Series: Sources and Studies in the History of Mathematics and
Physical Sciences
2007, Hardcover
ISBN-10: 0-387-49511-8
ISBN-13: 978-0-387-49511-8
Due: July 2007
About this book
Thomas Harriot's "Artis analyticae praxis" is an
essential work in the history of algebra. To some extent it is a
development work of Viete, who was among the first to use literal
symbols to stand for known and unknown quantities. But it was
Harriot who took the crucial step of creating an entirely
symbolic algebra, so that reasoning could be reduced to a quasi-mechanical
manipulation of symbols. Although his algebra was still limited
in scope (he insisted. for example, on strict homogeneity, so
only terms of the same powers could be added or equated to one
another), it is recognizably modern. Although Harriot's book was
highly influential in the development of analysis in England
before Newton, it has recently become clear that the posthumously
published Praxis contains only an incomplete account of Harriot's
achievement: his editor substantially rearranged the work before
publishing it, and omitted sections that were apparently beyond
his comprehension, such as negative and complex roots of
equations. The commentary included with the translation attempts
to restore the Praxis to the state of Harriot's draft. Basing
their work on manuscripts in the British Library, Pentworth
House, and Lambeth Palace, the commentary contains some of
Harriot's most novel and advanced mathematics, very little of
which has been published in the past. It will provide the basis
for a reassessment of the development of algebra.
The present work is the first ever English translation of the
original text of Thomas Harriot’s Artis Analyticae Praxis,
first published in 1631 in Latin. Thomas Harriot’s Praxis is an
essential work in the history of algebra. Even though Harriot’s
contemporary, Viete, was among the first to use literal symbols
to stand for known and unknown quantities, it was Harriott who
took the crucial step of creating an entirely symbolic algebra.
This allowed reasoning to be reduced to a quasi-mechanical
manipulation of symbols. Although Harriot’s algebra was still
limited in scope (he insisted, for example, on strict
homogeneity, so only terms of the same powers could be added or
equated to one another), it is recognizably modern.
While Harriot’s book was highly influential in the development
of analysis in England before Newton, it has recently become
clear that the posthumously published Praxis contains only an
incomplete account of Harriot’s achievement: his editor
substantially rearranged the work before publishing it, and
omitted sections that were apparently beyond comprehension, such
as negative and complex roots of equations.
The commentary included with this translation relates the
contents of the Praxis to the corresponding pages in his
manuscript papers, which enables much of Harriot's most novel and
advanced mathematics to be explored. This publication will become
an important contribution to the history of mathematics, and it
will provide the basis for a reassessment of the development of
algebra.
Table of contents
Preface.- Introduction.-The practice of the analytic art.-
Commentary.- Notes on the Definitions.- Notes on Section One.-
Notes on Section Two.- Notes on Section Three.- Notes on Section
Four.- Notes on Section Five.- Notes on Section Six.- Numerical
Exegesis.- Comparative table of equations solved.- Errata.-
Appendix.- Select Bibliography
Series: Texts in Computer Science
2007, Approx. 400 p., 17 illus., Hardcover
ISBN-10: 1-84628-658-1
ISBN-13: 978-1-84628-658-2
About this textbook
The increasing dependence of contemporary society on computers
and computer networks, has given rise to an increasing number of
computer security problems. Yet despite a high proliferation of
expert remedies, a viable solution to these security issues
remains elusive, and society continues to suffer at the hands of
cyber criminals, vandals, and hackers.
This third edition takes off where the second ended to examine
ethical, social, and policy challenges steaming from the
emergence of cyberspace and the convergence of telecommunication
and computing technologies, and the miniaturalization of
computing, telecommunication, and information enabling devices.
The book broadly surveys thought-provoking questions about the
impact of these new technologies, with particular emphasis on the
rapid growth of a multitude of computer networks including the
internet. It assumes a modest familiarity with the basic computer
literacy.
