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Author: Xi Chen
Publisher: Now Publishers Inc
Published: 2011
Total Pages: 157
ISBN-13: 1601984804
DOWNLOAD EBOOK →Partial Derivatives in Arithmetic Complexity and Beyond is devoted mainly to the study of polynomials from a computational perspective. The main point of this book is that one can learn a great deal about the structure and complexity of polynomials by studying (some of) their partial derivatives.
Author: Manindra Agrawal
Publisher: Springer
Published: 2014-07-16
Total Pages: 202
ISBN-13: 3319054465
DOWNLOAD EBOOK →This book brings together contributions by leading researchers in computational complexity theory written in honor of Somenath Biswas on the occasion of his sixtieth birthday. They discuss current trends and exciting developments in this flourishing area of research and offer fresh perspectives on various aspects of complexity theory. The topics covered include arithmetic circuit complexity, lower bounds and polynomial identity testing, the isomorphism conjecture, space-bounded computation, graph isomorphism, resolution and proof complexity, entropy and randomness. Several chapters have a tutorial flavor. The aim is to make recent research in these topics accessible to graduate students and senior undergraduates in computer science and mathematics. It can also be useful as a resource for teaching advanced level courses in computational complexity.
Author: J. M. Landsberg
Publisher: Cambridge University Press
Published: 2017-09-28
Total Pages: 353
ISBN-13: 110819141X
DOWNLOAD EBOOK →Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.
Author: Xujin Chen
Publisher: Springer Nature
Published:
Total Pages: 380
ISBN-13: 981972340X
DOWNLOAD EBOOK →Author: Ida Kantor
Publisher: American Mathematical Soc.
Published: 2015-08-27
Total Pages: 343
ISBN-13: 1470422611
DOWNLOAD EBOOK →Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.
Author: Avi Wigderson
Publisher: Princeton University Press
Published: 2019-10-29
Total Pages: 440
ISBN-13: 0691192545
DOWNLOAD EBOOK →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
Author: Yehuda Lindell
Publisher: Springer
Published: 2014-02-03
Total Pages: 752
ISBN-13: 3642542425
DOWNLOAD EBOOK →This book constitutes the refereed proceedings of the 11th Theory of Cryptography Conference, TCC 2014, held in San Diego, CA, USA, in February 2014. The 30 revised full papers presented were carefully reviewed and selected from 90 submissions. The papers are organized in topical sections on obfuscation, applications of obfuscation, zero knowledge, black-box separations, secure computation, coding and cryptographic applications, leakage, encryption, hardware-aided secure protocols, and encryption and signatures.
Author: Anne Canteaut
Publisher: Springer Nature
Published: 2021-06-16
Total Pages: 937
ISBN-13: 303077886X
DOWNLOAD EBOOK →The 3-volume-set LNCS 12696 – 12698 constitutes the refereed proceedings of the 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2021, which was held in Zagreb, Croatia, during October 17-21, 2021. The 78 full papers included in these proceedings were accepted from a total of 400 submissions. They were organized in topical sections as follows: Part I: Best papers; public-key cryptography; isogenies; post-quantum cryptography; lattices; homomorphic encryption; symmetric cryptanalysis; Part II: Symmetric designs; real-world cryptanalysis; implementation issues; masking and secret-sharing; leakage, faults and tampering; quantum constructions and proofs; multiparty computation; Part III: Garbled circuits; indistinguishability obfuscation; non-malleable commitments; zero-knowledge proofs; property-preserving hash functions and ORAM; blockchain; privacy and law enforcement.
Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
Published: 2014-02-26
Total Pages: 596
ISBN-13: 9814583952
DOWNLOAD EBOOK →An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author: Avi Wigderson
Publisher: Princeton University Press
Published: 2019-10-29
Total Pages: 434
ISBN-13: 0691189137
DOWNLOAD EBOOK →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
