Mathematical theory of computation Books

Book Synopsis"My absolute favorite for this kind of interview preparation is Steven Skiena’s The Algorithm Design Manual. More than any other book it helped me understand just how astonishingly commonplace … graph problems are -- they should be part of every working programmer’s toolkit. The book also covers basic data structures and sorting algorithms, which is a nice bonus. … every 1 – pager has a simple picture, making it easy to remember. This is a great way to learn how to identify hundreds of problem types." (Steve Yegge, Get that Job at Google)"Steven Skiena’s Algorithm Design Manual retains its title as the best and most comprehensive practical algorithm guide to help identify and solve problems. … Every programmer should read this book, and anyone working in the field should keep it close to hand. … This is the best investment … a programmer or aspiring programmer can make." (Harold Thimbleby, Times Higher Education)"It is wonderful to open to a random spot and discover an interesting algorithm. This is the only textbook I felt compelled to bring with me out of my student days.... The color really adds a lot of energy to the new edition of the book!" (Cory Bart, University of Delaware)"The is the most approachable book on algorithms I have." (Megan Squire, Elon University)---This newly expanded and updated third edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficiency. It serves as the primary textbook of choice for algorithm design courses and interview self-study, while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Practical Algorithm Design, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, the Hitchhiker's Guide to Algorithms, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations, and an extensive bibliography. NEW to the third edition: -- New and expanded coverage of randomized algorithms, hashing, divide and conquer, approximation algorithms, and quantum computing -- Provides full online support for lecturers, including an improved website component with lecture slides and videos -- Full color illustrations and code instantly clarify difficult concepts -- Includes several new "war stories" relating experiences from real-world applications -- Over 100 new problems, including programming-challenge problems from LeetCode and Hackerrank. -- Provides up-to-date links leading to the best implementations available in C, C++, and Java Additional Learning Tools: -- Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them -- Exercises include "job interview problems" from major software companies -- Highlighted "take home lessons" emphasize essential concepts -- The "no theorem-proof" style provides a uniquely accessible and intuitive approach to a challenging subject -- Many algorithms are presented with actual code (written in C) -- Provides comprehensive references to both survey articles and the primary literature Written by a well-known algorithms researcher who received the IEEE Computer Science and Engineering Teaching Award, this substantially enhanced third edition of The Algorithm Design Manual is an essential learning tool for students and professionals needed a solid grounding in algorithms. Professor Skiena is also the author of the popular Springer texts, The Data Science Design Manual and Programming Challenges: The Programming Contest Training Manual.Table of ContentsIntroduction to Algorithm DesignAlgorithm AnalysisData StructuresSorting and SearchingDivide and ConquerRandomized Algorithms and HashingGraph TraversalWeighted Graph AlgorithmsCombinatorial Search and Heuristic MethodsDynamic ProgrammingNP-CompletenessDealing with Hard Problems How to Design Algorithms14 A Catalog of Algorithmic Problems 43715 Data Structures 43915.1 Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44015.2 Priority Queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44515.3 Sux Trees and Arrays . . . . . . . . . . . . . . . . . . . . . . . 44815.4 Graph Data Structures . . . . . . . . . . . . . . . . . . . . . . . . 45215.5 Set Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . 45615.6 Kd-Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46016 Numerical Problems 46516.1 Solving Linear Equations . . . . . . . . . . . . . . . . . . . . . . 46716.2 Bandwidth Reduction . . . . . . . . . . . . . . . . . . . . . . . . 47016.3 Matrix Multiplication . . . . . . . . . . . . . . . . . . . . . . . . 47216.4 Determinants and Permanents . . . . . . . . . . . . . . . . . . . 47516.5 Constrained/Unconstrained Optimization . . . . . . . . . . . . . 47816.6 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . 48216.7 Random Number Generation . . . . . . . . . . . . . . . . . . . . 48616.8 Factoring and Primality Testing . . . . . . . . . . . . . . . . . . . 49016.9 Arbitrary-Precision Arithmetic . . . . . . . . . . . . . . . . . . . 49316.10Knapsack Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 49716.11Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . 50117 Combinatorial Problems 50517.1 Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50617.2 Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51017.3 Median and Selection . . . . . . . . . . . . . . . . . . . . . . . . . 51417.4 Generating Permutations . . . . . . . . . . . . . . . . . . . . . . 51717.5 Generating Subsets . . . . . . . . . . . . . . . . . . . . . . . . . . 52117.6 Generating Partitions . . . . . . . . . . . . . . . . . . . . . . . . 52417.7 Generating Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 52817.8 Calendrical Calculations . . . . . . . . . . . . . . . . . . . . . . . 53217.9 Job Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53417.10Satisability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53718 Graph Problems: Polynomial-Time 54118.1 Connected Components . . . . . . . . . . . . . . . . . . . . . . . 54218.2 Topological Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . 54618.3 Minimum Spanning Tree . . . . . . . . . . . . . . . . . . . . . . . 54918.4 Shortest Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55418.5 Transitive Closure and Reduction . . . . . . . . . . . . . . . . . . 55918.6 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56218.7 Eulerian Cycle/Chinese Postman . . . . . . . . . . . . . . . . . . 56518.8 Edge and Vertex Connectivity . . . . . . . . . . . . . . . . . . . . 56816 CONTENTS18.9 Network Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57118.10Drawing Graphs Nicely . . . . . . . . . . . . . . . . . . . . . . . 57418.11Drawing Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57818.12Planarity Detection and Embedding . . . . . . . . . . . . . . . . 58119 Graph Problems: NP-Hard 58519.1 Clique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58619.2 Independent Set . . . . . . . . . . . . . . . . . . . . . . . . . . . 58919.3 Vertex Cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59119.4 Traveling Salesman Problem . . . . . . . . . . . . . . . . . . . . . 59419.5 Hamiltonian Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 59819.6 Graph Partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60119.7 Vertex Coloring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60419.8 Edge Coloring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60819.9 Graph Isomorphism . . . . . . . . . . . . . . . . . . . . . . . . . 61019.10Steiner Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61419.11Feedback Edge/Vertex Set . . . . . . . . . . . . . . . . . . . . . . 61820 Computational Geometry 62120.1 Robust Geometric Primitives . . . . . . . . . . . . . . . . . . . . 62220.2 Convex Hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62620.3 Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63020.4 Voronoi Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 63420.5 Nearest Neighbor Search . . . . . . . . . . . . . . . . . . . . . . . 63720.6 Range Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64120.7 Point Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64420.8 Intersection Detection . . . . . . . . . . . . . . . . . . . . . . . . 64820.9 Bin Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65220.10Medial-Axis Transform . . . . . . . . . . . . . . . . . . . . . . . . 65520.11Polygon Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . 65820.12Simplifying Polygons . . . . . . . . . . . . . . . . . . . . . . . . . 66120.13Shape Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . 66420.14Motion Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . 66720.15Maintaining Line Arrangements . . . . . . . . . . . . . . . . . . . 67120.16Minkowski Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67421 Set and String Problems 67721.1 Set Cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67821.2 Set Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68221.3 String Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 68521.4 Approximate String Matching . . . . . . . . . . . . . . . . . . . . 68821.5 Text Compression . . . . . . . . . . . . . . . . . . . . . . . . . . 69321.6 Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69721.7 Finite State Machine Minimization . . . . . . . . . . . . . . . . . 70221.8 Longest Common Substring/Subsequence . . . . . . . . . . . . . 70621.9 Shortest Common Superstring . . . . . . . . . . . . . . . . . . . . 709CONTENTS 1722 Algorithmic Resources 71322.1 Algorithm Libraries . . . . . . . . . . . . . . . . . . . . . . . . . 71322.1.1 LEDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71322.1.2 CGAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71422.1.3 Boost Graph Library . . . . . . . . . . . . . . . . . . . . . 71422.1.4 Netlib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71422.1.5 Collected Algorithms of the ACM . . . . . . . . . . . . . 71522.1.6 GitHub and SourceForge . . . . . . . . . . . . . . . . . . . 71522.1.7 The Stanford GraphBase . . . . . . . . . . . . . . . . . . 71522.1.8 Combinatorica . . . . . . . . . . . . . . . . . . . . . . . . 71622.1.9 Programs from Books . . . . . . . . . . . . . . . . . . . . 71622.2 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71722.3 Online Bibliographic Resources . . . . . . . . . . . . . . . . . . . 71822.4 Professional Consulting Services . . . . . . . . . . . . . . . . . . 71823 Bibliography 719Index 771

