A Theory Revolutionizing Technology and Science by Avi Wigderson
A Theory Revolutionizing Technology and Science - Table of Contents
PART I: COMPLEXITY, RANDOMNESS & PROOFS
- 1. Introduction to Computational Theory
- 2. P, NP, and Computational Complexity
- 3. The Magic of Randomness in Computation
- 4. Structure, Statistics, and Error Correction
- 5. P vs. NP Problem: A Deep Look
- 6. Proof Complexity and Lower Bounds
- 7. Interactive Proofs and Zero-Knowledge
- 8. Theoretical Foundations of Cryptography
PART II: ADVANCED COMPLEXITY & THE SCIENTIFIC LENS
- 9. Randomness and Pseudorandomness
- 10. Arithmetic Complexity and Polynomials
- 11. Communication Complexity Models
- 12. On the Philosophical Nature of P vs. NP
- 13. Mathematics and Computation Interconnections
- 14. The Computational Lens on the Sciences
- 15. Complexity Theory: A Philosophical Perspective
- 16. Final Thoughts and Future Directions
What You Will Learn in A Theory Revolutionizing Technology and Science
Mathematics and Computation: A Theory Revolutionizing Technology and Science by Avi Wigderson (Abel Prize and Turing Award laureate) is a landmark volume that provides a unified, sweeping overview of computational complexity theory and its profound connections to pure mathematics, natural science, and philosophy. This comprehensive monograph guides readers through P versus NP, randomized algorithms, error-correcting codes, proof complexity, interactive proof systems, modern cryptography, arithmetic complexity, and communication complexity with exceptional clarity and visionary depth.
Designed for graduate students, mathematicians, computer science theorists, physicists, and quantitative researchers, this foundational text illustrates how viewing scientific phenomena through the "computational lens" transforms our understanding of physical processes, biological systems, and statistical physics. Wigderson details the conceptual foundations of pseudorandom generators, zero-knowledge proofs, and hardness-versus-randomness tradeoffs without getting bogged down in overly technical notation. Whether you are investigating circuit complexity, structural proof theory, or quantum computation, this book offers an indispensable roadmap.
Recognized globally as one of the most significant open-access surveys of computational theory, it stands as one of the best theoretical computer science books for self-study. By balancing mathematical rigor with broad conceptual themes, it serves as an essential tool for mastering computational complexity theory with confidence.
Book Details & Specifications
Title:
A Theory Revolutionizing Technology and Science by Avi Wigderson
Publisher:
Princeton University Press
Year:
2019
Pages:
440
Type:
PDF
Language:
English
ISBN-10 #:
0691189137
ISBN-13 #:
978-0691189130
License:
Free for Personal Use (as stated on the IAS website)
Amazon:
Amazon
About the Author: Avi Wigderson
The author Avi Wigderson
is a renowned "mathematician" and "computer scientist", famous for his work in "computational complexity", "algorithms", and "cryptography". As a professor at the Institute for Advanced Study, Princeton, he investigates the limits of computation and their impact on modern technology and science. Wigderson’s research connects "mathematics" and computer science, showing how theoretical insights influence practical applications. His contributions in efficient algorithms, cryptography, and optimization have shaped modern computation. Through teaching, writing, and lectures, he inspires learners to explore the power of "computation" and its revolutionary role in advancing both scientific understanding and technological innovation.
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