Proofs And Algorithms

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Proofs and Algorithms

Gilles Dowek
Proofs and Algorithms Book PDF

Author : Gilles Dowek
Publisher : Springer Science & Business Media
Page : 161 pages
File Size : 50,7 Mb
Release : 2011-01-11
Category : Computers
ISBN : 9780857291219

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Proofs and Algorithms by Gilles Dowek Pdf

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

Noah Fleming,Pravesh Kothari,Toniann Pitassi
Semialgebraic Proofs and Efficient Algorithm Design Book PDF

Author : Noah Fleming,Pravesh Kothari,Toniann Pitassi
Publisher : Unknown
Page : 234 pages
File Size : 50,5 Mb
Release : 2019-12-10
Category : Computers
ISBN : 1680836366

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Semialgebraic Proofs and Efficient Algorithm Design by Noah Fleming,Pravesh Kothari,Toniann Pitassi Pdf

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

Karin R Saoub
Graph Theory Book PDF

Author : Karin R Saoub
Publisher : CRC Press
Page : 421 pages
File Size : 41,5 Mb
Release : 2021-03-17
Category : Mathematics
ISBN : 9780429779886

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Graph Theory by Karin R Saoub Pdf

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

MEHTA, SHASHANK K.
COMPUTER ALGORITHMS Book PDF

Author : MEHTA, SHASHANK K.
Publisher : PHI Learning Pvt. Ltd.
Page : 473 pages
File Size : 47,6 Mb
Release : 2023-04-10
Category : Computers
ISBN : 9789391818852

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COMPUTER ALGORITHMS by MEHTA, SHASHANK K. Pdf

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

How to Think About Algorithms

Jeff Edmonds
How to Think About Algorithms Book PDF

Author : Jeff Edmonds
Publisher : Cambridge University Press
Page : 409 pages
File Size : 52,9 Mb
Release : 2008-05-19
Category : Computers
ISBN : 9781139471756

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How to Think About Algorithms by Jeff Edmonds Pdf

This textbook, for second- or third-year students of computer science, presents insights, notations, and analogies to help them describe and think about algorithms like an expert, without grinding through lots of formal proof. Solutions to many problems are provided to let students check their progress, while class-tested PowerPoint slides are on the web for anyone running the course. By looking at both the big picture and easy step-by-step methods for developing algorithms, the author guides students around the common pitfalls. He stresses paradigms such as loop invariants and recursion to unify a huge range of algorithms into a few meta-algorithms. The book fosters a deeper understanding of how and why each algorithm works. These insights are presented in a careful and clear way, helping students to think abstractly and preparing them for creating their own innovative ways to solve problems.

On the Shape of Mathematical Arguments

A. J. M. Gasteren
On the Shape of Mathematical Arguments Book PDF

Author : A. J. M. Gasteren
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 55,6 Mb
Release : 1990-07-24
Category : Computers
ISBN : 3540528490

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On the Shape of Mathematical Arguments by A. J. M. Gasteren Pdf

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. Its purpose is to show how completeness of argument, an important constraint especially for the correctness of algorithms, can be combined with brevity. The author stresses that the use of formalism is indispensible for achieving this. A second purpose of the book is to discuss matters of design. Rather than addressing psychological questions, the author deals with more technical questions like how analysis of the shape of the demonstrandum can guide the design of a proof. This technical rather than psychological view of heuristics together with the stress on exploiting formalism effectively are two key features of the book. The book consists of two independently readable parts. One part includes a number of general chapters discussing techniques for clear exposition, the use of formalism, the choice of notations, the choice of what to name and how to name it, and so on. The other part consists of a series of expositional essays, each dealing with a proof or an algorithm and illustrating the use of techniques discussed in the more general chapters.