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Book SynopsisHaskell is a purely functional language that allows programmers to rapidly develop clear, concise, and correct software. The language has grown in popularity in recent years, both in teaching and in industry. This book is based on the author''s experience of teaching Haskell for more than twenty years. All concepts are explained from first principles and no programming experience is required, making this book accessible to a broad spectrum of readers. While Part I focuses on basic concepts, Part II introduces the reader to more advanced topics. This new edition has been extensively updated and expanded to include recent and more advanced features of Haskell, new examples and exercises, selected solutions, and freely downloadable lecture slides and example code. The presentation is clean and simple, while also being fully compliant with the latest version of the language, including recent changes concerning applicative, monadic, foldable, and traversable types.Trade Review'The skills you acquire by studying this book will make you a much better programmer no matter what language you use to actually program in.' Erik Meijer, Facebook, from the ForewordReview of previous edition: 'The best introduction to Haskell available. There are many paths towards becoming comfortable and competent with the language but I think studying this book is the quickest path. I urge readers of this magazine to recommend Programming in Haskell to anyone who has been thinking about learning the language.' Duncan Coutts, The Monad.ReaderReview of previous edition: 'Where this book excels is in the order and style of its exposition … With its ripe selection of examples and its careful clarity of exposition, the book is a welcome addition to the introductory functional programming literature.' Journal of Functional ProgrammingTable of ContentsForeword; Preface; Part I. Basic Concepts: 1. Introduction; 2. First steps; 3. Types and classes; 4. Defining functions; 5. List comprehensions; 6. Recursive functions; 7. Higher-order functions; 8. Declaring types and classes; 9. The countdown problem; Part II. Going Further: 10. Interactive programming; 11. Unbeatable tic-tac-toe; 12. Monads and more; 13. Monadic parsing; 14. Foldables and friends; 15. Lazy evaluation; 16. Reasoning about programs; 17. Calculating compilers; Appendix A. Selected solutions; Appendix B. Standard prelude; Bibliography; Index.

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Book SynopsisThis introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles. While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. The goal of this book is to present important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other. Trade Review“He has written a book about principal bundles in the classical sense which is of great interest in and of itself … . a textbook which can be used in an advanced one-year course or for self-learning. … the book is also interesting for a physicist, because one can find the geometric basis of many mathematical tools used in physics. … reviewer has greatly enjoyed reading the book and acknowledges the author’s bravery in writing another text on differential geometry!” (Fernando Etayo Gordejuela, Mathematical Reviews, November, 2015)“The present book deals with principle bundles and their relevance in physics with a ground work on differential geometry. … The book will be helpful to the graduate and under graduate students of mathematics and physics. It can also be an informative hand book of the researchers in differential geometry and physics.” (Uday Chand De, zbMATH 1321.53004, 2015)Table of ContentsIntroduction.- Basics of Manifolds.- Vector Bundles.- Vectors and Covectors.- Differential Forms.- Lie Derivatives.- Lie Groups.- Frobenius Theorem.- Principle Bundles.- Connections on Principle Bundles.- Curvature of a Connection.- Classical Electromagnetism.- Yang-Mills Theory.- Gauge Theory.- The Dirac Monopole.- Instantons.- What Next?.- Discussion of the Exercises.

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Book SynopsisDeep learning from the ground up using R and the powerful Keras library! In Deep Learning with R, Second Edition you will learn: Deep learning from first principles Image classification and image segmentation Time series forecasting Text classification and machine translation Text generation, neural style transfer, and image generation Deep Learning with R, Second Edition shows you how to put deep learning into action. It's based on the revised new edition of François Chollet's bestselling Deep Learning with Python. All code and examples have been expertly translated to the R language by Tomasz Kalinowski, who maintains the Keras and Tensorflow R packages at RStudio. Novices and experienced ML practitioners will love the expert insights, practical techniques, and important theory for building neural networks. about the technology Deep learning has become essential knowledge for data scientists, researchers, and software developers. The R language APIs for Keras and TensorFlow put deep learning within reach for all R users, even if they have no experience with advanced machine learning or neural networks. This book shows you how to get started on core DL tasks like computer vision, natural language processing, and more using R. what's inside Image classification and image segmentation Time series forecasting Text classification and machine translation Text generation, neural style transfer, and image generation about the reader For readers with intermediate R skills. No previous experience with Keras, TensorFlow, or deep learning is required.

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Book SynopsisAlgebraic coding theory is a new and rapidly developing subject, motivated by immediate practical applications, but also rich in mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes.

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Book SynopsisThis concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as quantum mechanics and computational complexity is not required.Trade ReviewThe book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts. * MathSciNet *Table of ContentsPreface ; 1. Introduction and background ; 2. Linear algebra and the Dirac notation ; 3. Qubits and the framework of quantum mechanics ; 4. A quantum model of computation ; 5. Superdense coding and quantum teleportation ; 6. Introductory quantum algorithms ; 7. Algorithms with super-polynomial speed-up ; 8. Algorithms based on amplitude amplification ; 9. Quantum computational complexity theory and lower bounds ; 10. Quantum error correction ; Appendices ; Bibliography ; Index

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Book SynopsisThis book is a concise introduction to the key mathematical ideas that underpin computer science, continually stressing the application of discrete mathematics to computing. It is suitable for students with little or no knowledge of mathematics, and covers the key concepts in a simple and straightforward way.Table of Contents1. Introduction 2. Logic and Proof 3. Set Theory 4. Relations 5. Functions 6. Combinatorics 7. Graphs 8. Directed Graphs 9. Boolean Algebra Application: Designing a 2-Bit Adder

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Book SynopsisThe challenges of problems from international programming competitions are an effective way to improve your algorithmic and coding skills and understanding. This volume uses international programming competition-type problems to motivate the study of algorithms, programming, and other topics in computer science.Trade Review"Skiena and Revilla's new book 'Programming Challenges: The Programming Contest Training Manual' is just the ticket for those interested in a jumpstart to the world of contest programming. With special emphasis on the international ACM collegiate contests, the book's best feature is each chapter's pithy introduction that demystifies a particular scheme or algorithmic approach. The ensemble of these explications coupled with the contest strategy guidelines in the appendix can enable a novice to enhance contest results dramatically in a short time simply by solving the suggested exercises in each chapter. Even contest veterans are likely to be able to find a nugget or two in the explanations and strategies. "Presented in a logical order (contest programming has over a dozen different primary attacks), the book guides readers not only through the techniques and algorithms required but also through a huge set of problems that can be used for training. Solutions can be submitted to Valladolid University's online trainer for quick feedback and reinforcement. "If you're the sort who likes to have a single volume that covers the vast majority of a field, you'll love Skiena and Revilla's new tome." --Rob Kolstad, Ph.D., Head Coach, USA Computing OlympiadTable of Contents* Getting started * Data structures * Strings * Sorting * Arithmetic and algebra * Combinatorics * Number theory * Backtracking * Graph traversal * Graph algorithms * Dynamic programming * Grids * Geometry * Computational geometry * Appendix * Index

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Book Synopsis1 Naive Set Theory.- 1.1 What is a Set?.- 1.2 Operations on Sets.- 1.3 Notation for Sets.- 1.4 Sets of Sets.- 1.5 Relations.- 1.6 Functions.- 1.7 Well-Or der ings and Ordinals.- 1.8 Problems.- 2 The ZermeloFraenkel Axioms.- 2.1 The Language of Set Theory.- 2.2 The Cumulative Hierarchy of Sets.- 2.3 The ZermeloFraenkel Axioms.- 2.4 Classes.- 2.5 Set Theory as an Axiomatic Theory.- 2.6 The Recursion Principle.- 2.7 The Axiom of Choice.- 2.8 Problems.- 3 Ordinal and Cardinal Numbers.- 3.1 Ordinal Numbers.- 3.2 Addition of Ordinals.- 3.3 Multiplication of Ordinals.- 3.4 Sequences of Ordinals.- 3.5 Ordinal Exponentiation.- 3.6 Cardinality, Cardinal Numbers.- 3.7 Arithmetic of Cardinal Numbers.- 3.8 Regular and Singular Cardinals.- 3.9 Cardinal Exponentiation.- 3.10 Inaccessible Cardinals.- 3.11 Problems.- 4 Topics in Pure Set Theory.- 4.1 The Borel Hierarchy.- 4.2 Closed Unbounded Sets.- 4.3 Stationary Sets and Regressive Functions.- 4.4 Trees.- 4.5 Extensions of Lebesgue Measure.- 4.6 A ReTable of ContentsPreface; 1. Naïve Set Theory; 2. The Zermelo-Fraenkel Axioms; 3. Ordinal and Cardinal Numbers; 4. Topics in Pure Set Theory; 5. The Axiom of Constructibility; 6. Independence Proofs in Set Theory; 7. Non-Well-Founded Set Theory; Bibliography; Glossary of Symbols; Index

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Book SynopsisA classic book about life in a two-dimensional universe, written by a well-known author. Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland.Table of Contents1 Arde.- 2 A House by the Sea.- 3 On Fiddib Har.- 4 Walking to Is Felblt.- 5 City Below Ground.- 6 The Trek.- 7 The Punizlan Institute.- 8 Traveling on the Wind.- 9 High on Dahl Radam.- 10 Drabk the Sharak of Okbra.- 11 Higher Dimensions.- Ardean Science and Technology.- Acknowledgments.

