Series: New Mathematical Monographs
Hardback (ISBN-10: 0521846153 | ISBN-13: 9780521846158)
Publication is planned for January 2006 | 674 pages | 228 x 152
mm
Diophantine geometry has been studied by number theorists for
thousands of years, since the time of Pythagoras, and has
continued to be a rich area of ideas such as Fermat's Last
Theorem, and most recently the ABC conjecture. This monograph is
a bridge between the classical theory and modern approach via
arithmetic geometry. The authors provide a clear path through the
subject for graduate students and researchers. They have re-examined
many results and much of the literature, and give a thorough
account of several topics at a level not seen before in book form.
The treatment is largely self-contained, with proofs given in
full detail. Many results appear here for the first time. The
book concludes with a comprehensive bibliography. It is destined
to be a definitive reference on modern diophantine geometry,
bringing a new standard of rigor and elegance to the field.
* The authors have re-examined many results and much of the
literature, and give a thorough account of several topics at a
level not seen before in book form
* For graduate students and researchers, and is largely self-contained:
proofs are given in full detail, and many results appear here for
the first time
* Destined to be a definitive reference on modern diophantine
geometry, bringing a new standard of rigour and elegance to the
field
Contents
I. Heights; II. Weil heights; III. Linear tori; IV. Small points;
V. The unit equation; VI. Rothfs theorem; VII. The subspace
theorem; VIII. Abelian varieties; IX. Neron-tate heights; X. The
Mordell-Weil thereom; XI. Faltings theorem; XII. The ABC-conjecture;
XIII. Nevanlinna theory; XIV. The Vojta conjectures; Appendix A.
Algebraic geometry; Appendix B. Ramification; Appendix C.
Geometry of numbers; Bibliography; Glossary of notation; Index.
Hardback (ISBN-10: 0521852315 | ISBN-13: 9780521852319)
Paperback (ISBN-10: 0521617715 | ISBN-13: 9780521617710)
Not yet published - available from January 2006 (Stock level
updated: 17:56 GMT, 26 December 2005)
Courses: Computational Complexity Complexity Theory Cryptography
Levels: FINAL YEAR UNDERGRADUATE/MSC
Cryptography plays a crucial role in many aspects of today's
world, from internet banking and ecommerce to email and web-based
business processes. Understanding the principles on which it is
based is an important topic that requires a knowledge of both
computational complexity and a range of topics in pure
mathematics. This book provides that knowledge, combining an
informal style with rigorous proofs of the key results to give an
accessible introduction. It comes with plenty of examples and
exercises (many with hints and solutions), and is based on a
highly successful course developed and taught over many years to
undergraduate and graduate students in mathematics and computer
science.
* The first introductory textbook combining the topics of
Computational Complexity with Cryptography
* Self-contained - the Appendices contain all the required
mathematics
* Over 160 exercises and problems, many with hints and solutions
Contents
1. Basics of cryptography; 2. Complexity theory; 3. Non-deterministic
computation; 4. Probabilistic computation; 5. Symmetric
cryptosystems; 6. One-way functions; 7. Public key cryptography;
8. Digital signatures; 9. Key establishment protocols; 10. Secure
encryption; 11. Identification schemes; Appendix 1; Appendix 2;
Appendix 3; Appendix 4; Appendix 5; Appendix 6; Bibliography;
Index.
Series: Cambridge Monographs on Mechanics
Hardback (ISBN-10: 0521853109 | ISBN-13: 9780521853101)
Not yet published - available from January 2006
The emergence of observing systems such as acoustically-tracked floats in the deep ocean, and surface drifters navigating by satellite has seen renewed interest in Lagrangian fluid dynamics. Starting from the foundations of elementary kinematics and assuming some familiarity of Eulerian fluid dynamics, this book reviews the classical and new exact solutions of the Lagrangian framework, and then addresses the general solvability of the resulting general equations of motion. A unified account of turbulent diffusion and dispersion is offered, with applications among others to plankton patchiness in the ocean. Written at graduate level, the book provides the first detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics, of interest not only to applied mathematicians but also oceanographers, meteorologists, mechanical engineers, astrophysicists and indeed all investigators of the dynamics of fluids.
* The first book that gives a unified account of Lagrangian fluid dynamics
* Well-respected and experienced author in the fields of oceanography and mathematics
* Written at graduate level and can be used as an academic reference for oceanographers, meteorologists, mechanical engineers, astrophysicists or all investigators of the dynamics of fluids
Contents
Part I. The Lagrangian Formulation: 1. Lagrangian kinematics; 2. Lagrangian statistics; 3. Lagrangian dynamics; 4. Coordinates; 5. Real fluids; Part II. Lagrangian Flows: 6. Some analytical Lagrangian solutions; 7. Waves, instabilities and vortices; 8. Viscous incompressible flow; 9. General solvability; Part III. Diffusion: 10. Absolute dispersion; 11. Relative dispersion; 12. Convective subranges, scalar variance spectrum; 13. Diffusion; Part IV. Lagrangian data: 14. Observing systems; 15. Data analysis: the single particle; 16. Data analysis: particle clusters; References.
Series: Monographs & Surveys in Pure & Applied Math Volume: 136
ISBN: 1584885602
Publication Date: 11/1/2005
Number of Pages: 272
Presents an organized, accessible introduction to fractional Cauchy transforms
Includes new, previously unpublished research
Provides background and related earlier results about Cauchy transforms, giving a full perspective of the field
Features sources for results with additional references and comments
Presenting new results along with research spanning five decades, Fractional Cauchy Transforms provides a full treatment of the topic, from its roots in classical complex analysis to its current state. Self-contained, it includes introductory material and classical results, such as those associated with complex-valued measures on the unit circle, that form the basis of the developments that follow. The authors focus on concrete analytic questions, with functional analysis providing the general framework.
After examining basic properties, the authors study integral means and relationships between the fractional Cauchy transforms and the Hardy and Dirichlet spaces. They then study radial and nontangential limits, followed by chapters devoted to multipliers, composition operators, and univalent functions. The final chapter gives an analytic characterization of the family of Cauchy transforms when considered as functions defined in the complement of the unit circle.
About the authors:
Rita A. Hibschweiler is a Professor in the Department of Mathematics and Statistics at the University of New Hampshire, Durham, USA.
Thomas H. MacGregor is Professor Emeritus, State University of New York at Albany and a Research Associate at Bowdoin College, Brunswick, Maine, USA.\
Table of Contents
INTRODUCTION
Definition of the families Fa
Relations between F1and H1
The Riesz-Herglotz formula
Representations with real measures and h1
The F. and M. Riesz theorem
The representing measures for functions in F1
The one-to-one correspondence between measures and functions in the Riesz-Herglotz formula
The Banach space structure of Fa
Norm convergence and convergence uniform on compact sets
Notes
BASIC PROPERTIES OF Fa o
Properties of the gamma function and the binomial coefficients
A product theorem
Membership of f and f ' in Fa
The inclusion of Fa in Fb when 0 = a