Now in Paperback (ISBN-13: 9780521035361 | ISBN-10: 0521035368)
Cryptography is concerned with the conceptualization, definition
and construction of computing systems that address security
concerns. The design of cryptographic systems must be based on
firm foundations. This book presents a rigorous and systematic
treatment of the foundational issues: defining cryptographic
tasks and solving new cryptographic problems using existing tools.
It focuses on the basic mathematical tools: computational
difficulty (one-way functions), pseudorandomness and zero-knowledge
proofs. The emphasis is on the clarification of fundamental
concepts and on demonstrating the feasibility of solving
cryptographic problems, rather than on describing ad-hoc
approaches. The book is suitable for use in a graduate course on
cryptography and as a reference book for experts. The author
assumes basic familiarity with the design and analysis of
algorithms; some knowledge of complexity theory and probability
is also useful.
* Systematic and rigorous approach that is focused on concepts
* Each chapter has exercises and guidelines for solution
Contents
Preface; 1. Introduction; 2. Computational difficulty; 3.
Pseudorandom generators; 4. Zero-knowledge proof systems;
Appendix A: background in computational number theory; Appendix B:
brief outline of volume 2; Bibliography; Index.
Review
'The written style is excellent and natural, making the text
rather comfortable to read even on quite advanced topics. The
book is suitable for students in a graduate course on
cryptography, and is also a useful reference text for experts.'
The Mathematical Gazette
Series: Cambridge Series in Statistical and Probabilistic
Mathematics (No. 21)
Hardback (ISBN-13: 9780521871006 | ISBN-10: 052187100X)
Point-to-point vs. hub-and-spoke. Questions of network design are
real and involve many billions of dollars. Yet little is known
about optimizing design - nearly all work concerns optimizing
flow assuming a given design. This foundational book tackles
optimization of network structure itself, deriving comprehensible
and realistic design principles. With fixed material cost rates,
a natural class of models implies the optimality of direct source-destination
connections, but considerations of variable load and
environmental intrusion then enforce trunking in the optimal
design, producing an arterial or hierarchical net. Its
determination requires a continuum formulation, which can however
be simplified once a discrete structure begins to emerge.
Connections are made with the masterly work of Bendsoe and
Sigmund on optimal mechanical structures and also with neural,
processing and communication networks, including those of the
Internet and the Worldwide Web. Technical appendices are provided
on random graphs and polymer models and on the Klimov index.
* D'Arcy Thompson for the 21st century: path-breaking work on
optimisation of network structure
* Whittle is renowned for his fundamental work on networks and
optimisation
* Comprehensible, realistic design principles that accord with
the evolution of networks in nature
Contents
1. Tour d'horizon; Part I. Distribution Networks: 2. Simple
flows; 3. Continuum formulations; 4. Multi-class and destination-specific
flows; 5. Design optimality under variable loading; 6. Concave
costs and hierarchical structure; 7. Road networks; 8. Structural
optimisation; Michell structures; 9. Structures: computational
experience of evolutionary algorithms; 10. Structure design for
variable loading; Part II. Artificial Neural Networks: 11. Models
and learning; 12. Some particular nets; 13. Oscillatory
operation; Part III. Processing Networks: 14. Queuing networks;
15. Time-sharing networks; Part IV. Communication Networks: 16.
Loss networks: optimality and robustness; 17. Loss networks:
stochastics and self-regulation; 18. Operation of the Internet;
19. Evolving networks and the World-wide Web; Appendix 1. Spatial
integrals for the telephone problem; Appendix 2. Bandit and tax
processes; Appendix 3. Random graphs and polymer models;
References; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 106)
Hardback (ISBN-13: 9780521866293 | ISBN-10: 0521866294)
This wide ranging but self-contained account of the spectral
theory of non-self-adjoint linear operators is ideal for
postgraduate students and researchers, and contains many
illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt
and trace class operators are discussed, as are one-parameter
semigroups and perturbations of their generators. Two chapters
are devoted to using these tools to analyze Markov semigroups.
The text also provides a thorough account of the new theory of
pseudospectra, and presents the recent analysis by the author and
Barry Simon of the form of the pseudospectra at the boundary of
the numerical range. This was a key ingredient in the
determination of properties of the zeros of certain orthogonal
polynomials on the unit circle. Finally, two methods, both very
recent, for obtaining bounds on the eigenvalues of non-self-adjoint
Schrodinger operators are described. The text concludes with a
description of the surprising spectral properties of the non-self-adjoint
harmonic oscillator.
