Mathematics and Computation : A Theory Revolutionizing Technology and Science

By: Wigderson, AviLanguage: English Publication details: Princeton Princeton University Press 2019Description: xiii, 418pISBN: 9780691189130 (HB)Subject(s): Computational Complexity | Computer science -- Mathematics | Boolean Algebra | Cryptography | General
Contents:
1. Introduction 2. Prelude: computation, undecidability, and limits to mathematical knowledge 3. Computational complexity 101: the basics, P, and NP 4. Problems and classes inside (and around) NP 5. Lower bounds, Boolean circuits, and attacks on P vs NP 6. Proof complexity 7. Randomness in computation 8. Abstract pseudo-randomness 9. Weak random sources and randomness extractors 10. Randomness and interaction in proofs 11. Quantum computing 12. Arithmetic complexity 13. Interlude: concrete interactions between math and computational complexity 14. Space complexity: modeling limited memory 15. Communication complexity: modeling information bottlenecks 16. On-line algorithms: coping with an unknown future 17. Computational learning theory, AI, and beyond 18. Cryptography: modeling secrets and lies, knowledge and trust 19. Distributed computing: coping with asynchrony 20. Epilogue: a broader perspective of ToC.
Summary: 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.
Item type: BOOKS List(s) this item appears in: New Arrivals (01 June 2024) | New Arrivals (01 June, 2024)
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Includes References (349-418)

1. Introduction
2. Prelude: computation, undecidability, and limits to mathematical knowledge
3. Computational complexity 101: the basics, P, and NP
4. Problems and classes inside (and around) NP
5. Lower bounds, Boolean circuits, and attacks on P vs NP
6. Proof complexity
7. Randomness in computation
8. Abstract pseudo-randomness
9. Weak random sources and randomness extractors
10. Randomness and interaction in proofs
11. Quantum computing
12. Arithmetic complexity
13. Interlude: concrete interactions between math and computational complexity
14. Space complexity: modeling limited memory
15. Communication complexity: modeling information bottlenecks
16. On-line algorithms: coping with an unknown future
17. Computational learning theory, AI, and beyond
18. Cryptography: modeling secrets and lies, knowledge and trust
19. Distributed computing: coping with asynchrony
20. Epilogue: a broader perspective of ToC.

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.

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