304 pages 7 line diagrams 11 tables
Paperback |
ISBN:0-521-60415-X
Since the appearance of the authors’ first volume on elliptic
curve cryptography in 1999 there has been tremendous progress in
the field. In some topics, particularly point counting, the
progress has been spectacular. Other topics such as the Weil and
Tate pairings have been applied in new and important ways to
cryptographic protocols that hold great promise. Notions such as
provable security, side channel analysis and the Weil descent
technique have also grown in importance. This second volume
addresses these advances and brings the reader up to date.
Prominent contributors to the research literature in these areas
have provided articles that reflect the current state of these
important topics. They are divided into the areas of protocols,
implementation techniques, mathematical foundations and pairing
based cryptography. Each of the topics is presented in an
accessible, coherent and consistent manner for a wide audience
that will include mathematicians, computer scientists and
engineers.
Contents
Part I. Protocols: 1. Elliptic curve base protocols N. P. Smart;
2. On the provable security of ECDSA D. Brown; 3. Proofs of
security for ECIES A. W. Dent; Part II. Implementation Techniques:
4. Side channel analysis E. Oswald; 5. Defenses against side-channel
analysis M. Joye; Part III. Mathematical Foundations: 6. Advances
in point counting F. Vercauteren; 7. Hyperelliptic curves and the
HCDLP P. Guadry; 8. Weil descent attacks F. Hess; Part IV.
Pairing Based Techniques; 9. Pairings S. Galbraith; 10.
Cryptography from pairings K. G. Paterson.
Contributors
N. P. Smart, D. Brown, A. W. Dent, E. Oswald, M. Joye, F.
Vercauteren, P. Gaudry, F. Hess, S. Galbraith, K. G. Paterson
424 pages 13 figures
Paperback |
ISBN:0-521-60918-6
This is a unique, essentially self-contained, monograph in a new
field of fundamental importance for Representation Theory,
Harmonic Analysis, Mathematical Physics, and Combinatorics. It is
a major source of general information about the double affine
Hecke algebra, also called Cherednik痴 algebra, and its
impressive applications. Chapter 1 is devoted to the Knizhnik-Zamolodchikov
equations attached to root systems and their relations to affine
Hecke algebras, Kac-Moody algebras, and Fourier analysis. Chapter
2 contains a systematic exposition of the representation theory
of the one-dimensional DAHA. It is the simplest case but far from
trivial with deep connections in the theory of special functions.
Chapter 3 is about DAHA in full generality, including
applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg
integrals, Verlinde algebras, and Gaussian sums. This book is
designed for mathematicians and physicists, experts and students,
for those who want to master the new double Hecke algebra
technique. Visit http://arxiv.org/math.QA/0404307 to read Chapter
O. and selected topics from other chapters.
Contents
0. Introduction; 1. KZ and QMBP; 2. One-dimensional DAHA; 3.
General theory.
Publication is planned for November 2004
432 pages 10 line diagrams 75 half-tones 1 map
Hardback | Not yet published - available from November 2004
ISBN:0-52-180240-7 |
Alfred Tarski, one of the greatest logicians of all time, is
widely thought of as ‘the man who defined truth’. His
mathematical work on the concepts of truth and logical
consequence are cornerstones of modern logic, influencing
developments in philosophy, linguistics and computer science.
Tarski was a charismatic teacher and zealous promoter of his view
of logic as the foundation of all rational thought, a bon-vivant
and a womanizer, who played the ‘great man’ to the hilt. Born
in Warsaw in 1901 to Jewish parents, he changed his name and
converted to Catholicism, but was never able to obtain a
professorship in his home country. A fortuitous trip to the
United States at the outbreak of war saved his life and turned
his career around, even while it separated him from his family
for years. By the war's end he was established as a professor of
mathematics at the University of California, Berkeley. There
Tarski built an empire in logic and methodology that attracted
students and distinguished researchers from all over the world.
From the cafes of Warsaw and Vienna to the mountains and deserts
of California, this first full length biography places Tarski in
the social, intellectual and historical context of his times and
presents a frank, vivid picture of a personally and
professionally passionate man, interlaced with an account of his
major scientific achievements.
Contents
1. The two Tarskis; 2. Independence and university; Interlude I.
The Banach-Tarski paradox, set theory and the axiom of choice; 3.
Polot! The Polish attribute; Interlude II. The completeness and
decidability of algebra and geometry; 4. A wider sphere of
influence; Interlude III. Truth and definability; 5. How the ‘unity
of science’ saved Tarski’s Life; 6. Berkeley is so far from
Princeton; 7. Building a school; Interlude IV. The publication
campaigns; 8. ‘Papa Tarski’ and his students; 9. Three
meetings and two departures; 10. Logic and methodology, center
stage; 11. Heydays; Interlude V. Model theory and the 1963
Symposium; 12. Around the world; 13. Los Angeles and Berkeley;
Interlude VI. Algebras of logic; 14. A decade of honors; 15. The
last times.
488 pages 128 line diagrams 4 half-tones 74 exercises 132
figures 55 worked examples
Hardback
ISBN:0-521-84150-X
Lecturers can request inspection copies of this title
Courses: MEASUREMENT THEORY, STATISTICAL METHODS, ADVANCED DATA
ANALYSIS, BAYESIAN DATA ANALYSIS, ADVANCED NUMERICAL METHODS,
ADVANCED DATA ANALYSIS.