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Book SynopsisThe process of solving large problems by breaking them down into smaller, more simple problems that have identical forms. Thinking Recursively: A small text to solve large problems. Concentrating on the practical value of recursion. this text, the first of its kind, is essential to computer science students' education.Table of ContentsThe Idea of Recursion. Mathematical Preliminaries. Recursive Functions. The Procedural Approach. The Tower of Hanoi. Permutations. Sorting. Intelligent Algorithms. Graphical Applications. Recursive Data. Implementation of Recursion.

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Book SynopsisModern software places increasing reliance on dynamic memory allocation, but its direct management is not only notoriously error--prone. Garbage collection eliminates many of these bugs. This reference presents each of the most important algorithms in detail, often with illustrations of its characteristic features and animations of its use.Table of ContentsThe Classical Algorithms. Reference Counting. Mark-Sweep Garbage Collection. Mark-Compact Garbage Collection. Copying Garbage Collection. Generational Garbage Collection. Incremental and Concurrent Garbage Collection. Garbage Collection for C. Garbage Collection for C++. Cache-Conscious Garbage Collection. Distributed Garbage Collection. Glossary. Bibliography. Index.

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Book SynopsisThe aim of this work is to give breadth and depth to the C++ programmer's existing experience of the language. It presents a large number of algorithms, each of them implemented as ready-to-run (and standalone) programs.Table of ContentsSome Aspects of Programming in C++. Arithmetic. Sorting Arrays and Files. Stacks, Queues and Lists. Searching and String Processing. Binary Trees. B-trees. Tries, Priority Queues and File Compression. Graphs. Some Combinatorial Algorithms. Fundamentals of Interpreters and Compilers. Appendix. Bibliography. Index.

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Book SynopsisBuilding on the basic tools presented in the first volume, this second volume of Foundations of Cryptography contains a rigorous and systematic treatment of three basic applications: Encryption, Signatures, and General Cryptographic Protocols. It is suitable for use in a graduate course on cryptography and as a reference book for experts.Trade ReviewReview of the hardback: 'This is a very complete introduction to the basics of modern complexity-theoretic cryptography. It is a solid foundation for understanding much of the current work in this area.' ACM SIGACT NewsTable of ContentsList of figures; Preface; Acknowledgements; 5. Encryption schemes; 6. Digital signatures and message authentication; 7. General cryptographic protocols; Appendix C: corrections and additions to volume I; Bibliography; Index.

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Book SynopsisA comprehensive 2003 treatment of term rewriting systems from an elementary to an advanced level. Much of this material appeared here for the first time in book form. Ideal for teaching or research, it features numerous exercises with selected solutions on the web, an extensive bibliography and a chapter on applications.Trade Review'The book presents the state of the art of rewriting techniques, it gives (or scratches) proofs on a very precise level and gives hints to historical sources of the results and to further readings, so it is highly recommended to researchers working in this area.' Zentralblatt für Mathematik'… has extensive material … suffice it to say that this book is indispensable for a any serious student of rewriting.' Journal of TLP'… it will soon be a compulsory reference for anyone working in the area.' Journal of Functional ProgrammingTable of Contents1. Abstract reduction systems; 2. First-order term rewriting systems; 3. Examples of TRSs and special rewriting formats; 4. Orthogonality; 5. Properties of rewriting: decidability and modularity; 6. Termination; 7. Completion of equational specifications; 8. Equivalence of reductions; 9. Strategies; 10. Lambda calculus; 11. Higher order rewriting; 12. Infinitary rewriting; 13. Term graph rewriting; 14. Advanced ARS theory; 15. Rewriting based languages and systems; 16. Mathematical background.

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Book SynopsisThis book provides a unified understanding of the use of generating functions for labelled and unlabelled structures. Applications include graphical enumeration, Polya theory and analysis of data structures in computer science, special functions, functional equations, asymptotic analysis, and differential equations.Trade Review'This book can serve as an introduction to the subject; it will also be an extremely valuable reference book.' International Mathematical News' … the first complete presentation in English of the combinatorial theory of species.' L'Enseignment Mathématique' … a comprehensive account.' Zentralblatt für Mathematik und ihre GrenzgebieteTable of Contents1. Introduction to species of structures; 2. Complements on species of structures; 3. Combinatorial functional equations; 4. Complements on types of structures; 5. Species on totally ordered sets.

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Book SynopsisTyped lambda calculus is used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), which are used to design and verify IT products and mathematical proofs. This book reveals unexpected mathematical beauty in three classes of typing: simple types, recursive types and intersection types. Numerous exercises are provided.Trade Review'The book has a place in undergraduate libraries because of its uniquely comprehensive, if theoretical, treatment of a timely, widely important subject. Recommended.' D. V. Feldman, Choice'The authors have produced a well-written, organised and comprehensive account of three important type systems. These systems' properties have been rich sources of interest to logicians for many years; their problems are not all solved, and in future work this book will almost certainly become a standard reference about them. It will also allow the more mathematically inclined computer scientist to obtain a deeper understanding of the principles behind some of the higher order languages in current use.' Bulletin of the London Mathematical SocietyTable of ContentsList of contributors; Preface; Introduction; Part I. Simple Types: 1. The simply typed lambda calculus; 2. Properties; 3. Tools; 4. Definability, unification and matching; 5. Extensions; 6. Applications; Part II. Recursive Types: 7. The systems; 8. Properties of recursive types; 9. Properties of terms with types; 10. Models; 11. Applications; Part III. Intersection Types: 12. An exemplary system; 13. Type assignment systems; 14. Basic properties; 15. Type and lambda structures; 16. Filter models; 17. Advanced properties and applications; Bibliography; Symbol index; Names index; Definitions index.

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Book SynopsisThe is an introduction to simple type theory, exploring the relationship between proof and calculation. Each of its 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject. An appendix contains complete solutions to them.Trade Review'A well-written introduction to proof theory and its connections with computability.' Leon Harkleroad, Zentralblatt für Mathematik'… recommended for the student or researcher who's been exposed to bits and pieces of the Curry-Howard correspondence, but wants a sharper idea of the big picture and is willing to work through the exercises to see how the details fit together. Simmons has succeeded in pulling together the main fruits of the correspondence for simple types in a single text. … It can't be emphasized enough that the great thing about this book is its many well-chosen completely solved exercises. This alone makes it a valuable text, especially for self-study.' ACM SIGACT NewsTable of ContentsIntroduction; Preview; Part I. Development and Exercises: 1. Derivation systems; 2. Computation mechanisms; 3. The typed combinator calculus; 4. The typed l-calculus; 5. Substitution algorithms; 6. Applied l-calculi; 7. Multi-recursive arithmetic; 8. Ordinals and ordinal notation; 9. Higher order recursion; Part II. Solutions: A. Derivation systems; B. Computation mechanisms; C. The typed combinator calculus; D. The typed l-calculus; E. Substitution algorithms; F. Applied l-calculi; G. Multi-recursive arithmetic; H. Ordinals and ordinal notation; I. Higher order recursion; Postview; Bibliography; Commonly used symbols; Index.

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Book SynopsisThis new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.Trade Review'Recommended for every academic mathematics collection.' Choice'… an excellent introductory textbook on ordered sets and lattices and it is intended for undergraduate and beginning graduate students in mathematics.' Vaclav Slavic, Zentralblatt für Mathematik'I used Introduction to Lattices and Order as the sole textbook in a one semester course. The students enrolled were a heterogeneous group including modestly prepared undergraduates, well trained graduate students, and a few applications-oriented computer science students … In short, the textbook was a success.' Joel Berman, Australian Mathematical Society Gazette'… a well-written, satisfying, informative, and stimulating account of applications that are of great interest, particularly in computer science and social science … it will surely become a classic.' Mathematical Reviews'Altogether, this is a great book. It would be interesting (and educational) to give a course based on it - almost makes me wish I hadn't retired!' Australian Mathematical Society Gazette'… a valuable source to anyone who needs to use ordered structures in any context.' EMS Newsletter'It can be recommended as a valuable source to anyone who needs to use ordered structures in any context.' European Mathematical Society'The book is written in a very engaging and fluid style. The understanding of the content is aided tremendously by the very large number of beautiful lattice diagrams … The book provides a wonderful and accessible introduction to lattice theory, of equal interest to both computer scientists and mathematicians.' Jonathan Cohen, SIGACT NewsTable of ContentsPreface; Preface to the first edition; 1. Ordered sets; 2. Lattices and complete lattices; 3. Formal concept analysis; 4. Modular, distributive and Boolean lattices; 5. Representation theory: the finite case; 6. Congruences; 7. Complete lattices and Galois connections; 8. CPOs and fixpoint theorems; 9. Domains and information systems; 10. Maximality principles; 11. Representation: the general case; Appendix A. A topological toolkit; Appendix B. Further reading; Notation index; Index.

