Series: Bolyai Society Mathematical Studies , Vol. 18
2008, Approx. 600 p., Hardcover
ISBN: 978-3-540-69394-9
Due: July 2008
About this book
This handbook describes advances in large scale network studies that have taken place in the past 5 years since the publication of the Handbook of Graphs and Networks in 2003. It covers all aspects of large-scale networks, including mathematical foundations and rigorous results of random graph theory, modeling and computational aspects of large-scale networks, as well as areas in physics, biology, neuroscience, sociology and technical areas. Applications range from microscopic to mesoscopic and macroscopic models.
The book is based on the material of the NSF workshop on Large-scale Random Graphs held in Budapest in 2006, at the Alfred Renyi Institute of Mathematics, organized jointly with the University of Memphis.
Series: Springer Undergraduate Mathematics Series
2008, X, 274 p. 36 illus., Softcover
ISBN: 978-1-84800-272-2
Due: August 2008
By the author of the highly-praised text, Discrete Mathematics
Introduces the mathematical theories that find many applications in modern technology, bringing readers up-to-date with topics of great current interest, both in practice and in theory
Clear and concise, with complete proofs of the results and a wealth of examples and exercises to test understanding
Assumes only a modest mathematical background and provides careful explanations of the basic principles without recourse to jargon
Information is an important feature of the modern world. Mathematical techniques underlie the devices that we use to handle it, for example, mobile phones, digital cameras, and personal computers.
This book is an integrated introduction to the mathematics of coding, that is, replacing information expressed in symbols, such as a natural language or a sequence of bits, by another message using (possibly) different symbols. There are three main reasons for doing this: economy, reliability, and security, and each is covered in detail. Only a modest mathematical background is assumed, the mathematical theory being introduced at a level that enables the basic problems to be stated carefully, but without unnecessary abstraction. Other features include:
This modern introduction to all aspects of coding is suitable for advanced undergraduate or postgraduate courses in mathematics, computer science, electrical engineering, or informatics. It is also useful for researchers and practitioners in related areas of science, engineering and economics.
Coding and its uses.- Prefix-free codes.- Economical coding.- Data compression.- Noisy channels.- The problem of reliable communication.- The noisy coding theorems.- Linear codes.- Algebraic coding theory.- Coding natural languages.- The development of cryptography.- Cryptography in theory and practice.- The RSA cryptosystem.- Cryptography and calculation.- Elliptic curve cryptography.- Answers to odd-numbered exercises.- Index.
Series: Use R
2008, Softcover
ISBN: 978-0-387-75966-1
Due: August 22, 2008
Ideally suited for computer labs: Econometric theory/methods and their implementation within R is exhibited
Self-contained: The book can be used for self-study; code examples are elaborated
Wide audience is addressed: Upper-undergraduate/Graduate students and practitioners
The analysis of integrated and co-integrated time series can be considered as the main methodology employed in applied econometrics. This book not only introduces the reader to this topic but enables him to conduct the various unit root tests and co-integration methods on his own by utilizing the free statistical programming environment R. The book encompasses seasonal unit roots, fractional integration, coping with structural breaks, and multivariate time series models. The book is enriched by numerous programming examples to artificial and real data so that it is ideally suited as an accompanying text book to computer lab classes.
The second edition adds a discussion of vector auto-regressive, structural vector auto-regressive, and structural vector error-correction models. To analyze the interactions between the investigated variables, further impulse response function and forecast error variance decompositions are introduced as well as forecasting. The author explains how these model types relate to each other.
Univariate analysis of stationary time series.- Multivariate analysis of stationary time series.- Non-stationary time series.- Cointegration.- Testing for the order of integration.- Further considerations.- Single equation methods.- Multiple equation methods.- Appendix.- Abbreviations, nomenclature and symbols.- List of tables.- List of figures.- List of R code.- References.
Series: Algorithms and Computation in Mathematics , Vol. 23
2008, Approx. 150 p., Hardcover
ISBN: 978-3-540-68546-3
Due: August 2008
Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content.
Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized.
The book summarizes the present knowledge about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems.
1 Introduction to Computability.- 2 Dynamics of Rational Mappings.- 3 First Examples.- 4 Positive Results.- 5 Negative Results.- 6 Computability vs Topology.- References.- Index
Series: Lecture Notes in Mathematics , Vol. 1953
2008, Approx. 275 p., Softcover
ISBN: 978-3-540-69391-8
Due: August 6, 2008
This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.
1. Mathematical Statistics and Information Theory.- 2. Introduction to Riemannian Geometry.- 3. Information Geometry.- 4. Information Geometry of Bivariate Families.- 5. Neighbourhoods of Poisson Randomness, Independence and Uniformity.- 6. Cosmological Voids and Galactic Clustering.- 7. Amino Acid Clustering.- 8. Cryptographic Attacks and Dignal Clustering.- 9. Stochastic Fibre Networks. 10. Stochastic Porous Media and Hydrology.- 11. Quantum Chaology