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Search the UJLink: Library Catalogue for Mathematics and Statistics books on Level 4 @ the APK Library.
Problems and Solutions in Quantum Computing and Quantum Information by
Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest.This book presents a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. Each chapter gives a comprehensive introduction to the topics. All the important concepts and areas such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, teleportation, Bell states, Bell measurement, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, quantum games, number states and Bose operators, coherent states, squeezed states, Gaussian states, coherent Bell states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton operator are included. A chapter on quantum channels has also been added. Furthermore a chapter on boolean functions and quantum gates with mapping bits to qubits is included.The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Each chapter also contains supplementary problems to challenge the reader. Programming problems with Maxima and SymbolicC++ implementations are also provided.
Dualities for Structures of Applied Logics by
This book provides a framework for presenting algebras and frames arising as semantic structures for formal languages and for proving relationships between the structures. For this purpose a discrete framework, referred to as discrete duality, is used rather than a topological framework. Ideas from the classical dualities and representations of Stone, Priestley, and Urquhart are applied in such a way that topology is not part of any of the underlying structures or relationships. A key contribution of the book is the formulation of the concept of duality via truth for expressing that a class of algebras and a class of frames determine equivalent notions of truth for a given formal language. Discrete duality and duality via truth are applied to a wealth of case studies presented in three main parts, namely, classes of Boolean lattices, distributive lattices, and general, that is not necessarily distributive, lattices, respectively. The book is self-contained and all the results are proved in sufficient detail enabling an easy verification.
Are numbers real? by 
Contemporary Abstract Algebra by
CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian's text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.
The Riemann Hypothesis: the greatest unsolved problem in mathematics by
Since 1859, when the shy German mathematician Bernhard Riemann wrote an eight-page article giving a possible answer to a problem that had tormented mathematical minds for centuries, the world's greatest mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann hypothesis. They speak of it in awed terms and consider it to be an even more difficult problem than Fermat's last theorem, which was finally proven by Andrew Wiles in 1995. InThe Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world's finest mathematicians who have spent their lives working on the problem--and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities. Wryly humorous, lively, accessible and comprehensive,The Riemann Hypothesis is a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession--and a profound meditation on the ultimate meaning of mathematics.
Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity, and Applications (Print = Online, ProQuest) by
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.
The Theory of Open Quantum Systems by
This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantummechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to thestudy of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states.The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the lasercooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examplesfrom a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented.The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help ofnumerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.
Handbook of Graph Theory by
In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Editionprovides comprehensive coverage of the main topics in pure and applied graph theory. This second edition--over 400 pages longer than its predecessor--incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.
A first course in functional analysis by 
Applied Mathematics for Physical Chemistry by
A how to do it review and learn book on advanced mathematics necessary to physical chemistry. Coordinate systems, functions and graphs, logarithms, differential calculus, integral calculus, infinite series, differential equations, scalars and vectors, matrices and determinants, operators, numerical methods and the use of the computer, and mathematical methods in the laboratory. Educators, Technicians, and other professionals using mathematics in physical chemistry.