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Book SynopsisAutomata theory lies at the foundation of computer science, and is vital to a theoretical understanding of how computers work and what constitutes formal methods. This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways. The first part of the book is organised around notions of rationality and recognisability. The second part deals with relations between words realised by finite automata, which not only exemplifies the automata theory but also illustrates the variety of its methods and its fields of application. Many exercises are included, ranging from those that test the reader, to those that are technical results, to those that extend ideas presented in the text. Solutions or answers to many of these are included in the book.Trade Review'… a rich exposition … expertly translated by Reuben Thomas … its motivating ideas and substantive cross-currents fill almost every page … Nothing seems to be missing … should be on the shelf of every serious student and professional. It will enjoy a very long stay on my own.' Computing ReviewsTable of ContentsForeword; 0. Fundamental structures; 1. The simplest possible machine; 2. The power of algebra; 3. The pertinence of enumeration; 4. The richness of transducers; 5. The simplicity of functional transducers; Bibliography; Index.

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Book SynopsisWritten for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that integrates literature from several fields into a coherent source for teaching and reference in applications including robotics, computational biology, computer graphics, manufacturing, aerospace applications and medicine.Trade Review'This is a terrific book, a milestone in the robotics literature.' Matt Mason, Director of The Carnegie Mellon Robotics Institute'Motion planning is an important field of research with applications in such diverse terrains as robotics, molecular modeling, virtual environments, and games. Over the past two decades a huge number of techniques have been developed, all with their merits and shortcomings. The book by Steve LaValle gives an excellent overview of the current state of the art in the field. It should lie on the desk of everybody that is involved in motion planning research or the use of motion planning in applications.' Mark Overmars, Utrecht University'A great book at the junction where Robotics, Artificial Intelligence, and Control are crossing their paths. For many problems you will find in-depth discussion and algorithms; for virtually all others in the field, an intriguing introduction to make you at ease and entice you to further probing the matter.' Antonio Bicchi, della Università di Pisa'Since the early 90s, Latombe's book has been the authoritative source for students and researchers working on motion planning problems in robotics. During the succeeding decade and half, the motion planning field moved forward with significant developments. LaValle's book picks up the field where Latombe's book left it, describing in detail major developments such as probabilistic roadmaps, manipulation, and coverage planning. Moreover, the book describes a fundamental generalization of configuration spaces to information spaces. The chapters on information spaces appear here for the first time, making them accessible to students and researchers who wish to tackle progressively more challenging real-world motion planning problems in robotics.' Elon Rimon, Technion'Planning Algorithms is a daring title. It aims at being ecumenical gathering students and their professors scattered in various departments of Engineering and calling them to share the same mathematical foundations. The story starts with motion planning algorithms. Steve LaValle's deep extensive understanding and his effective expertise in that area are shared in this book. They allow the author to go further and to generalize the famous configuration space of the piano mover problem into the information space. This is the core of the title ambition. All the seminal material born with Robotics, Artificial Intelligence and Control, and developed for more than thirty years in a sparse way, are there uniquely unified. The book is not a catalogue of methods. It is the coherent view of a single researcher. The style is nice making the reading fluent: there is a good balance between informal introduction of concepts and the necessary technical developments. Students, researchers and engineers exploring routes in Artificial Intelligence and Robotics, in Graphics and CAD/CAM, and even Molecular Biology now, will find here amazing computational foundations for their topics.' Jean-Paul Laumond, LAAS-CNRS' … this book really is monumental and well-written piece of work, and although few will have cause to read more than a fraction of its content, at its price it deserves to find its way onto the bookshelves of many of us, as well as being recommended to our students.' ScienceDirectTable of ContentsPart I. Introductory Material: 1. Introduction; 2. Discrete planning; Part II. Motion Planning: 3. Geometric representations and transformations; 4. The configuration space; 5. Sampling-based motion planning; 6. Combinatorial motion planning; 7. Extensions of basic motion planning; 8. Feedback motion planning; Part III. Decision-Theoretic Planning: 9. Basic decision theory; 10. Sequential decision theory; 11. Information spaces; 12. Planning under sensing uncertainty; Part IV. Planning Under Differential Constraints: 13. Differential models; 14. Sampling-based planning under differential constraints; 15. System theory and analytical techniques.

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Book SynopsisA hands-on 2007 introductory guide to CALPHAD, the reader can directly apply the methods in the book to their own research. Several case studies put the methods into a practical context. Suitable for advanced materials design and engineering courses and to those using thermodynamic data in their research or simulations.Trade Review"Lukas (U. Stuttgart emeritus) and co-authors Sundman (Paul Sabatier U.) and independent scientist Fries provide the first introductory guide to this method of computation that combines data from thermodynamics, phase diagrams, and atomistic properties such as magnetism into a unified and consistent model. They introduce the science and art of computational thermodynamics and the past and present of the Calphad technique, the scientific basis of the technique (including thermodynamics, crystallography, equilibrium calculations and optimization methods), first principles and thermodynamic properties, experimental data needed for optimization, models for the Gibbs energy element, assessment methodology, optimization tools, and thermodynamic databases. They also offer a series of case studies, including a complete assessment of the Cu-Mg system and a complete binary system (Ca-Ng) and provide a list of websites along with comprehensive references." --Book NewsTable of ContentsPreface; 1. Introduction; 2. Basis; 3. First principles and thermodynamic properties; 4. Experimental data used for the optimisation; 5. Models for the Gibbs energy; 6. Assessment methodology; 7. Optimisation tools; 8. Creating thermodynamic databases; 9. Case studies; Bibliography; Index.

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Book SynopsisA conceptual introduction to the study of the intrinsic complexity of computational tasks. It will serve advanced undergraduate and graduate students, either as a textbook or for self-study. It provides explanations of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness, and probabilistic proof systems.Trade Review"This interesting book... is refreshing to read his [Goldreichs'] opinions... The very strong focus on conceptual issues makes the book indispensible as a reference volume for research libraries." M. Bona, University of Florida, CHOICE"This book provides very well developed material that should interest advanced students either studying or doing new work on computational complexity. It would also be a valuable text for professionals challenged with solving "hard" computing problems of intending to exploit these types of problems when designing of new types computing systems." Brian A. Lawler, Software Engineering Notes"The book offers a conceptual perspective on several sub-areas of complexity theory and is intended to be used as a textbook for students and educators as well as for experts who seek an overview of of several sub-areas." Gerhard Lischke, Mathematical ReviewsTable of Contents1. Introduction and preliminaries; 2. P, NP and NP-completeness; 3. Variations on P and NP; 4. More resources, more power?; 5. Space complexity; 6. Randomness and counting; 7. The bright side of hardness; 8. Pseudorandom generators; 9. Probabilistic proof systems; 10. Relaxing the requirements; Epilogue; Appendix A. Glossary of complexity classes; Appendix B. On the quest for lower bounds; Appendix C. On the foundations of modern cryptography; Appendix D. Probabilistic preliminaries and advanced topics in randomization; Appendix E. Explicit constructions; Appendix F. Some omitted proofs; Appendix G. Some computational problems.

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Book SynopsisBased on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.Trade Review'Has climbing up onto the MCMC juggernaut seemed to require just too much effort? This delightful little monograph provides an effortless way in. The chapters are bite-sized with helpful, do-able exercises (by virtue of strategically placed hints) that complement the text.' Publication of the International Statistical Institute'… a very nice introduction to the modern theory of Markov chain simulation algorithms.' R. E. Maiboroda, Zentralblatt MATH' … extremely elegant. I am sure that students will find great pleasure in using the book - and that teachers will have the same pleasure in using it to prepare a course on the subject.' Mathematics of Computation'This elegant little book is a beautiful introduction to the theory of simulation algorithms, using (discrete) Markov chains (on finite state spaces) … highly recommended to anyone interested in the theory of Markov chain simulation algorithms.' Nieuw Archief voor WiskundeTable of Contents1. Basics of probability theory; 2. Markov chains; 3. Computer simulation of Markov chains; 4. Irreducible and aperiodic Markov chains; 5. Stationary distributions; 6. Reversible Markov chains; 7. Markov chain Monte Carlo; 8. Fast convergence of MCMC algorithms; 9. Approximate counting; 10. Propp-Wilson algorithm; 11. Sandwiching; 12. Propp-Wilson with read once randomness; 13. Simulated annealing; 14. Further reading.

