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A detailed introduction to the development of complexity and its connections and interactions with math and applications to science, the social sciences, and engineering.

Wigderson, Avi

Mathematics and Computation

A Theory Revolutionizing Technology and Science


    81,95 € / $93.75 / £73.00*

    eBook (PDF)
    Publication Date:
    Copyright year:
    To be published:
    October 2019
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    Aims and Scope

    An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy

    Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors.

    Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered.

    Useful for undergraduates in mathematics and computer science as well as researchers and teachers in the field, Mathematics and Computation brings conceptual clarity to a central and dynamic scientific discipline.

    · Comprehensive coverage of computational complexity theory

    · High-level, intuitive exposition

    · Historical accounts of the evolution and motivations of central concepts and models

    · A resourceful look at the theory’s influence on science, technology, and society

    · Extensive bibliography


    440 pages
    25 b/w illus.
    General/trade;Professional and scholarly;College/higher education;

    More ...

    Avi Wigderson is the Herbert H. Maass Professor in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.


    “This is a remarkable book. It surveys the entire current scope of theoretical computer science, in a way only Avi Wigderson, our field’s consummate generalist, could do. It also sets out Wigderson’s vision for the future and his sociological thoughts about theoretical computer science and its interactions with neighboring fields. I recommend it to anyone looking for a panoramic view of the subject.”—Scott Aaronson, University of Texas, Austin

    “This book is a real gem. Avi Wigderson has woven together very big and deep ideas from the field, such as pseudorandomness and hardness of computation, in a way that is accessible to a general scientific audience.”—Toniann Pitassi, University of Toronto

    "A beautiful, broad view of theoretical computer science, by a giant in the field. A must-read."—Ryan O'Donnell, Carnegie Mellon University

    “This wonderful exposition of modern complexity theory distills complex arguments down to their main insights, and deftly explains the interconnections between entire subfields. This book will have a major impact on the way we teach complexity theory, and the way that graduate students in the field learn it.”—Ankur Moitra, Massachusetts Institute of Technology

    Mathematics and Computation presents a panoramic view of the theory of computation, starting from its origins in the 1930s to modern directions and developments, with an emphasis on the latter. With impressive breadth and depth, this book covers an amazing amount of ground.”—Mark Braverman, Princeton University

    “A delightful, lucid, and personal guide that perfectly captures the spirit of the field, and does full justice to both its depth and breadth.”—Leslie Valiant, Harvard University

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