July 2004 | Hardback | 456 pages 3 line diagrams 296 exercises
| ISBN: 0-521-83357-4
This revised and expanded new edition will continue to meet the
needs for an authoritative, up-to-date, self contained, and
comprehensive account of the rapidly growing field of basic
hypergeometric series, or q-series. Simplicity, clarity,
deductive proofs, thoughtfully designed exercises, and useful
appendices are among its strengths. The first five chapters cover
basic hypergeometric series and integrals, whilst the next five
are devoted to applications in various areas including Askey-Wilson
integrals and orthogonal polynomials, partitions in number
theory, multiple series, orthogonal polynomials in several
variables, and generating functions. Chapters 9-11 are new for
the second edition, the final chapter containing a simplified
version of the main elements of the theta and elliptic
hypergeometric series as a natural extension of the single-base q-series.
Some sections and exercises have been added to reflect recent
developments, and the Bibliography has been revised to maintain
its comprehensiveness.
Reviews
‘I love this book! It is great! This really is a book you can
learn the subject from. The plentiful exercises vary from
elementary to challenging with lots of each. Congratulations and
thanks are due the authors.’ George Andrews, American Math.
Monthly
‘The book is remarkable in many ways. It is comprehensive, at
least, comprehensive to date. As is typical of most works on the
subject, it is clearly and carefully written. While no book can
conceivably incorporate all the important results, particularly
those obtained in the last decade, many of them are included as
exercises. And this is the feature all other books on the subject
lack: a set of exercises. Each chapter is topped off by a
challenging series of problems which lead the reader to recreate
recent discoveries. Anyone who works even a small percentage of
them will soon be an expert. A generous series of historical
notes concludes each chapter. The book is user friendly in every
respect. The book has two excellent Appendices which summarize
the identities and summation formulas derived in the text, an
exhaustive 25 page list of references, and a nontrivial index.
Now anyone working in combinatorics, group representation theory,
coding theory, and related fields will want to own it. Many
physicists will find it bears directly on matters of interest to
them. Computer scientists may find the book increasingly timely.
Those who have refrained from entering the field because of the
tortuous notation can now have untroubled access to its mysteries.
I say, come in, the water’s fine.’ Jet Wimp, SIAM Review
Publication is planned for August 2004 | Hardback | 304 pages
| ISBN: 0-521-79186-3
Publication is planned for August 2004 | Paperback | 304 pages |
ISBN: 0-521-79636-9
The problem of evaluating integrals is well known to every
student who has had a year of calculus. It was an especially
important subject in 19th century analysis and it has now been
revived with the appearance of symbolic languages. In this book,
the authors use the problem of exact evaluation of definite
integrals as a starting point for exploring many areas of
mathematics. The questions discussed here are as old as calculus
itself. In presenting the combination of methods required for the
evaluation of most integrals, the authors take the most
interesting, rather than the shortest, path to the results. Along
the way, they illuminate connections with many subjects,
including analysis, number theory, algebra and combinatorics.
This will be a guided tour of exciting discovery for
undergraduates and their teachers in mathematics, computer
science, physics, and engineering.
Publication is planned for October 2004 | Hardback | 382 pages
24 line diagrams 50 exercises | ISBN: 0-521-83904-1
Publication is planned for October 2004 | Paperback| 382 pages 24
line diagrams 50 exercises | ISBN: 0-521-54774-1
Even the simplest singularities of planar curves, e.g. where the
curve crosses itself, or where it forms a cusp, are best
understood in terms of complex numbers. The full treatment uses
techniques from algebra, algebraic geometry, complex analysis and
topology and makes an attractive chapter of mathematics, which
can be used as an introduction to any of these topics, or to
singularity theory in higher dimensions. This book is designed as
an introduction for graduate students and draws on the author痴
experience of teaching MSc courses; moreover, by synthesising
different perspectives, he gives a novel view of the subject, and
a number of new results.
July 2004 | Paperback | 312 pages 47 line diagrams 9 tables |
ISBN: 0-521-83663-8
Line graphs have the property that their least eigenvalue is
greater than or equal to ?2, a property shared by generalized
line graphs and a finite number of so-called exceptional graphs.
This book deals with all these families of graphs in the context
of their spectral properties. The authors discuss the three
principal techniques that have been employed, namely ‘forbidden
subgraphs’, ‘root systems’ and ‘star complements’. They
bring together the major results in the area, including the
recent construction of all the maximal exceptional graphs.
Technical descriptions of these graphs are included in the
appendices, while the bibliography provides over 250 references.
This will be an important resource for all researchers with an
interest in algebraic graph theory.
July 2004 | Hardback | 410 pages 50 line diagrams 339
exercises 80 worked examples | ISBN: 0-521-83185-7
This is a revised edition of McEliece’s classic, published with
students in mind. It is a self-contained introduction to all
basic results in the theory of information and coding. This
theory was developed to deal with the fundamental problem of
communication, that of reproducing at one point, either exactly
or approximately, a message selected at another point. There is a
short and elementary overview introducing the reader to the
concept of coding. Then, following the main results, the channel
and source coding theorems, there is a study of specific coding
schemes which can be used for channel and source coding. This
volume can be used either for self-study, or for a graduate/undergraduate
level course at university. It includes dozens of worked examples
and several hundred problems for solution. The exposition will be
easily comprehensible to readers with some prior knowledge of
probability and linear algebra.