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Download or read book Computer Assisted Proofs and Their Effects on Pure Mathematics: A Case Study of the Four Colour Theorem written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas L. Saaty
Publisher :
ISBN 13 : 9780486650920
Total Pages : 217 pages
Book Rating : 4.6/5 (59 download)
Download or read book The Four-color Problem written by Thomas L. Saaty and published by . This book was released on 1986 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolf Fritsch
Publisher : Springer Science & Business Media
ISBN 13 : 1461217202
Total Pages : 269 pages
Book Rating : 4.4/5 (612 download)
Download or read book The Four-Color Theorem written by Rudolf Fritsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
Author : Kenneth I. Appel
Publisher : American Mathematical Soc.
ISBN 13 : 0821851039
Total Pages : 760 pages
Book Rating : 4.8/5 (218 download)
Download or read book Every Planar Map is Four Colorable written by Kenneth I. Appel and published by American Mathematical Soc.. This book was released on 1989 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.
Author : Ashay Dharwadker
Publisher : Institute of Mathematics
ISBN 13 : 1466265302
Total Pages : 84 pages
Book Rating : 4.4/5 (662 download)
Download or read book The Four Colour Theorem written by Ashay Dharwadker and published by Institute of Mathematics. This book was released on 2000-08-05 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new proof of the famous four colour theorem using algebraic and topological methods. This proof was first announced by the Canadian Mathematical Society in 2000 and subsequently published by Orient Longman and Universities Press of India in 2008. Recent research in physics shows that this proof directly implies the Grand Unification of the Standard Model with Quantum Gravity in its physical interpretation and conversely the existence of the standard model of particle physics shows that nature applies this proof of the four colour theorem at the most fundamental level.
Author : Andrew Aberdein
Publisher : Springer Science & Business Media
ISBN 13 : 9400765347
Total Pages : 392 pages
Book Rating : 4.4/5 (7 download)
Download or read book The Argument of Mathematics written by Andrew Aberdein and published by Springer Science & Business Media. This book was released on 2013-07-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
Author :
Publisher : National Geographic Books
ISBN 13 : 9781426201240
Total Pages : 520 pages
Book Rating : 4.2/5 (12 download)
Download or read book The Knowledgebook written by and published by National Geographic Books. This book was released on 2007 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, visual reference, enhanced by two thousand photographs and illustrations, provides information on all major fields of knowledge and includes timelines, sidebars, cross-reference, and other useful features.
Author :
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Education written by and published by . This book was released on 1986 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : National Geographic
Publisher : National Geographic Books
ISBN 13 : 142620518X
Total Pages : 404 pages
Book Rating : 4.4/5 (262 download)
Download or read book The Knowledgebook written by National Geographic and published by National Geographic Books. This book was released on 2009 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Indispensable for every home, library, and office, this handbook distills thousands of years of humankind's most significant ideas and achievements, explains how they are linked, and packs everything into a single, irresistibly readable volume. Illustrations.
Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author : Eric Lehman
Publisher :
ISBN 13 : 9789888407064
Total Pages : 988 pages
Book Rating : 4.4/5 (7 download)
Download or read book Mathematics for Computer Science written by Eric Lehman and published by . This book was released on 2017-03-08 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Author :
Publisher : Academic Press
ISBN 13 : 0080873391
Total Pages : 277 pages
Book Rating : 4.0/5 (88 download)
Download or read book The Four-Color Problem written by and published by Academic Press. This book was released on 2011-08-29 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Four-Color Problem
Author : Frank Allaire
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (713 download)
Download or read book Another Proof of the Four Colour Theorem written by Frank Allaire and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gary Haggard
Publisher : Cengage Learning
ISBN 13 : 9780534495015
Total Pages : 0 pages
Book Rating : 4.4/5 (95 download)
Download or read book Discrete Mathematics for Computer Science written by Gary Haggard and published by Cengage Learning. This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master the fundamentals of discrete mathematics with DISCRETE MATHEMATICS FOR COMPUTER SCIENCE with Student Solutions Manual CD-ROM! An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems and this mathematics text shows you how to express precise ideas in clear mathematical language. Through a wealth of exercises and examples, you will learn how mastering discrete mathematics will help you develop important reasoning skills that will continue to be useful throughout your career.
Author : Kenneth R. Meyer
Publisher : Springer
ISBN 13 : 9781461390947
Total Pages : 0 pages
Book Rating : 4.3/5 (99 download)
Download or read book Computer Aided Proofs in Analysis written by Kenneth R. Meyer and published by Springer. This book was released on 2011-12-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.
Author : Robin J. Wilson
Publisher :
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.6/5 (531 download)
Download or read book Four Colours Suffice written by Robin J. Wilson and published by . This book was released on 2003 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-colour problem was one of the most famous and controversial conundrums ever known, and stumped thousands of puzzlers for over a century. It sounded simple- what is the least number of colours needed to fill in any map, so that neighbouring countries are always coloured differently? However, it would take over a hundred years for amateur problem-solvers and mathematicians alike to answer the question first posed by Francis Guthrie in 1852. And, even when a solution was finally found using computers, debate raged over whether this technology could ever provide the proof that traditional pen-and-paper calculations could. This is the gripping story of the race to solve the riddle - a tale of dedicated puzzlers, mind-boggling maps, human ingenuity and the great rhombicuboctahedron
Author : Norman Megill
Publisher : Lulu.com
ISBN 13 : 0359702236
Total Pages : 250 pages
Book Rating : 4.3/5 (597 download)
Download or read book Metamath: A Computer Language for Mathematical Proofs written by Norman Megill and published by Lulu.com. This book was released on 2019-06-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the "Formalizing 100 Theorems" challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.