Table of contents
Introduction to Social and Ethical Computing.- Morality and the
Law.- Ethics, Technology and Value, Ethics and the Professions.-
Anonymity, Security, Privacy and Civil Liberties.- Intellectual
Property Rights and Computer Technology.- Social Context of
Computing.- Software Issues: Risks and Liabilities.- Computer
Crimes.- New Frontiers for Computer Ethics: Artificial
Intelligence, Cyberspace and Virtual Reality.- Cyberspace and
Cyberethics.- Computer Networks Crimes.- Computer Crime
Investigations ? Computer Forensics.- Biometrics.- Appendix A:
The Digital Millennium Copyright Act.- Appendix B: The Federal
False Claims Act.- Appendix C.- Projects
Series: Texts in Computer Science
Originally published in the series: Texts and Monographs in
Computer Science
2008, Approx. 800 p., 41 illus., Hardcover
ISBN-10: 0-387-33998-1
ISBN-13: 978-0-387-33998-6
Due: September 2007
About this textbook
"The book is outstanding and admirable in many respects. ...
is necessary reading for all kinds of readers from undergraduate
students to top authorities in the field." Journal of
Symbolic Logic
Written by two experts in the field, this is the only
comprehensive and unified treatment of the central ideas and
their applications of Kolmogorov complexity. The book presents a
thorough treatment of the subject with a wide range of
illustrative applications. Such applications include the
randomness of finite objects or infinite sequences, Martin-Loef
tests for randomness, information theory, computational learning
theory, the complexity of algorithms, and the thermodynamics of
computing. It will be ideal for advanced undergraduate students,
graduate students, and researchers in computer science,
mathematics, cognitive sciences, philosophy, artificial
intelligence, statistics, and physics. The book is self-contained
in that it contains the basic requirements from mathematics and
computer science. Included are also numerous problem sets,
comments, source references, and hints to solutions of problems.
New topics in this edition include Omega numbers, Kolmogorov-Loveland
randomness, universal learning, communication complexity,
Kolmogorov's random graphs, time-limited universal distribution,
Shannon information and others.
Table of contents
Preliminaries.- Algorithmic Complexity.- Algorithmic Prefix
Complexity.- Algorithmic Probability.- Inductive Reasoning.- The
Incompressibility Method.- Resource-Bounded Complexity.- Physics,
Information, and Computation.- Shannon Information and Kolmogorov
Complexity.- Information Distance
2007, XXVIII, 789 p., 23 illus., Hardcover
ISBN-10: 3-540-30307-3
ISBN-13: 978-3-540-30307-7
About this book
The relation between mathematics and physics has a long history,
in which the role of number theory and of other more abstract
parts of mathematics has recently become more prominent.
More than ten years after a first meeting in 1989 between number
theorists and physicists at the Centre de Physique des Houches, a
second 2-week event focused on the broader interface of number
theory, geometry, and physics.
This book is the result of that exciting meeting, and collects,
in 2 volumes, extended versions of the lecture courses, followed
by shorter texts on special topics, of eminent mathematicians and
physicists.
The present volume has three parts: Conformal Field Theories,
Discrete Groups, Renomalization.
The companion volume is subtitled: On Random Matrices, Zeta
Functions and Dynamical Systems (Springer, 3-540-23189-7).
Table of contents
Part I: Conformal Field Theory. E. Frenkel: Lectures on the
Langlands Program and Conformal Field Theory.- W. Nahm: Conformal
Field Theory and Torsion Elements of the Bloch Group.- P.
Cvitanovic: Tracks, Lie’s, and Exceptional Magic.- P. Di
Vecchia/A. Liccardo: Gauge Theories from D. Branes.- K. Wendland:
On Superconformal Field Theories Associated to Very Attractive
Quartics.- Part II: Discrete Groups. C. Soule: An Introduction to
Arithmetic Groups.- B. Pioline/A. Waldron: Automorphic Forms: A
Physicist’s Survey.- J. McKay/A. Sebbar: Replicable Functions:
An Introduction.- D. Zagier: The Dilogarithm Function in Geometry
and Number Theory.- H. Gangl/A.B.Goncharov/A. Levin: Multiple
Logarithms, Algebraic Cycles and Trees.- M. Marcolli: Modular
Curves, C-Algebras and Chaotic Cosmology.- G. Moore: Strings and
Arithmetic.- Part III: Renormalization. A. Connes/M. Marcolli:
Renormalization, The Riemann-Hilbert correspondence, and Motivic
Galois Theory.- D. Kreimer: Factorization in Quantum Field Theory:
An Exercise in Hopf Algebras and Local Singularities.- S.
Weinzierl: Algebraic Algorithms in Perturbative Calculations.
