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Most papers published in this volume are based on lectures
presented at the Chico Conference on Semigroups held on the Chico
campus of the Cal ifornia State University on April 10-12, 1986.
The conference was spon sored by the California State University,
Chico in cooperation with the Engineering Computer Sciences
Department of the Pacific Gas and Electric Company. The program
included seven 50-minute addresses and seventeen 30-minute
lectures. Speakers were invited by the organizing committee
consisting of S. M. Goberstein and P. M. Higgins. The purpose of
the conference was to bring together some of the leading
researchers in the area of semigroup theory for a discussion of
major recent developments in the field. The algebraic theory of
semigroups is growing so rapidly and new important results are
being produced at such a rate that the need for another meeting was
well justified. It was hoped that the conference would help to
disseminate new results more rapidly among those working in semi
groups and related areas and that the exchange of ideas would
stimulate research in the subject even further. These hopes were
realized beyond all expectations."
Most papers published in this volume are based on lectures
presented at the Chico Conference on Semigroups held on the Chico
campus of the Cal ifornia State University on April 10-12, 1986.
The conference was spon sored by the California State University,
Chico in cooperation with the Engineering Computer Sciences
Department of the Pacific Gas and Electric Company. The program
included seven 50-minute addresses and seventeen 30-minute
lectures. Speakers were invited by the organizing committee
consisting of S. M. Goberstein and P. M. Higgins. The purpose of
the conference was to bring together some of the leading
researchers in the area of semigroup theory for a discussion of
major recent developments in the field. The algebraic theory of
semigroups is growing so rapidly and new important results are
being produced at such a rate that the need for another meeting was
well justified. It was hoped that the conference would help to
disseminate new results more rapidly among those working in semi
groups and related areas and that the exchange of ideas would
stimulate research in the subject even further. These hopes were
realized beyond all expectations."
This book introduces recently developed ideas and techniques in
semigroup theory to provide a handy reference guide previously
unavailable in a single volume. The opening chapter provides
sufficient background to enable the reader to follow any of the
subsequent chapters, and would by itself be suitable for a first
course in semigroup theory. The second chapter gives an account of
free inverse semigroups leading to proofs of the McAlister
P-theorems. Subsequent chapters have the underlying theme of
diagrams and mappings, and the new material includes the theory of
biordered sets of Nambooripad and Easdown, the semigroup diagrams
of Remmers and Jackson with applications to the one-relator, and
other word problems, a short proof of Isbell's Zigzag theorem with
applications to epimorphisms and amalgams, together with
combinatorial, probabalistic and graphical techniques used to prove
results including Schein's Covering Theorem and Howie's Gravity
Formula for finite full transformation semigroups. Nearly two
hundred exercises serve the dual purpose of illustrating the
richness of the subject while allowing the reader to come to grips
with the material.
Numbers are integral to our everyday lives and feature in
everything we do. In this Very Short Introduction Peter M. Higgins,
the renowned mathematics writer, unravels the world of numbers;
demonstrating its richness, and providing a comprehensive view of
the idea of the number. Higgins paints a picture of the number
world, considering how the modern number system matured over
centuries. Explaining the various number types and showing how they
behave, he introduces key concepts such as integers, fractions,
real numbers, and imaginary numbers. By approaching the topic in a
non-technical way and emphasising the basic principles and
interactions of numbers with mathematics and science, Higgins also
demonstrates the practical interactions and modern applications,
such as encryption of confidential data on the internet. ABOUT THE
SERIES: The Very Short Introductions series from Oxford University
Press contains hundreds of titles in almost every subject area.
These pocket-sized books are the perfect way to get ahead in a new
subject quickly. Our expert authors combine facts, analysis,
perspective, new ideas, and enthusiasm to make interesting and
challenging topics highly readable.
Algebra marked the beginning of modern mathematics, moving it
beyond arithmetic, which involves calculations featuring given
numbers, to problems where some quantities are unknown. Now, it
stands as a pillar of mathematics, underpinning the quantitative
sciences, both social and physical. This Very Short Introduction
explains algebra from scratch. Over the course of ten logical
chapters, Higgins offers a step by step approach for readers keen
on developing their understanding of algebra. Using theory and
example, he renews the reader's aquaintance with school
mathematics, before taking them progressively further and deeper
into the subject. ABOUT THE SERIES: The Very Short Introductions
series from Oxford University Press contains hundreds of titles in
almost every subject area. These pocket-sized books are the perfect
way to get ahead in a new subject quickly. Our expert authors
combine facts, analysis, perspective, new ideas, and enthusiasm to
make interesting and challenging topics highly readable.
What can you do with your maths? You can use it to thoroughly
understand all manner of things that cannot be dealt with in any
other way. This book serves up a variety of problems and shows how
mathematics answers them. Topics range from cracking codes to the
persistence of recessive genes; from logic puzzles to classical
geometry; and from planetary motion questions to predicting the
market share of competing companies. And there are other problems
where the mathematics itself is intrinsically surprising and
interesting.
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