* The first genuinely accessible account of non-self-adjoint
operator theory and spectral theory; for graduate students and
academic researchers
* Written by a well-known and respected author, with much
experience in this field
* Gives the first account of pseudospectra written from a pure
mathematical point of view
Contents
Preface; 1. Elementary operator theory; 2. Function spaces; 3.
Fourier transforms and bases; 4. Intermediate operator theory; 5.
Operators on Hilbert space; 6. One-parameter semigroups; 7.
Special classes of semigroup; 8. Resolvents and generators; 9.
Quantitative bounds on operators; 10. Quantitative bounds on
semigroups; 11. Perturbation theory; 12. Markov chains and
graphs; 13. Positive semigroups; 14. NSA Schrodinger operators.
Series: Encyclopedia of Mathematics and its Applications (No.
110)
Hardback (ISBN-13: 9780521875929 | ISBN-10: 0521875927)
Spline functions are universally recognized as highly effective
tools in approximation theory, computer-aided geometric design,
image analysis, and numerical analysis. The theory of univariate
splines is well known but this text is the first comprehensive
treatment of the analogous bivariate theory. A detailed
mathematical treatment of polynomial splines on triangulations is
outlined, providing a basis for developing practical methods for
using splines in numerous application areas. The detailed
treatment of the Bernstein-Bezier representation of polynomials
will provide a valuable source for researchers and students in
CAGD. Chapters on smooth macro-element spaces will allow
engineers and scientists using the FEM method to solve partial
differential equations numerically with new tools. Workers in the
geosciences will find new tools for approximation and data
fitting on the sphere. Ideal as a graduate text in approximation
theory, and as a source book for courses in computer-aided
geometric design or in finite-element methods.
* First book to offer a detailed treatment of bivariate splines
* Provides a basis for developing practical methods for using
splines in numerous application areas
* Up-to-date and comprehensive account, suitable for
mathematicians, statisticians, engineers, geoscientists,
biologists and computer scientists working in academia or
industry
Contents
Preface; 1. Bivariate polynomials; 2. Bernstein-Bezier methods
for bivariate polynomials; 3. B-patches; 4. Triangulations and
quadrangulations; 5. Bernstein-Bezier methods for spline spaces;
6. C1 Macro-element spaces; 7. C2 Macro-element spaces; 8. Cr
Macro-element spaces; 9. Dimension of spline splines; 10.
Approximation power of spline spaces; 11. Stable local minimal
determining sets; 12. Bivariate box splines; 13. Spherical
splines; 14. Approximation power of spherical splines; 15.
Trivariate polynomials; 16. Tetrahedral partitions; 17.
Trivariate splines; 18. Trivariate macro-element spaces;
Bibliography; Index.
Hardback (ISBN-13: 9780521870948 | ISBN-10: 0521870941)
Paperback (ISBN-13: 9780521691413 | ISBN-10: 0521691419)
Algebraic geometry, central to pure mathematics, has important
applications in such fields as engineering, computer science,
statistics and computational biology, which exploit the
computational algorithms that the theory provides. Users get the
full benefit, however, when they know something of the underlying
theory, as well as basic procedures and facts. This book is a
systematic introduction to the central concepts of algebraic
geometry most useful for computation. Written for advanced
undergraduate and graduate students in mathematics and
researchers in application areas, it focuses on specific examples
and restricts development of formalism to what is needed to
address these examples. In particular, it introduces the notion
of Grobner bases early on and develops algorithms for most
everything covered. It is based on courses given over the past
five years in a large interdisciplinary programme in
computational algebraic geometry at Rice University, spanning
mathematics, computer science, biomathematics and bioinformatics.
* Exposition of theory motivated by computational applications
* Lots of carefully chosen problems and exercises - many with
hints and morals - build intuition and facility
* Solutions to a significant number of exercises available at
author's website
Contents
Introduction; 1. Guiding problems; 2. Division algorithm and
Grobner bases; 3. Affine varieties; 4. Elimination; 5.
Resultants; 6. Irreducible varieties; 7. Nullstellensatz; 8.
Primary decomposition; 9. Projective geometry; 10. Projective
elimination theory; 11. Parametrizing linear subspaces; 12.
Hilbert polynomials and Bezout; Appendix. Notions from abstract
algebra; References; Index.