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Books in Theory and mathematics

Our portfolio includes foundational theories, algorithms, formal methods, and computational complexity. Featuring rigorous research, mathematical frameworks, and practical applications, these titles support theorists, mathematicians, and computer scientists in advancing the theoretical underpinnings of computing. Addressing emerging areas like quantum algorithms and formal verification, the collection fuels innovation and scientific discovery.

BooksJournals

    • Logical Foundations of Artificial Intelligence

      • 1st Edition
      • July 5, 2012
      • Michael R. Genesereth + 1 more
      • English
      • Paperback
        9 7 8 1 4 9 3 3 0 5 9 8 8
      • eBook
        9 7 8 0 1 2 8 0 1 5 5 4 4
      Intended both as a text for advanced undergraduates and graduate students, and as a key reference work for AI researchers and developers, Logical Foundations of Artificial Intelligence is a lucid, rigorous, and comprehensive account of the fundamentals of artificial intelligence from the standpoint of logic.The first section of the book introduces the logicist approach to AI--discussing the representation of declarative knowledge and featuring an introduction to the process of conceptualization, the syntax and semantics of predicate calculus, and the basics of other declarative representations such as frames and semantic nets. This section also provides a simple but powerful inference procedure, resolution, and shows how it can be used in a reasoning system.The next several chapters discuss nonmonotonic reasoning, induction, and reasoning under uncertainty, broadening the logical approach to deal with the inadequacies of strict logical deduction. The third section introduces modal operators that facilitate representing and reasoning about knowledge. This section also develops the process of writing predicate calculus sentences to the metalevel--to permit sentences about sentences and about reasoning processes. The final three chapters discuss the representation of knowledge about states and actions, planning, and intelligent system architecture.End-of-... bibliographic and historical comments provide background and point to other works of interest and research. Each chapter also contains numerous student exercises (with solutions provided in an appendix) to reinforce concepts and challenge the learner. A bibliography and index complete this comprehensive work.

    • Quantum Information Processing and Quantum Error Correction

      • 1st Edition
      • April 16, 2012
      • Ivan B. Djordjevic
      • English
      • Hardback
        9 7 8 0 1 2 3 8 5 4 9 1 9
      • eBook
        9 7 8 0 1 2 3 8 5 4 9 2 6
      Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice. This book is ideal for the electronics, photonics and computer engineer who requires an easy- to-understand foundation on the principles of quantum information processing and quantum error correction, together with insight into how to develop quantum electronic and photonic circuits. Readers of this book will be ready for further study in this area, and will be prepared to perform independent research. The reader completed the book will be able design the information processing circuits, stabilizer codes, Calderbank-Shor-Stea... (CSS) codes, subsystem codes, topological codes and entanglement-assiste... quantum error correction codes; and propose corresponding physical implementation. The reader completed the book will be proficient in quantum fault-tolerant design as well. Unique Features Unique in covering both quantum information processing and quantum error correction – everything in one book that an engineer needs to understand and implement quantum-level circuits. Gives an intuitive understanding by not assuming knowledge of quantum mechanics, thereby avoiding heavy mathematics. In-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits. Provides the right balance among the quantum mechanics, quantum error correction, quantum computing and quantum communication. Dr. Djordjevic is an Assistant Professor in the Department of Electrical and Computer Engineering of College of Engineering, University of Arizona, with a joint appointment in the College of Optical Sciences. Prior to this appointment in August 2006, he was with University of Arizona, Tucson, USA (as a Research Assistant Professor); University of the West of England, Bristol, UK; University of Bristol, Bristol, UK; Tyco Telecommunications, Eatontown, USA; and National Technical University of Athens, Athens, Greece. His current research interests include optical networks, error control coding, constrained coding, coded modulation, turbo equalization, OFDM applications, and quantum error correction. He presently directs the Optical Communications Systems Laboratory (OCSL) within the ECE Department at the University of Arizona.

    • Dynamic Programming

      • 1st Edition
      • Volume 37
      • October 14, 2011
      • A. Kaufmann + 1 more
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 5 4 4 5
      This work discusses the value of dynamic programming as a method of optimization for the sequential phenomena encountered in economic studies or in advanced technological programs such as those associated with space flights. The dynamic programs which are considered are defined for a deterministic universe, or one with probabilities; both categories are of equal importance in the practice of operations research or of scientific management.

    • Probabilities and Potential, B

      • 1st Edition
      • Volume 72
      • August 18, 2011
      • C. Dellacherie + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 6 3 6
      • eBook
        9 7 8 0 0 8 0 8 7 1 8 3 7

    • Probabilities and Potential, C

      • 1st Edition
      • Volume 151
      • August 18, 2011
      • C. Dellacherie + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 0 7 0
      • eBook
        9 7 8 0 0 8 0 8 7 2 6 2 9
      This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents.The fourth and last part of the English edition will be devoted to the theory of Markov processes.

    • Theories of Computational Complexity

      • 1st Edition
      • Volume 35
      • August 18, 2011
      • C. Calude
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 0 4 9
      • Hardback
        9 7 8 0 4 4 4 7 0 3 5 6 9
      • eBook
        9 7 8 0 0 8 0 8 6 7 7 5 5
      This volume presents four machine-independent theories of computational complexity, which have been chosen for their intrinsic importance and practical relevance. The book includes a wealth of results - classical, recent, and others which have not been published before.In developing the mathematics underlying the size, dynamic and structural complexity measures, various connections with mathematical logic, constructive topology, probability and programming theories are established. The facts are presented in detail. Extensive examples are provided, to help clarify notions and constructions. The lists of exercises and problems include routine exercises, interesting results, as well as some open problems.

    • Combinatory Logic

      • 1st Edition
      • Volume 65
      • June 17, 2009
      • Lev D. Beklemishev
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 4 7 7 6

Related subjects

Analysis of algorithms and problem complexity

Computation by abstract devices

Logics and meanings of programs

Mathematical logic and formal languages

Natural computation

Quantum computing

Theory and mathematics general