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Book SynopsisThe definitive treatment of analytic combinatorics. This self-contained text covers the mathematics underlying the analysis of discrete structures, with thorough treatment of a large number of applications. Exercises, examples, appendices and notes aid understanding: ideal for individual self-study or for advanced undergraduate or graduate courses.Trade Review'… thorough and self-contained … presentation of … topics is very well organised … provides an ample amount of examples and illustrations, as well as a comprehensive bibliography. It is valuable both as a reference work for researchers working in the field and as an accessible introduction suitable for students at an advanced graduate level.' EMS NewsletterTable of ContentsPreface; An invitation to analytic combinatorics; Part A. Symbolic Methods: 1. Combinatorial structures and ordinary generating functions; 2. Labelled structures and exponential generating functions; 3. Combinatorial parameters and multivariate generating functions; Part B. Complex Asymptotics: 4. Complex analysis, rational and meromorphic asymptotics; 5. Applications of rational and meromorphic asymptotics; 6. Singularity analysis of generating functions; 7. Applications of singularity analysis; 8. Saddle-Point asymptotics; Part C. Random Structures: 9. Multivariate asymptotics and limit laws; Part D. Appendices: Appendix A. Auxiliary elementary notions; Appendix B. Basic complex analysis; Appendix C. Concepts of probability theory; Bibliography; Index.

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Book SynopsisTrade Review"Avi Wigderson, Co-Winner of the Abel Prize, Norwegian Academy of Science and Letters""Avi Wigderson's new 440-page book, Mathematics and Computation: A Theory Revolutionizing Technology and Science (Princeton University Press, October 2019), lays out a commanding overview of the theory of computing and argues for its central role in human thought."---Allyn Jackson, Communications of the ACM"This must-read book provides a high-level, enjoyable overview of numerous parts of mathematics that are related to computation in general, and computational complexity in particular." * Choice *

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Book SynopsisCryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional:It serves as an introduction to the more practical aspects of both conventionalTrade Review"…very well suited for the reader who wants an encyclopedic description of the state of the art of applied modern cryptography."-Mathematical Reviews, Issue 99g "[This book] is an incredible achievement. … [T]he handbook is complete. If I want to check what problems there were with a proposed system, determine how the variations on a particular algorithm developed, see what research preceded and followed an idea, I go to the Handbook. The Handbook has accurate, clear, and correct information. It is wonderful. … If I were limited to only one cryptography text on my shelves, it would be the Handbook of Applied Cryptography." - Bulletin of the AMS Table of ContentsForeword by Ronald L. Rivest Overview of Cryptography Introduction Information security and cryptography Background on functions Functions(1-1, one-way, trapdoor one-way) Permutations Involutions Basic terminology and concepts Symmetric-key encryption Overview of block ciphers and stream ciphers Substitution ciphers and transposition ciphers Composition of ciphers Stream ciphers The key space Digital signatures Authentication and identification Identification Data origin authentication Public-key cryptography Public-key encryption The necessity of authentication in public-key systems Digital signatures from reversible public-key encryption Symmetric-key versus public-key cryptography Hash functions Protocols and mechanisms Key establishment, management, and certification Key management through symmetric-key techniques Key management through public-key techniques Trusted third parties and public-key certificates Pseudorandom numbers and sequences Classes of attacks and security models Attacks on encryption schemes Attacks on protocols Models for evaluating security Perspective for computational security Notes and further references Mathematical Background Probability theory Basic definitions Conditional probability Random variables Binomial distribution Birthday attacks Random mappings Information theory Entropy Mutual information Complexity theory Basic definitions Asymptotic notation Complexity classes Randomized algorithms Number theory The integers Algorithms in Z The integers modulo n Algorithms in Zn The Legendre and Jacobi symbols Blum integers Abstract algebra Groups Rings Fields Polynomial rings Vector spaces Finite fields Basic properties The Euclidean algorithm for polynomials Arithmetic of polynomials N

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Book Synopsisshowing that the study of programming languages does not consist of studying languages one after another, but is organized around the features that are present in these various languages.Trade ReviewFrom the reviews:“The book is divided into eight chapters and an epilogue. … Faculty teaching an undergraduate programming languages course may find this book to be a useful reference. Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (J. Beidler, Choice, Vol. 48 (10), June, 2011)“It is a short book--of about 100 pages--consisting of eight chapters and an epilogue. The book focuses on the formal description of programming language semantics and compilation using denotational semantics, small-step operational semantics (reduction semantics), and big-step operational semantics (natural semantics). … The book provides a good description of programming language concepts and motivates the necessary theory well. … The book is suitable for both professionals and graduate- and advanced undergraduate-level classes.” (Michael Oudshoorn, ACM Computing Reviews, November, 2011)Table of Contents1. Terms and Relations.- 2. The Language PCF.- 3. From Evaluation to Interpretation.- 4. Compilation.- 5. PCF with Types.- 6. Type Inference.- 7. References and Assignment.- 8. Records and Objects.- 9. Epilogue.- 10. Index.- 11. Bibliography

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Book SynopsisThis is the first self-contained introduction to the use of string diagrams to reason in elementary category theory. Written in an informal expository style, it features hundreds of carefully chosen diagrams to aid understanding. With numerous worked examples and exercises, the text is ideal for graduate students and advanced undergraduates.Trade Review'String diagrams have proven an indispensable tool in modern category theory, enabling intuitive graphical reasoning while doing away with much of the bookkeeping that tends to bog down equational arguments. This textbook introduces category theory by way of string diagrams, making it an excellent choice both for beginners in category theory, as well as for more experienced category theorists seeking to add string diagrammatic reasoning to their repertoire.' Robin Kaarsgaard, University of Edinburgh'Well-chosen notation plays a vital role in constructive calculation because it facilitates the exploitation of algebraic properties. This book's exemplary use of string diagrams in category theory will inspire and invigorate the calculational method. Peruse and ponder its colourful beauty.' Roland Backhouse, University of NottinghamTable of ContentsPrologue; 1. Category theory; 2. String diagrams; 3. Monads; 4. Adjunctions; 5. Putting it all together; Epilogue; Appendix. Notation; References; Index.

