A Primer On Pseudorandom Generators
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| Author | : Oded Goldreich |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 130 |
| Release | : 2010 |
| Genre | : Computers |
| ISBN | : 0821851926 |
The primer assumes basic familiarity with the notion of efficient algorithms and with elementary probability theory, but provides a basic introduction to all notions that are actually used. as a result, the primer is essentially self-contained, although the interested reader is at times referred to other sources for more detail. --Book Jacket.
| Author | : |
| Publisher | : World Scientific |
| Total Pages | : 1131 |
| Release | : |
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| Author | : Ilya M. Sobol |
| Publisher | : CRC Press |
| Total Pages | : 126 |
| Release | : 2018-04-24 |
| Genre | : Mathematics |
| ISBN | : 1351469584 |
The Monte Carlo method is a numerical method of solving mathematical problems through random sampling. As a universal numerical technique, the method became possible only with the advent of computers, and its application continues to expand with each new computer generation. A Primer for the Monte Carlo Method demonstrates how practical problems in science, industry, and trade can be solved using this method. The book features the main schemes of the Monte Carlo method and presents various examples of its application, including queueing, quality and reliability estimations, neutron transport, astrophysics, and numerical analysis. The only prerequisite to using the book is an understanding of elementary calculus.
| Author | : B. Jack Copeland |
| Publisher | : MIT Press |
| Total Pages | : 373 |
| Release | : 2015-01-30 |
| Genre | : Computers |
| ISBN | : 0262527480 |
Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani
| Author | : Vijay Nagarajan |
| Publisher | : Springer Nature |
| Total Pages | : 276 |
| Release | : 2022-05-31 |
| Genre | : Technology & Engineering |
| ISBN | : 3031017641 |
Many modern computer systems, including homogeneous and heterogeneous architectures, support shared memory in hardware. In a shared memory system, each of the processor cores may read and write to a single shared address space. For a shared memory machine, the memory consistency model defines the architecturally visible behavior of its memory system. Consistency definitions provide rules about loads and stores (or memory reads and writes) and how they act upon memory. As part of supporting a memory consistency model, many machines also provide cache coherence protocols that ensure that multiple cached copies of data are kept up-to-date. The goal of this primer is to provide readers with a basic understanding of consistency and coherence. This understanding includes both the issues that must be solved as well as a variety of solutions. We present both high-level concepts as well as specific, concrete examples from real-world systems. This second edition reflects a decade of advancements since the first edition and includes, among other more modest changes, two new chapters: one on consistency and coherence for non-CPU accelerators (with a focus on GPUs) and one that points to formal work and tools on consistency and coherence.
| Author | : Ludger Hovestadt |
| Publisher | : Birkhäuser |
| Total Pages | : 224 |
| Release | : 2014-09-23 |
| Genre | : Design |
| ISBN | : 3990435787 |
domesticating symbols looks at the entropic dissolution of symbolic structures we are experiencing today and explores various approaches towards learning to create code. Photovoltaics and its capacity to capture energy by coding instead of exploitation of resources, and of integrating in additional or surplus quantities of energy into the ecosphere of the planet‘s natural balance is the central focus of this publication. Energythereby also encompasses the genuinely abstract format of electricity, which makes it possible to convert any form of energy into any other form. This is the second volume of the Applied Virtuality book series based on the Metalithicum Conferences by the Laboratory of Applied Virtuality at the Chair for Computer Aided Architectural Design, Swiss Federal Institute of Technology (ETH) Zurich.
| Author | : Armand Borel |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 133 |
| Release | : 2019-11-07 |
| Genre | : Education |
| ISBN | : 1470452316 |
Fifty years after it made the transition from mimeographed lecture notes to a published book, Armand Borel's Introduction aux groupes arithmétiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory, which is crucial in the study of discrete subgroups of Lie groups and the corresponding homogeneous spaces. The review of the original French version in Mathematical Reviews observes that “the style is concise and the proofs (in later sections) are often demanding of the reader.” To make the translation more approachable, numerous footnotes provide helpful comments.
| Author | : Jeffrey C. Lagarias |
| Publisher | : American Mathematical Society |
| Total Pages | : 360 |
| Release | : 2023-04-19 |
| Genre | : Mathematics |
| ISBN | : 1470472899 |
The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.
| Author | : Shiho Moriai |
| Publisher | : Springer Nature |
| Total Pages | : 818 |
| Release | : 2020-12-04 |
| Genre | : Computers |
| ISBN | : 3030648346 |
The three-volume proceedings LNCS 12491, 12492, and 12493 constitutes the proceedings of the 26th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2020, which was held during December 7-11, 2020. The conference was planned to take place in Daejeon, South Korea, but changed to an online format due to the COVID-19 pandemic. The total of 85 full papers presented in these proceedings was carefully reviewed and selected from 316 submissions. The papers were organized in topical sections as follows: Part I: Best paper awards; encryption schemes.- post-quantum cryptography; cryptanalysis; symmetric key cryptography; message authentication codes; side-channel analysis. Part II: public key cryptography; lattice-based cryptography; isogeny-based cryptography; quantum algorithms; authenticated key exchange. Part III: multi-party computation; secret sharing; attribute-based encryption; updatable encryption; zero knowledge; blockchains and contact tracing.
| Author | : Imre Bárány |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 148 |
| Release | : 2021-11-04 |
| Genre | : Education |
| ISBN | : 1470467097 |
This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
