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Mathematics and Computation: A Theory Revolutionizing Technology and Science
  • Author Image
    Avi Wigderson
  • Publisher Logo
    Princeton University Press

Mathematics and Computation: A Theory Revolutionizing Technology and Science

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Key Metrics

  • Avi Wigderson
  • Princeton University Press
  • Hardcover
  • 9780691189130
  • 10 X 7.2 X 1.2 inches
  • 2.05 pounds
  • Mathematics > General
  • English
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Book Description

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.

Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation.

  • Comprehensive coverage of computational complexity theory, and beyond
  • High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline
  • Historical accounts of the evolution and motivations of central concepts and models
  • A broad view of the theory of computation's influence on science, technology, and society
  • Extensive bibliography
Mathematics and Computation: A Theory Revolutionizing Technology and Science

Author Bio

I am a Professor at the School of Mathematics, Institute for Advanced Study, Princeton. I organize the school activities in CSDM (Computer Science and Discrete Mathematics).

Professor Wigderson was awarded Abel Prize by Norwegian Academy of Science and Letters in 2021 and  Knuth Prize, by Association for Computing Machinery in 2019. 

 

Research Interests

  • Randomness and Computation
  • Algorithms and Optimization
  • Complexity Theory
  • Circuit Complexity
  • Proof Complexity
  • Quantum Computation and Communication
  • Cryptography and Distributed Computation

 

Education 

1983 — Ph.D in Computer Science, Princeton University, Department of Electrical Engineering and Computer Science. Thesis: Studies in Combinatorial Complexity Advisor: Prof. R.J. Lipton 

1982 — M.A in Computer Science, Princeton University. 

1981 — M.S.E in Computer Science, Princeton University. 

1980 — B.Sc Summa cum laude in Computer Science, Technion - Israel Institute of Technology. 

 

Source:  Institute for Advanced Study 

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