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Book SynopsisOccultism and the Origins of Psychoanalysis traces the origins of key psychoanalytic ideas back to their roots in hypnosis and the occult. Maria Pierri follows Freud’s early interest in ‘thought-transmission’, now known as telepathy. Trade Review"This book gives back to contemporary psychoanalysis the pleasure of exploring really little-known territories, fascinatingly restoring the connection between the past, present and "elsewhere" of communications between human beings, using the Freudian experience as its starting point, in order to reconsider in a reflective way the less visible, sometimes disorienting and mysterious levels of psychoanalytic practice. offers us an especially valuable reflection on the mysterious communicating paths which put individual and group unconsciouses in contact with each other, often bypassing in an apparently disconcerting manner the border controls." - Stefano Bolognini, past President of the IPA and the Italian Psychoanalytic Society"Following the thread of thought-transference, Maria Pierri goes through the events of the Freudian endeavour starting from its roots in hypnosis and occultism, through the dialogue with the masters, the pupils and the great female patients, the leading actresses of the cure. In his disquieting curiosity for telepathy, which he shared intimately with Ferenczi, Freud discovers that fortune-tellers, who do not know the future, can read the unconscious of their clients. But the "golden coin" of occultism, the generative mother-child communication, will be the great discovery of Ferenczi." - Luis J. Martin Cabré, Training analyst, past President Madrid Psychoanalytical Association."Today we know much about the polyphonic complex of contexts, experiences, relationships and ideas which made psychoanalysis possible and still nourish its current debates. We can be very grateful to Maria Pierri for bringing us up to date with the role and meaning of some little-known aspects of Freud’s life and work concerning occultism and the fascinating dialogue of the unconsciouses developed with Ferenczi: what the Author identifies as one of the matrices of the developments of contemporary psychoanalysis." - Marco Conci, MC, IPA Committee on the History of Psychoanalysis"This book gives back to contemporary psychoanalysis the pleasure of exploring really little-known territories, fascinatingly restoring the connection between the past, present and 'elsewhere' of communications between human beings, using the Freudian experience as its starting point, in order to reconsider in a reflective way the less visible, sometimes disorienting and mysterious levels of psychoanalytic practice. It offers us an especially valuable reflection on the mysterious communicating paths which put individual and group unconsciouses in contact with each other, often bypassing in an apparently disconcerting manner the border controls." - Stefano Bolognini, past president of the IPA and the Italian Psychoanalytic Society"Following the thread of thought-transference, Maria Pierri goes through the events of the Freudian endeavour starting from its roots in hypnosis and occultism, through the dialogue with the masters, the pupils and the great female patients, the leading actresses of the cure. In his disquieting curiosity for telepathy, which he shared intimately with Ferenczi, Freud discovers that fortune-tellers, who do not know the future, can read the unconscious of their clients. But the 'golden coin' of occultism, the generative mother-child communication, will be the great discovery of Ferenczi." - Luis J. Martin Cabré, training analyst, past president, Madrid Psychoanalytical Association"Today we know much about the polyphonic complex of contexts, experiences, relationships and ideas which made psychoanalysis possible and still nourish its current debates. We can be very grateful to Maria Pierri for bringing us up to date with the role and meaning of some little-known aspects of Freud’s life and work concerning occultism and the fascinating dialogue of the unconsciouses developed with Ferenczi: what the Author identifies as one of the matrices of the developments of contemporary psychoanalysis." - Marco Conci, MC, IPA Committee on the History of PsychoanalysisTable of ContentsIntroductionStefano BologniniPrologue: a result of character: the cocaine, this magical substance1. Vienna, Porta Orientis of the Unconscious The force of suggestion: the "wonderful somnambulists" HypnosisVienna, laboratory of modernity2. The Young FreudA passionate young researcher into natureFirst love Martha and Bertha: the languages of passion3. The Lesson of Jean Martin Charcot At the SalpêtrièreThe apparatus of language The magic of words4. The lesson of Josef Breuer and the "descent to the mothers"Studies on hysteriaA difficult separation: not all debts can be paidA foundation myth: a false pregnancy and a cure with a defect.5. Sigmund Freud’s lessonThe discovery of a false connection Irma’s throat and the feminine at the origin of psychoanalysis.Dream as desire 6. Fliess and the invention of psychoanalysis A secret correspondence My friend in BerlinFreud’s heart trouble7. The discovery of infantile sexualitySelf-analysis and the writing cure Cherchez la femme: the case of Emma Eckstein8. Original thought requires a ruptureThe "reader of thoughts" The accusation of plagiarism A future in the image of the past: predestination and superstition 9. Occultism made in the USASpiritualism Medium, media, and "mental telegraphy"First hypotheses about the unconscious10 Jung, spiritualism, and countertransference: the world of the deadJung, Poltergeist phenomena, and séances The arrival at Burghölzli First visit to ViennaEaster 1909: Jung’s spiritual complex and Sabina The dangerous fascination of the "beautiful Jewess"11. Ferenczi, the unclassifiableThe sultan and his "clairvoyant" A psychoanalyst "of a restless mind"Ferenczi and the hidden treasure of SpiritualismThe encounter with Freud: a postponed transferential appointment12. A journey to America Three men and an eventful, mutually analytic crossing: the outward journey… … and back again13. The Danaan gift The clairvoyant who reads Ferenczi’s mindThe patient who reads Ferenczi’s mindThe Palermo incident, or the interpretation of paranoiaThe psychic work of the clairvoyant: two unfulfilled prophecies14. An epistolary novelFerenczi and incestuous countertransferential storms: from mother to daughter What is still missing is the fatherly blessing: fatefulness and Oedipal coincidencesElma Pàlos, fragment of the analysis of a seduction The open wound in Ferenczi’s heart, a source of creativity 15. The Saturday goy: getting to know Dr Jones The Welsh liar Difficult beginnings Freud’s first pupil from BritainDr Jones’s stethoscope: rationalisation and censorship of excess countertransferenceA prescribed training analysis in Budapest 16. The intergenerational transmission of psychoanalysis Love and death: the three women of the three pupils"If you go to women, don't forget the whip"At school with Freud: the transmission of psychoanalysis17. The secret committeeThe transformations and the desertion of JungA missed meeting: the "Kreuzlingen gesture" The Committee: the Männerbund and the defence of the "Cause" (Die Sache)Totem and taboo: unconscious intelligence and intergenerational transmission of thought 18. 1913 - the year before the warThe last congress with JungA black tide of occultism The question of telepathyThe dialogues of the unconsciousEpilogue: a fortune-teller visits Freud in BerggasseCorrespondenceIndex

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Book SynopsisComputational Framework for the Finite Element Method in MATLAB and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However, basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and

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Book SynopsisHandbook of Price Impact Modeling provides practitioners and students with a mathematical framework grounded in academic references to apply price impact models to quantitative trading and portfolio management. Automated trading is now the dominant form of trading across all frequencies. Furthermore, trading algorithm rise introduces new questions professionals must answer, for instance: How do stock prices react to a trading strategy? How to scale a portfolio considering its trading costs and liquidity risk? How to measure and improve trading algorithms while avoiding biases? Price impact models answer these novel questions at the forefront of quantitative finance. Hence, practitioners and students can use this Handbook as a comprehensive, modern view of systematic trading.For financial institutions, the Handbookâs framework aims to minimize the firmâs price impact, measure market liquiditTrade Review"Kevin Webster has written a remarkable textbook that studies these problems in a uniquely comprehensive manner. To wit, he covers theory, empirics, and implementation by bringing together insights developed in a number of different research communities, ranging from Industry Practitioners, Financial Economists, Econophysicists, to Applied Mathematicians. In doing so, Kevin develops the underlying theory in a very accessible manner. He also presents important practical applications beyond optimal trading (such as risk management), which showcase that a good grasp of the mechanics of price impact is an essential part of any modern financial engineer's toolkit."- Johannes Muhle-Karbe, Imperial College London.Full article: Handbook of Price Impact Modeling (tandfonline.com)Table of Contents1. Introduction to Modeling Price Impact. 2. Mathematical Models of Price Impact. 3. Applications of Price Impact Models. 4. Further Applications of Price Impact Models. 5. An Introduction to the Mathematics of Causal Inference. 6. Dealing with Biases when Fitting Price Impact Models. 7. Empirical Analysis of Price Impact Models.

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Book SynopsisIntroduction to Python for Science and Engineering offers a quick and incisive introduction to the Python programming language for use in any science or engineering discipline. The approach is pedagogical and âœbottom up,â which means starting with examples and extracting more general principles from that experience. No prior programming experience is assumed.Readers will learn the basics of Python syntax, data structures, input and output, conditionals and loops, user-defined functions, plotting, animation, and visualization. They will also learn how to use Python for numerical analysis, including curve fitting, random numbers, linear algebra, solutions to nonlinear equations, numerical integration, solutions to differential equations, and fast Fourier transforms.Readers learn how to interact and program with Python using JupyterLab and Spyder, two simple and widely used integrated development environments.All the major Python libraries for science and e

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Book SynopsisPython's simplicity and versatility make it an ideal language for both beginners and experienced programmers. Its syntax facilitates a smooth learning curve, enabling individuals to concentrate on grasping programming concepts instead of wrestling with intricate syntax rules. The extensive standard library reinforces its practicality, offering pre-built modules and functions that reduce manual coding efforts. Python's versatility is evident in its applications, spanning web development, data analysis, Machine Learning and automation.The language's interactive nature supports real-time code experimentation, stepping up the learning process and enhancing understanding. Python's wealth of online resources further enriches the learning experience, fostering a community where individuals can develop their programming skills. Python: A Practical Learning Approach exemplifies Python's simplicity and versatility with numerous examples, ensuring a seamless learning journ

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Book SynopsisPython Programming for Mathematics focuses on the practical use of the Python language in a range of different areas of mathematics. Through fifty-five exercises of increasing difficulty, the book provides an expansive overview of the power of using programming to solve complex mathematical problems.This book is intended for undergraduate and graduate students who already have learned the basics of Python programming and would like to learn how to apply that programming skill in mathematics.Features Innovative style that teaches programming skills via mathematical exercises. Ideal as a main textbook for Python for Mathematics courses, or as a supplementary resource for Numerical Analysis and Scientific Computing courses.

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Book SynopsisCoinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.Table of ContentsPreface; List of contributors; 1. Origins of bisimulation and coinduction Davide Sangiorgi; 2. An introduction to (co)algebra and (co)induction Bart Jacobs and Jan Rutten; 3. The algorithmics of bisimilarity Luca Aceto, Anna Ingolfsdottir and Jiří Srba; 4. Bisimulation and logic Colin Stirling; 5. Howe's method for higher-order languages Andrew Pitts; 6. Enhancements of the bisimulation proof method Damien Pous and Davide Sangiorgi; 7. Probabilistic bisimulation Prakash Panangaden.