- Written by leading logicians and philosophers
- Comprehensive authoritative coverage of all major areas of
contemporary research in symbolic logic
- Clear, in-depth expositions of technical detail
- Progressive organization from general considerations to
informal to symbolic logic to nonclassical logics
- Presents current work in symbolic logic within a unified
framework
- Accessible to students, engaging for experts and professionals
- Insightful philosophical discussions of all aspects of logic
- Useful bibliographies in every chapter
Description
The papers presented in this volume examine topics of central
interest in contemporary philosophy of logic. They include
reflections on the nature of logic and its relevance for
philosophy today, and explore in depth developments in informal
logic and the relation of informal to symbolic logic,
mathematical metatheory and the limiting metatheorems, modal
logic, many-valued logic, relevance and paraconsistent logic,
free logics, extensional v. intensional logics, the logic of
fiction, epistemic logic, formal logical and semantic paradoxes,
the concept of truth, the formal theory of entailment, objectual
and substitutional interpretation of the quantifiers, infinity
and domain constraints, the Lowenheim-Skolem theorem and Skolem
paradox, vagueness, modal realism v. actualism, counterfactuals
and the logic of causation, applications of logic and mathematics
to the physical sciences, logically possible worlds and
counterpart semantics, and the legacy of Hilbert’s program and
logicism. The handbook is meant to be both a compendium of new
work in symbolic logic and an authoritative resource for students
and researchers, a book to be consulted for specific information
about recent developments in logic and to be read with pleasure
for its technical acumen and philosophical insights.
Contents
General Preface (Dov Gabbay, Paul Thagard and John Woods)
Preface
List of Contributors
Introduction: Philosophy of Logic Today (Dale Jacquette)
What is Logic? (Jaakko Hintikka and Gabriel Sandu)
The Scope and Limits of Logic (Wilfrid Hodges)
Logic in Philosophy (Johan van Benthem)
Informal Logic and the Concept of Argument (David Hitchcock)
On the Relation of Informal to Symbolic Logic (Dale Jacquette)
Vagueness and the Logic of Ordinary Language (Roy A. Sorensen)
Logic and Semantic Analysis (Ernest Lepore and Matthew Stone)
Justificatory Irrelevance of Formal Semantics (Charles F.
Kielkopf)
A Brief History of Truth (Stewart Candlish and Nic Damnjanovic)
Truth and Paradox: A Philosophical Sketch (J.C. Beall)
Hilbert's Program Then and Now (Richard Zach)
Logicism and its Contemporary Legacy (Herbert Hochberg)
Classical Logic's Coming of Age (John W. Dawson, Jr.)
Infinity (Peter Fletcher)
Lowenheim-Skolem Theorems (Heinz-Dieter Ebbinghaus)
The Mathematics of Skolem's Paradox (Timothy Bays)
Objectual and Substitutional Interpretations of the Quantifiers (Michael
Hand)
Many-Valued Logics (Siegfried Gottwald)
Relevance Logics (Katalin Bimbo)
Paraconsistent Lgoics and Paraconsistency (Newton C.A. da Costa,
Otavio Bueno and Decio Krause)
Extensional vs Intensional Logic (Jaroslav Peregrin)
Logically Possible Worlds and Counterpart Semantics for Modal
Logic (Marcus Kracht and Oliver Kutz)
Modal Realism and its Roots in Mathematical Realism (Charles S.
Chihara)
Free Logics (John Nolt)
Fictions and their Logic (John Woods)
Counterfactuals, Causation, and Preemption (John Collins)
Logic, Mathematics, and the Natural Sciences (Neil Tennant)
Default Reasoning (Nicholas Rescher)
Index
Availability: In stock.
Summary
A collection of ca. 30 mathematical essays by Phil Davis. From
the Preface: “This book is addressed to all who are curious
about the nature of mathematics and its role in society. It is
neither a text book nor a specialists’ book. It consists of a
number of loosely linked essays that may be read independently
and for which I have tried to provide a leitmotif by throwing
light on the relationship between mathematics and common sense.
In these essays I hope to foster a critical attitude towards both
the existence of common sense in mathematics and the ambiguous
role that it can play.”
Details
ISBN: 1-56881-270-1
Year: 2006
Format: Hardcover
Pages: 250
Phil Davis is one of a very small group of mathematicians who are
interested and able to step outside the community and take a hard
look at what mathematics really ’is’. Its uses, misuses,
customs, relations with the so-called ’real’ world,
psychology and deep nature are all grist for his voracious mill.”
----David Mumford