Computer Arithmetic and Formal Proofs

Sylvie Boldo,Guillaume Melquiond
Computer Arithmetic and Formal Proofs Book PDF

Author : Sylvie Boldo,Guillaume Melquiond
Publisher : Elsevier
Page : 326 pages
File Size : 40,9 Mb
Release : 2017-11-17
Category : Computers
ISBN : 9780081011706

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Computer Arithmetic and Formal Proofs by Sylvie Boldo,Guillaume Melquiond Pdf

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

Semialgebraic Proofs and Efficient Algorithm Design

NOAH FLEMING;PRAVESH KOTHARI;TONIANN PITASSI.,Noah Fleming,Pravesh Kothari
Semialgebraic Proofs and Efficient Algorithm Design Book PDF

Author : NOAH FLEMING;PRAVESH KOTHARI;TONIANN PITASSI.,Noah Fleming,Pravesh Kothari
Publisher : Unknown
Page : 221 pages
File Size : 46,8 Mb
Release : 2019
Category : Algorithms
ISBN : 1680836374

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Semialgebraic Proofs and Efficient Algorithm Design by NOAH FLEMING;PRAVESH KOTHARI;TONIANN PITASSI.,Noah Fleming,Pravesh Kothari Pdf

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.

Sams Teach Yourself Data Structures and Algorithms in 24 Hours

Robert Lafore
Sams Teach Yourself Data Structures and Algorithms in 24 Hours Book PDF

Author : Robert Lafore
Publisher : Sams Publishing
Page : 570 pages
File Size : 51,6 Mb
Release : 1999
Category : Algorithms
ISBN : UCSD:31822027930551

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Sams Teach Yourself Data Structures and Algorithms in 24 Hours by Robert Lafore Pdf

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Algorithms from THE BOOK

Kenneth Lange
Algorithms from THE BOOK Book PDF

Author : Kenneth Lange
Publisher : SIAM
Page : 227 pages
File Size : 42,5 Mb
Release : 2020-05-04
Category : Mathematics
ISBN : 9781611976175

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Algorithms from THE BOOK by Kenneth Lange Pdf

Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Written in clear, instructive language within the constraints of mathematical rigor, Algorithms from THE BOOK includes a large number of classroom-tested exercises at the end of each chapter. The appendices cover background material often omitted from undergraduate courses. Most of the algorithm descriptions are accompanied by Julia code, an ideal language for scientific computing. This code is immediately available for experimentation. Algorithms from THE BOOK is aimed at first-year graduate and advanced undergraduate students. It will also serve as a convenient reference for professionals throughout the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences.

Book of Proof

Richard H. Hammack
Book of Proof Book PDF

Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 49,5 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116

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Book of Proof by Richard H. Hammack Pdf

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Mathematical Writing

Donald E. Knuth,Tracy Larrabee,Paul M. Roberts
Mathematical Writing Book PDF

Author : Donald E. Knuth,Tracy Larrabee,Paul M. Roberts
Publisher : Cambridge University Press
Page : 132 pages
File Size : 53,9 Mb
Release : 1989
Category : Language Arts & Disciplines
ISBN : 088385063X

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Mathematical Writing by Donald E. Knuth,Tracy Larrabee,Paul M. Roberts Pdf

This book will help those wishing to teach a course in technical writing, or who wish to write themselves.

Understanding Machine Learning

Shai Shalev-Shwartz,Shai Ben-David
Understanding Machine Learning Book PDF

Author : Shai Shalev-Shwartz,Shai Ben-David
Publisher : Cambridge University Press
Page : 415 pages
File Size : 49,6 Mb
Release : 2014-05-19
Category : Computers
ISBN : 9781107057135

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Understanding Machine Learning by Shai Shalev-Shwartz,Shai Ben-David Pdf

Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.

Modern Cryptography, Probabilistic Proofs and Pseudorandomness

Oded Goldreich
Modern Cryptography Probabilistic Proofs and Pseudorandomness Book PDF

Author : Oded Goldreich
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 50,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662125212

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Modern Cryptography, Probabilistic Proofs and Pseudorandomness by Oded Goldreich Pdf

Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.

A = B

Marko Petkovsek,Herbert S Wilf,Doron Zeilberger
A B Book PDF

Author : Marko Petkovsek,Herbert S Wilf,Doron Zeilberger
Publisher : CRC Press
Page : 224 pages
File Size : 41,5 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 9781439864500

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A = B by Marko Petkovsek,Herbert S Wilf,Doron Zeilberger Pdf

This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics. From the table of contents: * Proof Machines * Tightening the Target * The Hypergeometric Database * The Five Basic Algorithms: Sister Celine's Method, Gosper&'s Algorithm, Zeilberger's Algorithm, The WZ Phenomenon, Algorithm Hyper * Epilogue: An Operator Algebra Viewpoint * The WWW Sites and the Software (Maple and Mathematica) Each chapter contains an introduction to the subject and ends with a set of exercises.