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Book SynopsisThis new edition of Wilde's popular book promises over 100 pages of new material, exercises and references. New attention is given to the derivation of the Choi-Kraus theorem for quantum channels, the CHSH game, quantum relative entropy, and sequential decoding. The text offers an ideal entry point into the topic for graduate students.Trade Review'For years, I have been hoping that somebody would write a book on quantum information theory that was clear, comprehensive, and up to date. This is that book. And the second edition is even better than the first.' Peter Shor, Massachusetts Institute of Technology'Mark M. Wilde's Quantum Information Theory is a natural expositor's labor of love. Accessible to anyone comfortable with linear algebra and elementary probability theory, Wilde's book brings the reader to the forefront of research in the quantum generalization of Shannon's information theory. What had been a gaping hole in the literature has been replaced by an airy edifice, scalable with the application of reasonable effort and complete with fine vistas of the landscape below. Wilde's book has a permanent place not just on my bookshelf but on my desk.' Patrick Hayden, Stanford University, CaliforniaReview of previous edition: '… [its] clear, thorough, and above all self-contained presentation will aid quantum information researchers in coming up to speed with the latest results in this area of the field. Meanwhile, the familiar setting and language will help classical information theorists who wish to become more acquainted with the quantum aspects of information processing … The presentation is well-structured, making it easy to jump to the desired topic and quickly determine on what that topic depends and how it is used going forward … Quantum Information Theory fills an important gap in the existing literature and will, I expect, help propagate the latest and greatest results in quantum Shannon theory to both quantum and classical researchers.' Joseph M. Renes, Quantum Information ProcessingReview of previous edition: '… a modern self-contained text … suitable for graduate-level courses leading up to research level.' Journal of Discrete Mathematical Sciences and CryptographyReview of previous edition: '… the book does a phenomenal job of introducing, developing and nurturing a mathematical sense of quantum information processing … In a nutshell, this is an essential reference for students and researchers who work in the area or are trying to understand what it is that quantum information theorists study. Wilde, as mentioned in his book, beautifully illustrates 'the ultimate capability of noisy physical systems, governed by the laws of quantum mechanics, to preserve information and correlations' through this book. I would strongly recommend it to anyone who plans to continue working in the field of quantum information.' Subhayan Roy Moulick, SIGCAT NewsTable of ContentsPreface to the second edition; Preface to the first edition; How to use this book; Part I. Introduction: 1. Concepts in quantum Shannon theory; 2. Classical Shannon theory; Part II. The Quantum Theory: 3. The noiseless quantum theory; 4. The noisy quantum theory; 5. The purified quantum theory; Part III. Unit Quantum Protocols: 6. Three unit quantum protocols; 7. Coherent protocols; 8. Unit resource capacity region; Part IV. Tools of Quantum Shannon Theory: 9. Distance measures; 10. Classical information and entropy; 11. Quantum information and entropy; 12. Quantum entropy inequalities and recoverability; 13. The information of quantum channels; 14. Classical typicality; 15. Quantum typicality; 16. The packing lemma; 17. The covering lemma; Part V. Noiseless Quantum Shannon Theory: 18. Schumacher compression; 19. Entanglement manipulation; Part VI. Noisy Quantum Shannon Theory: 20. Classical communication; 21. Entanglement-assisted classical communication; 22. Coherent communication with noisy resources; 23. Private classical communication; 24. Quantum communication; 25. Trading resources for communication; 26. Summary and outlook; Appendix A. Supplementary results; Appendix B. Unique linear extension of a quantum physical evolution; References; Index.

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Book SynopsisAccurate, robust and fast image reconstruction is a critical task in many scientific, industrial and medical applications. Over the last decade, image reconstruction has been revolutionized by the rise of compressive imaging. It has fundamentally changed the way modern image reconstruction is performed. This in-depth treatment of the subject commences with a practical introduction to compressive imaging, supplemented with examples and downloadable code, intended for readers without extensive background in the subject. Next, it introduces core topics in compressive imaging including compressed sensing, wavelets and optimization in a concise yet rigorous way, before providing a detailed treatment of the mathematics of compressive imaging. The final part is devoted to recent trends in compressive imaging: deep learning and neural networks. With an eye to the next decade of imaging research, and using both empirical and mathematical insights, it examines the potential benefits and the piTable of Contents1. Introduction; Part I. The Essentials of Compressive Imaging: 2. Images, transforms and sampling; 3. A short guide to compressive imaging; 4. Techniques for enhancing performance; Part II. Compressed Sensing, Optimization and Wavelets: 5. An introduction to conventional compressed sensing; 6. The LASSO and its cousins; 7. Optimization for compressed sensing; 8. Analysis of optimization algorithms; 9. Wavelets; 10. A taste of wavelet approximation theory; Part III. Compressed Sensing with Local Structure: 11. From global to local; 12. Local structure and nonuniform recovery; 13. Local structure and uniform recovery; 14. Infinite-dimensional compressed sensing; Part IV. Compressed Sensing for Imaging: 15. Sampling strategies for compressive imaging; 16. Recovery guarantees for wavelet-based compressive imaging; 17. Total variation minimization; Part V. From Compressed Sensing to Deep Learning: 18. Neural networks and deep learning; 19. Deep learning for compressive imaging; 20. Accuracy and stability of deep learning for compressive imaging; 21. Stable and accurate neural networks for compressive imaging; 22. Epilogue; Appendices: A. Linear Algebra; B. Functional analysis; C. Probability; D. Convex analysis and convex optimization; E. Fourier transforms and series; F. Properties of Walsh functions and the Walsh transform; Notation; Abbreviations; References; Index.

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Book SynopsisThis book presents mathematical logic from the syntactic point of view, with an emphasis on aspects that are fundamental to computer science. It is an excellent introduction for graduate students and advanced undergraduates interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for professional logicians.Trade Review'Avigad provides a much needed introduction to mathematical logic that foregrounds the role of syntax and computability in our understanding of consistency and inconsistency. The result provides a jumping off point to any of the fields of modern logic, not only teaching the technical groundwork, but also providing a window into how to think like a logician.' Henry Towsner, University of Pennsylvania'This book by one of the most knowledgeable researchers in the field covers a remarkably broad selection of material without sacrificing depth. Its clear organization and unified approach - focused on a syntactic approach and on the role of computation - make it suitable for a wide range of introductory logic sequences at the upper-level undergraduate and graduate level, as well as a valuable resource for background material in more advanced logic courses.' Denis Hirschfeldt, University of Chicago'… an excellent addition to the literature, with plenty more than enough divergences and side-steps from the more well-trodden paths through the material to be consistently interesting … this is most certainly a book to make sure your library gets.' Peter Smith, Logic MattersTable of ContentsPreface; 1. Fundamentals; 2. Propositional Logic; 3. Semantics of Propositional Logic; 4. First-Order Logic; 5. Semantics of First-Order Logic; 6. Cut Elimination; 7. Properties of First-Order Logic; 8. Primitive Recursion; 9. Primitive Recursive Arithmetic; 10. First-Order Arithmetic; 11. Computability 12. Undecidability and Incompleteness; 13. Finite Types; 14. Arithmetic and Computation; 15. Second-Order Logic and Arithmetic; 16. Subsystems of Second-Order Arithmetic; 17. Foundations; Appendix; References; Notation; Index.

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Book SynopsisUsing basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel''s incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing''s Halting problem, and much more. The concepts come alive with many examples and exercises.Table of Contents1. Introduction; 2. Aide-Mémoire for Category Theory; 3. Models of Computation; 4. Computability Theory; 5. Complexity Theory; 6. Diagonal Arguments; 7. Conclusion; References.

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Book SynopsisThe continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.Table of ContentsPart I. Background: 1. Introduction; 2. Data; Part II. Theory: 3. Topology; 4. Shape of data; 5. Structures on spaces of barcodes; Part III. Practice: 6. Case studies; References; Index.

