of figures.- List of tables.- Preface to the second edition.- Preface to the first edition.- Introduction.- Some basic things about computer arithmetic.- Part I. Algorithms based on polynomial approximation and/or table lookup, multiple-precision evaluation of functions.- Polynomial or rational approximations.- Table-based methods.- Multiple-precision evaluation of functions.- Part II. Shift-and-add algorithms.- Introduction to shift-and-add algorithms.- The CORDIC algorithm.- Some other shift-and-add algorithms.- Part III. Range reduction, final rounding and exceptions.- Range reduction.- Final rounding.- Miscellaneous.- Examples of implementation.- Bibliography.- Index

Pavicic, Mladen

Quantum Computation and Quantum Communication:
Theory and Experiments

2006, 250 p., Hardcover
ISBN: 0-387-24412-3

About this book

The field of quantum computing has experienced rapid development and many different experimental and theoretical groups have emerged worldwide.This book presents the key elements of quantum computation and communication theories and their implementation in an easy-to-read manner for readers coming from physics, mathematics and computer science backgrounds. Integrating both theoretical aspects and experimental verifications of developing quantum computers, the author explains why particular mathematical methods, physical models and realistic implementations might provide critical steps towards achieving the final goal - constructing quantum computers and quantum networks. The book serves as an excellent introduction for new researchers and also provides a useful review for specialists in the field.

Table of contents

Introduction.- Bits and Qubits: Theory and Its Implications.- Experiments.- Perspectives.- References.