Increasingly, researchers in many branches of science are coming
into contact with Bayesian statistics or Bayesian probability
theory. By encompassing both inductive and deductive logic,
Bayesian analysis can improve model parameter estimates by many
orders of magnitude. It provides a simple and unified approach to
all data analysis problems, allowing the experimenter to assign
probabilities to competing hypotheses of interest, on the basis
of the current state of knowledge. This book provides a clear
exposition of the underlying concepts with large numbers of
worked examples and problem sets. The book also discusses
numerical techniques for implementing the Bayesian calculations,
including an introduction to Markov Chain Monte-Carlo integration
and linear and nonlinear least-squares analysis seen from a
Bayesian perspective. In addition, background material is
provided in appendices and supporting Mathematica notebooks are
available, providing an easy learning route for upper-undergraduates,
graduate students, or any serious researcher in physical sciences
or engineering.
Contents
1. Role of probability theory in science; 2. Probability theory
as extended logic; 3. The how-to of Bayesian inference; 4.
Assigning probabilities; 5. Frequentist statistical inference; 6.
What is a statistic?; 7. Frequentist hypothesis testing; 8.
Maximum entropy probabilities; 9. Bayesian inference (Gaussian
errors); 10. Linear model fitting (Gaussian errors); 11.
Nonlinear model fitting; 12. Markov Chain Monte Carlo; 13.
Bayesian spectral analysis; 14. Bayesian inference (Poisson
sampling); Appendix A. Singular value decomposition; Appendix B.
Discrete Fourier Transform; Appendix C. Difference in two
samples; D. Poisson ON/OFF details; Appendix E. Multivariate
Gaussian from maximum entropy.
395 pages 71 line diagrams 5 tables 80 exercises 39 worked examples
Hardback
ISBN:0-521-77290-7 |
Geometric integrators are time-stepping methods, designed such
that they exactly satisfy conservation laws, symmetries or
symplectic properties of a system of differential equations. In
this book the authors outline the principles of geometric
integration and demonstrate how they can be applied to provide
efficient numerical methods for simulating conservative models.
Beginning from basic principles and continuing with discussions
regarding the advantageous properties of such schemes, the book
introduces methods for the N-body problem, systems with holonomic
constraints, and rigid bodies. More advanced topics treated
include high-order and variable stepsize methods, schemes for
treating problems involving multiple time-scales, and
applications to molecular dynamics and partial differential
equations. The emphasis is on providing a unified theoretical
framework as well as a practical guide for users. The inclusion
of examples, background material and exercises enhance the
usefulness of the book for self-instruction or as a text for a
graduate course on the subject.
Contents
1. Introduction; 2. Numerical methods; 3. Hamiltonian mechanics;
4. Geometric integrators; 5. The modified equations; 6. Higher
order methods; 7. Contrained mechanical systems; 8. Rigid Body
dynamics; 9. Adaptive geometric integrators; 10. Highly
oscillatory problems; 11. Molecular dynamics; 12. Hamiltonian
PDEs.
Publication is planned for November 2004
286 pages 37 line diagrams 8 tables
Hardback | Not yet published - available from November 2004
ISBN:0-521-80197-4
The rapidly expanding area of algebraic graph theory uses two
different branches of algebra to explore various aspects of graph
theory: linear algebra (for spectral theory) and group theory (for
studying graph symmetry). These areas have links with other areas
of mathematics, such as logic and harmonic analysis, and are
increasingly being used in such areas as computer networks where
symmetry is an important feature. Other books cover portions of
this material, but this book is unusual in covering both of these
aspects and there are no other books with such a wide scope.
Peter J. Cameron, internationally recognized for his substantial
contributions to the area, served as academic consultant for this
volume, and the result is ten expository chapters written by
acknowledged international experts in the field. Their well-written
contributions have been carefully edited to enhance readability
and to standardize the chapter structure, terminology and
notation throughout the book. To help the reader, there is an
extensive introductory chapter that covers the basic background
material in graph theory, linear algebra and group theory. Each
chapter concludes with an extensive list of references.
Contents
Foreword Peter J. Cameron; Introduction; 1. Eigenvalues of graphs
Michael Doob; 2. Graphs and matrices Richard A. Brualdi and Bryan
L. Shader; 3. Spectral graph theory Dragos Cvetkovic and Peter
Rowlinson; 4. Graph Laplacians Bojan Mohar; 5. Automorphism
groups Peter J. Cameron; 6. Cayley graphs Brian Alspach; 7.
Finite symmetric graphs Cheryle E. Praeger; 8. Strongly regular
graphs Peter J. Cameron; 9. Distance-transitive graphs Arjeh M.
Cohen; 10. Computing with graphs and groups Leonard H. Soicher.
Publication is planned for February 2005
264 pages 118 line diagrams 2 colour plates
Hardback
ISBN:0-521-83666-2
The emerging field of computational topology utilizes theory from
topology and the power of computing to solve problems in diverse
fields. Recent applications include computer graphics, computer-aided
design (CAD), and structural biology, all of which involve
understanding the intrinsic shape of some real or abstract space.
A primary goal of this book is to present basic concepts from
topology and Morse theory to enable a non-specialist to grasp and
participate in current research in computational topology. The
author gives a self-contained presentation of the mathematical
concepts from a computer scientist痴 point of view, combining
point set topology, algebraic topology, group theory,
differential manifolds, and Morse theory. He also presents some
recent advances in the area, including topological persistence
and hierarchical Morse complexes. Throughout, the focus is on
computational challenges and on presenting algorithms and data
structures when appropriate.
Contents
1. Introduction; Part I. Mathematics: 2. Spaces and filtrations;
3. Group theory; 4. Homology; 5. Morse theory; 6. New results;
Part II. Algorithms: 7. The persistence algorithms; 8.
Topological simplification; 9. The Morse-Smale algorithm; 10. The
linking number algorithm; Part III. Applications: 11. Software;
12. Experiments; 13. Applications.