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Proofs and Algorithms

2011-01-11 Computers
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Release : 2011-01-11
Genre : Computers
Kind : eBook
Book Rating : 211/5 ( reviews)

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Book Synopsis Proofs and Algorithms by : Gilles Dowek

Download or read book Proofs and Algorithms written by Gilles Dowek. This book was released on 2011-01-11. Available in PDF, EPUB and Kindle. Book excerpt: Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

Semialgebraic Proofs and Efficient Algorithm Design

2019-12-10 Computers
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Release : 2019-12-10
Genre : Computers
Kind : eBook
Book Rating : 363/5 ( reviews)

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Book Synopsis Semialgebraic Proofs and Efficient Algorithm Design by : Noah Fleming

Download or read book Semialgebraic Proofs and Efficient Algorithm Design written by Noah Fleming. This book was released on 2019-12-10. Available in PDF, EPUB and Kindle. Book excerpt: The book provides the advanced reader with a deep insight into the exciting line of research, namely, proof that a solution exists has enabled an algorithm to find that solution itself with applications in many areas of computer science. It will inspire readers in deploying the techniques in their own further research.

Graph Theory

2021-03-17 Mathematics
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Release : 2021-03-17
Genre : Mathematics
Kind : eBook
Book Rating : 887/5 ( reviews)

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Book Synopsis Graph Theory by : Karin R Saoub

Download or read book Graph Theory written by Karin R Saoub. This book was released on 2021-03-17. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory: An Introduction to Proofs, Algorithms, and Applications Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis. This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results. Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations. Current applications and exploratory exercises are provided to further the reader’s mathematical reasoning and understanding of the relevance of graph theory to the modern world. Features The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths. The third chapter focuses entirely on trees – terminology, applications, and theory. Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach. Hints and Solutions to selected exercises provided at the back of the book. Author Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She earned her PhD in mathematics from Arizona State University and BA from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.

COMPUTER ALGORITHMS

2023-04-10 Computers
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Release : 2023-04-10
Genre : Computers
Kind : eBook
Book Rating : 854/5 ( reviews)

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Book Synopsis COMPUTER ALGORITHMS by : MEHTA, SHASHANK K.

Download or read book COMPUTER ALGORITHMS written by MEHTA, SHASHANK K.. This book was released on 2023-04-10. Available in PDF, EPUB and Kindle. Book excerpt: The book is self-contained and includes the desired mathematical background. The book covers most of the data structures and classical graphs algorithms, string algorithms, matroid algorithms, linear algebra algorithms, flow and circulation algorithms, linear programming solvers, and integer algorithms. It covers several topics which are rarely covered in the existing textbooks. Pseudocode is provided for every algorithm. Proof of correctness and the complexity analysis is given for every algorithm. Examples are also provided to help explain several algorithms. The book is designed for an introductory as well as an advance course in the design and analysis of algorithms. It is intended for undergraduate as well as postgraduate students of computer science and engineering. Some of the topics covered in the book are as follows. i) String homomorphism and isomorphism ii) Detailed proof of graph matching algorithm including augmenting path computation iii) Gallai Edmonds decomposition algorithm iv) Matroid Intersection algorithm Klein’s Cycle Cancellation algorithm and Goldberg-Karp’s Minimum Cost Circulation algorithm v) Lower-triangular Upper-triangular decomposition of a matrix using Gaussian Elimination Interior Point method for Linear Programs using Primal-Dual technique vi) Minimum weight Graph Matching algorithm vii) Schonhage-Strassen’s algorithm for integer multiplication and Agarwal-Kayal-Saxena’s algorithm for primality testing

Computer Arithmetic and Formal Proofs

2017-11-17 Computers
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Release : 2017-11-17
Genre : Computers
Kind : eBook
Book Rating : 709/5 ( reviews)

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Book Synopsis Computer Arithmetic and Formal Proofs by : Sylvie Boldo

Download or read book Computer Arithmetic and Formal Proofs written by Sylvie Boldo. This book was released on 2017-11-17. Available in PDF, EPUB and Kindle. Book excerpt: Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. Describes the notions of specification and weakest precondition computation and their practical use Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic Includes real analysis and a case study about numerical analysis

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