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Book SynopsisArguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities, within seconds, on light hardware.AAD recently became a centerpiece of modern financial systems and a key skill for all quantitative analysts, developers, risk professionals or anyone involved with derivatives. It is increasingly taught in Masters and PhD programs in finance.Danske Bank''s wide scale implementation of AAD in its production and regulatory systems won the In-House System of the Year 2015 Risk award. The Modern Computational Finance books, written by three of the very people who designed Danske Bank''s systems, offer a unique insight into the modern implementation of financial models. The volumes combine financial modelling, mathematics and programming to resolve real life financial problems and produce effective derivatives Table of ContentsModern Computational Finance xi Preface by Leif Andersen xv Acknowledgments xix Introduction xxi About the Companion C++ Code xxv PART I Modern Parallel Programming 1 Introduction 3 CHAPTER 1 Effective C++ 17 CHAPTER 2 Modern C++ 25 2.1 Lambda expressions 25 2.2 Functional programming in C++ 28 2.3 Move semantics 34 2.4 Smart pointers 41 CHAPTER 3 Parallel C++ 47 3.1 Multi-threaded Hello World 49 3.2 Thread management 50 3.3 Data sharing 55 3.4 Thread local storage 56 3.5 False sharing 57 3.6 Race conditions and data races 62 3.7 Locks 64 3.8 Spinlocks 66 3.9 Deadlocks 67 3.10 RAII locks 68 3.11 Lock-free concurrent design 70 3.12 Introduction to concurrent data structures 72 3.13 Condition variables 74 3.14 Advanced synchronization 80 3.15 Lazy initialization 83 3.16 Atomic types 86 3.17 Task management 89 3.18 Thread pools 96 3.19 Using the thread pool 108 3.20 Debugging and optimizing parallel programs 113 PART II Parallel Simulation 123 Introduction 125 CHAPTER 4 Asset Pricing 127 4.1 Financial products 127 4.2 The Arbitrage Pricing Theory 140 4.3 Financial models 151 CHAPTER 5 Monte-Carlo 185 5.1 The Monte-Carlo algorithm 185 5.2 Simulation of dynamic models 192 5.3 Random numbers 200 5.4 Better random numbers 202 CHAPTER 6Serial Implementation 213 6.1 The template simulation algorithm 213 6.2 Random number generators 223 6.3 Concrete products 230 6.4 Concrete models 245 6.5 User interface 263 6.6 Results 268 CHAPTER 7 Parallel Implementation 271 7.1 Parallel code and skip ahead 271 7.2 Skip ahead with mrg32k3a 276 7.3 Skip ahead with Sobol 282 7.4 Results 283 PART III Constant Time Differentiation 285 Introduction 287 CHAPTER 8 Manual Adjoint Differentiation 295 8.1 Introduction to Adjoint Differentiation 295 8.2 Adjoint Differentiation by hand 308 8.3 Applications in machine learning and finance 315 CHAPTER 9 Algorithmic Adjoint Differentiation 321 9.1 Calculation graphs 322 9.2 Building and applying DAGs 328 9.3 Adjoint mathematics 340 9.4 Adjoint accumulation and DAG traversal 344 9.5 Working with tapes 349 CHAPTER 10 Effective AAD and Memory Management 357 10.1 The Node class 359 10.2 Memory management and the Tape class 362 10.3 The Number class 379 10.4 Basic instrumentation 398 CHAPTER 11 Discussion and Limitations 401 11.1 Inputs and outputs 401 11.2 Higher-order derivatives 402 11.3 Control flow 402 11.4 Memory 403 CHAPTER 12 Differentiation of the Simulation Library 407 12.1 Active code 407 12.2 Serial code 409 12.3 User interface 417 12.4 Serial results 424 12.5 Parallel code 426 12.6 Parallel results 433 CHAPTER 13 Check-Pointing and Calibration 439 13.1 Check-pointing 439 13.2 Explicit calibration 448 13.3 Implicit calibration 475 CHAPTER 14 Multiple Differentiation in Almost Constant Time 483 14.1 Multidimensional differentiation 483 14.2 Traditional Multidimensional AAD 484 14.3 Multidimensional adjoints 485 14.4 AAD library support 487 14.5 Instrumentation of simulation algorithms 494 14.6 Results 499 CHAPTER 15 Acceleration with Expression Templates 503 15.1 Expression nodes 504 15.2 Expression templates 507 15.3 Expression templated AAD code 524 Debugging AAD Instrumentation 541 Conclusion 547 References 549 Index 555

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Book SynopsisMany students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method.Table of ContentsPreface to Fifth Edition xv Acknowledgements xvii 1 Preliminaries: Computer Strategies 1 1.1 Introduction 1 1.2 Hardware 2 1.3 Memory Management 2 1.4 Vector Processors 3 1.5 Multi-core Processors 3 1.6 Co-processors 4 1.7 Parallel Processors 4 1.8 Applications Software 5 1.9 Array Features 9 1.10 Third-party Libraries 17 1.11 Visualisation 18 1.12 Conclusions 23 References 24 2 Spatial Discretisation by Finite Elements 25 2.1 Introduction 25 2.2 Rod Element 25 2.3 The Eigenvalue Equation 28 2.4 Beam Element 29 2.5 Beam with an Axial Force 31 2.6 Beam on an Elastic Foundation 32 2.7 General Remarks on the Discretisation Process 33 2.8 Alternative Derivation of Element Stiffness 33 2.9 Two-dimensional Elements: Plane Stress 35 2.10 Energy Approach and Plane Strain 38 2.11 Plane Element Mass Matrix 40 2.12 Axisymmetric Stress and Strain 40 2.13 Three-dimensional Stress and Strain 42 2.14 Plate Bending Element 44 2.15 Summary of Element Equations for Solids 47 2.16 Flow of Fluids: Navier–Stokes Equations 47 2.17 Simplified Flow Equations 50 2.18 Further Coupled Equations: Biot Consolidation 54 2.19 Conclusions 56 References 56 3 Programming Finite Element Computations 59 3.1 Introduction 59 3.2 Local Coordinates for Quadrilateral Elements 59 3.3 Local Coordinates for Triangular Elements 64 3.4 Multi-Element Assemblies 66 3.5 ‘Element-by-Element’ Techniques 68 3.6 Incorporation of Boundary Conditions 72 3.7 Programming using Building Blocks 75 3.8 Solution of Equilibrium Equations 95 3.9 Evaluation of Eigenvalues and Eigenvectors 96 3.10 Solution of First-Order Time-Dependent Problems 99 3.11 Solution of Coupled Navier–Stokes Problems 103 3.12 Solution of Coupled Transient Problems 104 3.13 Solution of Second-Order Time-Dependent Problems 106 4 Static Equilibrium of Structures 115 4.1 Introduction 115 4.2 Conclusions 157 4.3 Glossary of Variable Names 157 4.4 Exercises 159 References 168 5 Static Equilibrium of Linear Elastic Solids 169 5.1 Introduction 169 5.2 Glossary of Variable Names 221 5.3 Exercises 224 References 232 6 Material Non-linearity 233 6.1 Introduction 233 6.2 Stress–strain Behaviour 235 6.3 Stress Invariants 236 6.4 Failure Criteria 238 6.5 Generation of Body Loads 240 6.6 Viscoplasticity 240 6.7 Initial Stress 242 6.8 Corners on the Failure and Potential Surfaces 243 6.9 Elastoplastic Rate Integration 270 6.10 Tangent Stiffness Approaches 275 6.11 The Geotechnical Processes of Embanking and Excavation 289 6.12 Undrained Analysis 305 6.13 Glossary of Variable Names 322 6.14 Exercises 327 References 331 7 Steady State Flow 333 7.1 Introduction 333 7.2 Glossary of Variable Names 359 7.3 Exercises 361 References 367 8 Transient Problems: First Order (Uncoupled) 369 8.1 Introduction 369 8.2 Comparison of Programs 8.4, 8.5, 8.6 and 8.7 397 8.3 Glossary of Variable Names 416 8.4 Exercises 419 References 422 9 Coupled Problems 423 9.1 Introduction 423 9.2 Glossary of Variable Names 454 9.3 Exercises 459 References 460 10 Eigenvalue Problems 461 10.1 Introduction 461 10.2 Glossary of Variable Names 477 10.3 Exercises 480 References 482 11 Forced Vibrations 483 11.1 Introduction 483 11.2 Glossary of Variable Names 517 11.3 Exercises 521 References 522 12 Parallel Processing of Finite Element Analyses 523 12.1 Introduction 523 12.2 Differences between Parallel and Serial Programs 525 12.3 Graphics Processing Units 589 12.4 Cloud Computing 594 12.5 Conclusions 596 12.6 Glossary of Variable Names 597 References 602 Appendix A Equivalent Nodal Loads 605 Appendix B Shape Functions and Element Node Numbering 611 Appendix C Plastic Stress-Strain Matrices and Plastic Potential Derivatives 619 Appendix D main Library Subprograms 623 Appendix E geom Library Subroutines 635 Appendix F Parallel Library Subroutines 639 Appendix G External Subprograms 645 Author Index 649 Subject Index 653

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