Series: Encyclopaedia of Mathematical Sciences, Vol. 142
2004, XIII, 213 p. 97 illus., Hardcover
ISBN: 3-540-21040-7
About this book
Surfaces in 4-Space, written by leading specialists in the field,
discusses knotted surfaces in 4-dimensional space and surveys
many of the known results in the area. Results on knotted surface
diagrams, constructions of knotted surfaces, classically defined
invariants, and new invariants defined via quandle homology
theory are presented. The last chapter comprises many recent
results, and techniques for computation are presented. New tables
of quandles with a few elements and the homology groups thereof
are included. This book contains many new illustrations of
knotted surface diagrams. The reader of the book will become
intimately aware of the subtleties in going from the classical
case of knotted circles in 3-space to this higher dimensional
case. As a survey, the book is a guide book to the extensive
literature on knotted surfaces and will become a useful reference
for graduate students and researchers in mathematics and physics.
Written for:
Geometric topologists, algebraic topologists, advanced graduate
students, mathematicians, and physicists
Table of contents
Prologue.- Diagrams of Knotted Surfaces.- Constructions of
Knotted Surfaces.- Topological Invariants.- Quandle Cocycle
Invariants.- Epilogue.- Appendix.- References.- Index.
Series: Encyclopaedia of Mathematical Sciences, Vol. 87
2004, XIV, 412 p. 35 illus., Hardcover
ISBN: 3-540-21019-9
About this book
This book presents some facts and methods of Mathematical Control
Theory treated from the geometric viewpoint. It is devoted to
finite-dimensional deterministic control systems governed by
smooth ordinary differential equations. The problems of
controllability, state and feedback equivalence, and optimal
control are studied. Some of the topics treated by the authors
are covered in monographic or textbook literature for the first
time while others are presented in a more general and flexible
setting than elsewhere. Although being fundamentally written for
mathematicians, the authors make an attempt to reach both the
practitioner and the theoretician by blending the theory with
applications. They maintain a good balance between the
mathematical integrity of the text and the conceptual simplicity
that might be required by engineers. It can be used as a text for
graduate courses and will become most valuable as a reference
work for graduate students and researchers.
Series: Lecture Notes in Mathematics, Vol. 1840
2004, VII, 200 p., Softcover
ISBN: 3-540-21316-3
About this book
This is yet another indispensable volume for all probabilists and
collectors of the Saint-Flour series, and is also of great
interest for mathematical physicists. It contains two of the
three lecture courses given at the 32nd Probability Summer School
in Saint-Flour (July 7-24, 2002). Tsirelson's lectures introduce
the notion of nonclassical noise produced by very nonlinear
functions of many independent random variables, for instance
singular stochastic flows or oriented percolation. Werner's
contribution gives a survey of results on conformal invariance,
scaling limits and properties of some two-dimensional random
curves. It provides a definition and properties of the Schramm-Loewner
evolutions, computations (probabilities, critical exponents), the
relation with critical exponents of planar Brownian motions,
planar self-avoiding walks, critical percolation, loop-erased
random walks and uniform spanning trees.
Table of contents
Series: Undergraduate Texts in Mathematics
2nd ed., 2004, Approx. 275 p. 27 illus., Softcover
ISBN: 0-387-20756-2
About this textbook
Cryptography is a key technology in electronic key systems. It is
used to keep data secret, digitally sign documents, access
control, and so forth. Users therefore should not only know how
its techniques work, but they must also be able to estimate their
efficiency and security. Based on courses taught by the author,
this book explains the basic methods of modern cryptography. It
is written for readers with only basic mathematical knowledge who
are interested in modern cryptographic algorithms and their
mathematical foundation. Several exercises are included following
each chapter. This revised and extended edition includes new
material on the AES encryption algorithm, the SHA-1 Hash
algorithm, on secret sharing, as well as updates in the chapters
on factoring and discrete logarithms. Johannes A. Buchmann is
Professor of Computer Science and Mathematics at the Technical
University of Darmstadt, and an Associate Editor of the Journal
of Cryptology. In 1985, he received a Feodor Lynen Fellowship of
the Alexander von Humboldt Foundation. He has also received the
most prestigious award in science in Germany, the Leibniz Award
of the German Science Foundation (Deutsche Forschungsgemeinschaft).
Table of contents
* Integers * Congruences and Residue Class Rings * Encryption *
Probability and Perfect Secrecy * DES * AES * Prime Number
Generation * Public-Key Encryption * Factoring.* Discrete
Logarithms * Cryptographic Hash Functions * Digital Signatures *
Other Systems * Identification * Public-Key Infrastructures *
Solutions of the Odd Exercises * Subject Index * Bibliography
Series: Universitext
2004, XIV, 292 p., Softcover
ISBN: 3-540-20493-8
About this textbook
This book, based on a graduate course on Riemannian geometry and
analysis on manifolds, held in Paris, covers the topics of
differential manifolds, Riemannian metrics, connections,
geodesics and curvature, with special emphasis on the intrinsic
features of the subject. Classical results on the relations
between curvature and topology are treated in detail. The book is
quite self-contained, assuming of the reader only differential
calculus in Euclidean space. It contains numerous exercises with
full solutions and a series of detailed examples which are picked
up repeatedly to illustrate each new definition or property
introduced. For this third edition, some topics about the
geodesic flow and Lorentzian geometry have been added and worked
out in the same spirit.
Table of contents
Differential Manifolds.- Riemannian Metrics.- Curvature.-
Analysis on Manifolds and the Ricci Curvature.- Riemannian
Submanifolds.- Some Extra Problems.- Solutions of Exercises.-
Bibliography.- Index.