Paperback | ISBN: 9780262526678 | 392 pp. | 7 x 9 in | 3 graphs, 79 figures, 2 tables| September 2014
The combination of two of the twentieth century’s most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. The fundamental unit of computation is no longer the bit but the quantum bit or qubit. This comprehensive introduction to the field offers a thorough exposition of quantum computing and the underlying concepts of quantum physics, explaining all the relevant mathematics and offering numerous examples. With its careful development of concepts and thorough explanations, the book makes quantum computing accessible to students and professionals in mathematics, computer science, and engineering. A reader with no prior knowledge of quantum physics (but with sufficient knowledge of linear algebra) will be able to gain a fluent understanding by working through the book.
288 pages | 24 b/w line drawings | 246x171mm
978-0-19-870996-1 | Hardback | August 2014 (estimated)
978-0-19-870997-8| Paperback
Directed at first and second year undergraduates
A concise introduction to probability
An honest approach to mathematical rigour
Careful choice of material, from probability to stochastic processes
Enhanced by exercises and problems
New chapter on Markov chains
Has been developed in response to the evolution of course syllabuses
Further examples, exercises, and problems including problems from the Oxford and Cambridge finals papers
Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.
A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford.
The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time.
This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.
Readership: - Undergraduate mathematicians taking introductory courses in probability follow-up undergraduate courses (years 1 and 2). - Undergraduate computer scientists taking courses in probability theory. - Other science-based undergraduates wanting a well-written but rigorous introduction to the subject.
Part A
BASIC PROBABILITY
1: Events and probabilities
2: Discrete random variables
3: Multivariate discrete distributions and independence
4: Probability generating functions
5: Distribution functions and density functions
PART B
FURTHER PROBABILITY
6: Multivariate distributions and independence
7: Moments, and moment generating functions
8: The main limit theorems
9: Branching processes
10: Random walks
11: Random processes in continuous time
12: Markov chains
978-0-19-965703-2 Hardback
978-0-19-965704-9 | Paperback | November 2014 (estimated)
November 2014 (estimated)
Introduces students to some of the most exciting contemporary topics of physics
Mathematical descriptions are kept at a middle-undergraduate level for easy comprehension
Contains many worked examples and computer simulations
Includes current high-interest topics (network theory, econophysics, and evolutionary dynamics)
Replaces traditional junior-level dynamics texts
The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile populations, or the synchronization of global economies are governed by universal principles just as profound as Newton's laws. Nonetheless, the conventional university physics curriculum reserves most of these topics for advanced graduate study. Two justifications are given for this situation: first, that the mathematical tools needed to understand these topics are beyond the skill set of undergraduate students, and second, that these are speciality topics with no common theme and little overlap.
Introduction to Modern Dynamics dispels these myths. The structure of this book combines the three main topics of modern dynamics - chaos theory, dynamics on complex networks, and general relativity - into a coherent framework. By taking a geometric view of physics, concentrating on the time evolution of physical systems as trajectories through abstract spaces, these topics share a common and simple mathematical language through which any student can gain a unified physical intuition. Given the growing importance of complex dynamical systems in many areas of science and technology, this text provides students with an up-to-date foundation for their future careers.
Readership: Undergraduate and graduate students in physics and engineering.
Part I: Geometric Mechanics
1: Physics and Geometry
2: Hamiltonian Dynamics and Phase Space
Part II: Nonlinear Dynamics
3: Nonlinear Dynamics and Chaos
4: Coupled Oscillators and Synchronization
5: Network Dynamics
Part III: Complex Systems
6: Neurodynamics and Neural Networks
7: Evolutionary Dynamics
8: Economic Dynamics
Part IV: Relativity and Space-Time
9: Metric Spaces and Geodesic Motion
10: Relativistic Dynamics
11: The General Theory of Relativity and Gravitation
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International Series of Monographs on Physics 131
224 pages | Numerous line drawings | 234x153mm
978-0-19-872633-3 | Paperback | December 2014 (estimated)
Only existing book on exciting new developments
Pedagogical style, based on lectures
Attractive to both mathematicians and physicists
Covers well-established and important subjects
In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge theory in three dimensions which describes knot and three-manifold invariants, to topological string theory, which is deeply related to Gromov-Witten invariants. This has led to some surprising relations between three-manifold geometry and enumerative geometry. This book gives the first coherent presentation of this and other related topics. After an introduction to matrix models and Chern-Simons theory, the book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implications of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory. It is written in a pedagogical style and will be useful reading for graduate students and researchers in both mathematics and physics willing to learn about these developments.
Readership: Primary market: graduate students and academic professionals in string theory, mathematical physics, algebraic geometry, and three-manifold topology. Secondary market: the theoretical physics and pure mathematics community at large.
Part I: Matrix Models, Chern-Simons Theory, and the Large N Expansion
1: Matrix models
2: Chern-Simons theory and knot invariants
Part II: Topological Strings
3: Topological sigma models
4: Topological strings
5: Calabi-Yau geometries
Part III: The Topological String / Gauge Theory Correspondence
6: String theory and gauge theory
7: String field theory and gauge theories
8: Geometric transitions
9: The topological vertex
10: Applications of the topological string / gauge theory correspondence
A: Symmetric polynomials
Series: Mathematical Physics Studies
2015, XVI, 232 p. 28 illus., 2 illus. in color.
Hardcover
ISBN 978-94-017-9161-8
Due: August 2014
Introduces noncommutative geometry in a novel pedagogical way, starting from finite noncommutative spaces
Contains a detailed treatment of the applications of noncommutative geometry to gauge theories appearing in high-energy physics
Model of particle physics is derived and its phenomenology discussed
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.
Preface.- Introduction.- Part 1. Noncommutative geometric spaces.- Finite noncommutative spaces.- Finite real noncommutative spaces.- Noncommutative Riemannian spin manifolds.- The local index formula in noncommutative geometry.- Part 2. Noncommutative geometry and gauge theories.- Gauge theories from noncommutative manifolds.- Spectral invariants.- Almost-commutative manifolds and gauge theories.- The noncommutative geometry of electrodynamics.- The noncommutative geometry of Yang-Mills fields.- The noncommutative geometry of the Standard Model.- Phenomenology of the noncommutative Standard Model.- Bibliography.