An infinitely entertaining and informative
journey into mathematical thinking
Robert Kaplan's The Nothing That Is: A Natural
History of Zero
was an international best-seller, translated
into eight languages.
The Times called it "elegant, discursive,
and littered with
quotes and allusions from Aquinas via Gershwin
to Woolf" and
The Philadelphia Inquirer praised it as "absolutely
scintillating."
In this delightful new book, Robert Kaplan,
writing together with
his wife Ellen Kaplan, once again takes us
on a witty, literate,
and accessible tour of the world of mathematics.
Where The
Nothing That Is looked at math through the
lens of zero, The Art
of the Infinite takes infinity, in its countless
guises, as a
touchstone for understanding mathematical
thinking. Tracing a
path from Pythagoras, whose great Theorem
led inexorably to a
discovery that his followers tried in vain
to keep secret (the
existence of irrational numbers); through
Descartes and Leibniz;
to the brilliant, haunted Georg Cantor, who
proved that infinity
can come in different sizes, the Kaplans
show how the attempt to
grasp the ungraspable embodies the essence
of mathematics. The
Kaplans guide us through the "Republic
of Numbers,"
where we meet both its upstanding citizens
and more shadowy
dwellers; and we travel across the plane
of geometry into the
unlikely realm where parallel lines meet.
Along the way, deft
character studies of great mathematicians
(and equally colorful
lesser ones) illustrate the opposed yet intertwined
modes of
mathematical thinking: the intutionist notion
that we discover
mathematical truth as it exists, and the
formalist belief that
math is true because we invent consistent
rules for it.
"Less than All," wrote William
Blake, "cannot
satisfy Man." The Art of the Infinite
shows us some of the
ways that Man has grappled with All, and
reveals mathematics as
one of the most exhilarating expressions
of the human imagination.
Robert and Ellen Kaplan are the founders
of The Math Circle, a
school, open to anyone of any age, that teaches
the enjoyment of
mathematics. They have been invited to lecture
on mathematics
teaching and the Math Circle to organizations
such as the
American Mathematical Society and universities
in Spain and
Switzerland. They live in Cambridge, Massachusetts.
288 pp.; 25 line illus; 4-3/4 x 7-3/4; 0-19-514743-X
Description
Written in a clear and informal style Discrete
Mathematics for
Computing is aimed at first year undergraduate
computing students
with very little mathematical background.
It is a low-level
introductory text which provides the information
at a very gentle
pace, covering all the essential material
that forms the
background for studies in computing and information
systems .
This new edition includes new sections on
proof methods and
recurrences, and the examples have been updated
throughout to
reflect chang
Contents
List of Symbols Preface Bases and Number
Representation Computer
Representation and Arithmetic Logic Sets
and Relations Functions
Induction and Recursion Boolean Algebra and
Digital Circuits
Combinatories Introduction to Graph Theory
Trees Number Theory
Algorithms and Computational Complexity
ISBN
0-333-98111-1
Published Date
2002
Pages
300 pages
Binding
Pb
2002. X, 276 pp. 43 figs., 2 tabs. Softcover
3-540-42253-6
This book by I.R.Shafarevich aims to show
on the example of some
particular questions that algebra is not
less beautiful then any
other part of mathematics. It contains an
exposition of some
rudiments of algebra, number theory, set
theory and probability
presupposing very limited knowledge of mathematics.
I.R.Shafarevich
is known to be one of the best mathematicians
of this century, as
well as one of the best mathematical writers.
Keywords: algebra, integers, polynomials,
sets
Contents: Integers.- Simplest Properties
of Polynomials.- Finite
Sets.- Prime Numbers.- Real Numbers and Polynomials.-
Infinite
Sets.- Power Series
Series: Universitext.
1st ed. 2001. 3rd printing 2002. XXII, 754
p. 186 illus. Softcover
1-85233-611-0
The study of directed graphs has developed
enormously over recent
decades, yet no book covers more than a tiny
fraction of the
results from more than 3000 research articles
on the topic.
Digraphs is the first book to present a unified
and comprehensive
survey of the subject. In addition to covering
the theoretical
aspects, including detailed proofs of many
important results, the
authors present a number of algorithms and
applications. The
applications of digraphs and their generalizations
include among
other things recent developments in the Travelling
Salesman
Problem, genetics and network connectivity.
More than 700
exercises and 180 figures will help readers
to study the topic
while open problems and conjectures will
inspire further research.
This book will be essential reading and reference
for all
graduate students, researchers and professionals
in mathematics,
operational research, computer science and
other areas who are
interested in graph theory and its applications.
Contents: Basic Terminology, Notation and
Results.- Distances.-
Flows in Networks.- Classes of Digraphs.-
Hamiltonicity and
Related Problems.- Hamiltonian Refinements.-
Global Connectivity.-
Orientations of Graphs.- Disjoint Paths and
Trees.- Cycle
Structure of Digraphs.- Generalizations of
Digraphs.- Additional
Topics.- References.- Symbol Index, Author
Index, Subject Index.
2002. Approx. 530 pp. 68 figs. Softcover
0-387-95217-9
The purpose of the book is to introduce new
users to the use of
the TeX system, in particular document preparation
using LaTeX.
It seeks to avoid the pitfalls of having
to search through
several advanced books on the subject, by
collecting together the
more frequently required tools and presenting
these in a single
accessible volume. It will also describe
the recent developments
in multilingual typesetting using TeX that
now make it
straightforward for users to prepare documents
in their own
language and alphabet, giving the book a
global readership. The
main presentation will be independent of
any particular type of
computer hardware, though a section will
contain details of some
of the more popular versions of TeX for each
type of machine and
details of where they can be downloaded on
the Internet from, or
purchased at low cost on a convenient compact
disk. Topics and
features: *multi-lingual uses of LaTeX*discussion
of hardware
implementations*use and misuse of particular
LaTeX commands*some
treatment of graphics*inclusion of exercises
with solutions*discussion
of common errors*inclusion of many examples
Contents: 1.Introduction; 2.Document structure;
3.Fonts; 4.List
environments;
5.Mathematical text; 6.General document preparation;
7.Preparing
the
bibliography and indices; 8.Additional packages;
9.Graphics; 10.LaTeX
speaks many languages; 11.To err is human;
12.Advanced typography
2002. XIX, 287 p. 31 illus. Hardcover
3-540-43447-X
Timing issues are of growing importance for the conceptualization
and design of computer-based systems. Timing may simply be
essential for the correct behaviour of a system, e.g. of a
controller. Even if timing is not essential for the correct
behaviour of a system, there may be good reasons to introduce it
in such a way that suitable timing becomes relevant for the
correct behaviour of a complex system. This book is unique in
presenting four algebraic theories about processes, each dealing
with timing from a different point of view, in a coherent and
systematic way. The timing of actions is either relative or
absolute and the underlying time scale is either discrete or
continuous. All presented theories are extensions of the algebra
of communicating processes. The book is essential reading for
researchers and advanced students interested in timing issues in
the context of the design and analysis of concurrent and
communicating processes.
Keywords: Process Algebra, Relative Timing, Absolute Timing,
Discrete Timing, Continuous Time, Dependable Computing, Correct
System Design, Reactive Systems
Contents: Preface; 1. No Timing; 2. Discrete Relative Timing; 3.
Discrete Absolute Timing; 4. Continuous Relative Timing; 5.
Continuous Absolute Timing; 6. Abstraction; 7. Features; A.
Soundness and Completeness; B. Background Material; Bibliography;
Glossary; Index.
Series: Monographs in Theoretical Computer Science. An EATCS
Series.