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Author : A. Hajnal,László Lovász,Vera T. Sós
Publisher : North Holland
Page : 446 pages
File Size : 51,8 Mb
Release : 1984
Category : Mathematics
ISBN : PSU:000011067368
Author : A. Hajnal,L. Lovász,V. T. Sós
Publisher : Elsevier
Page : 438 pages
File Size : 50,8 Mb
Release : 2014-05-15
Category : Mathematics
ISBN : 9781483161228
Colloquia Mathematica Societatis Jânos Bolyai, 37: Finite and Infinite Sets, Vol. I focuses on the principles, operations, and approaches involved in finite and infinite sets. The selection first elaborates on essential chains and squares, cellular automata in trees, almost disjoint families of countable sets, and application of Lovasz local lemma. Discussions focus on deleting operations, number of all and self-dual E-chains, transversality of E-chains and E-squares, and binary E-chains and E-squares. The text then elaborates on induced subgraphs, inverse extremal digraph problems, two Sperner-type conditions, and minimal decomposition of all graphs with equinumerous vertices and edges into mutually isomorphic subgraphs. Topics include general digraph extremal problem, matrix graphs and quadratic forms, augmentation of matrices, set of attained densities, proof of the continuity theorem, and inverse extremal multigraph problems. The text examines circular flows in graphs, two-colorings of simple arrangements, monochromatic paths in infinite colored graphs, and graphs associated with an integral domain and their applications. The selection is a dependable reference for researchers interested in finite and infinite sets.
Author : Harrie de Swart
Publisher : Springer
Page : 539 pages
File Size : 46,7 Mb
Release : 2018-11-28
Category : Philosophy
ISBN : 9783030032555
This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo
Author : Larry Gerstein
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 46,9 Mb
Release : 2013-11-21
Category : Science
ISBN : 9781468467086
This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.
Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 43,7 Mb
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 0131877186
Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
Author : David Gries,Fred B. Schneider
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 48,7 Mb
Release : 1993-10-22
Category : Computers
ISBN : 0387941150
Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in its willingness to go one step further. The book traets logic as a basic tool which may be applied in essentially every other area.
Author : Edward B. Burger,Michael Starbird
Publisher : Springer Science & Business Media
Page : 798 pages
File Size : 47,7 Mb
Release : 2004-08-18
Category : Mathematics
ISBN : 1931914419
Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.
Author : Norbert W Sauer,R.E. Woodrow,B. Sands
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401120807
This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.
Author : Cristian S. Calude,Gheorghe Paun
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447107514
The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g. , does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g. , what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus' activity, to whom this volume is dedicated. They range from real analysis to DNA com puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical "open problems". They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.
Author : J. R. Conner
Publisher : Xlibris Corporation
Page : 173 pages
File Size : 40,9 Mb
Release : 2011-08-01
Category : Philosophy
ISBN : 9781669829362
“The present volume is the first in a projected trilogy, the other two of which are ‘On the Logical Demonstration of Divine Existence’ and ‘On the Logical Origins of Right’. The entire work could be described as an essay concerning the ontological basis of political philosophy. “What an elementary work on the logic of infinitary sets can possibly have to do with political philosophy will become apparent only as the various arguments unfold. The connection is reasonably straightforward, however, and has to do with the relation of what I call ‘analytic impressionism’ to the general rationale of revolution: it is to regard a contradictory, anomalous, or even immoral situation—a fantasia of some kind—as a done thing and then cook up a story about how, notwithstanding, it might have been accomplished or justified rationally. The goal of all this is to be able to do with a certain impunity whatever you can contrive to get away with, and in particular to appropriate the primacy of right for oneself: all of which is rooted in the desiccated ontology of virtualization and results in a narcissistic and infantilized culture.” From the Preface
Author : James Carse
Publisher : Simon and Schuster
Page : 256 pages
File Size : 49,5 Mb
Release : 2011-10-11
Category : Philosophy
ISBN : 9781451657296
“There are at least two kinds of games,” states James Carse as he begins this extraordinary book. “One could be called finite; the other infinite.” Finite games are the familiar contests of everyday life; they are played in order to be won, which is when they end. But infinite games are more mysterious. Their object is not winning, but ensuring the continuation of play. The rules may change, the boundaries may change, even the participants may change—as long as the game is never allowed to come to an end. What are infinite games? How do they affect the ways we play our finite games? What are we doing when we play—finitely or infinitely? And how can infinite games affect the ways in which we live our lives? Carse explores these questions with stunning elegance, teasing out of his distinctions a universe of observation and insight, noting where and why and how we play, finitely and infinitely. He surveys our world—from the finite games of the playing field and playing board to the infinite games found in culture and religion—leaving all we think we know illuminated and transformed. Along the way, Carse finds new ways of understanding everything from how an actress portrays a role, to how we engage in sex, from the nature of evil, to the nature of science. Finite games, he shows, may offer wealth and status, power and glory. But infinite games offer something far more subtle and far grander. Carse has written a book rich in insight and aphorism. Already an international literary event, Finite and Infinite Games is certain to be argued about and celebrated for years to come. Reading it is the first step in learning to play the infinite game.
Author : Fred Katz
Publisher : Unknown
Page : 120 pages
File Size : 53,6 Mb
Release : 2017-03-05
Category : Electronic
ISBN : 1544217609
Cantor's theory of cardinality violates common sense. It says, for example, thatall infinite sets of integers are the same size. This thesis criticizes the argumentsfor Cantor's theory and presents an alternative.The alternative is based on a general theory, CS (for Class Size). CSconsists of all sentences in the �rst order language with a subset predicate and aless-than predicate which are true in all interpretations of that language whosedomain is a �nite power set. Thus, CS says that less than is a linear orderingwith highest and lowest members and that every set is larger than any of itsproper subsets. Because the language of CS is so restricted, CS will have infiniteinterpretations. In particular, the notion of one-one correspondence cannotbe expressed in this language, so Cantor's definition of similarity will not be inCS, even though it is true for all finite sets.
Author : Sterling K. Berberian
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 42,7 Mb
Release : 2013-03-15
Category : Mathematics
ISBN : 0387984801
"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS
Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 41,9 Mb
Release : 2014-06-01
Category : Mathematics
ISBN : 9780486795492
Accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Topics include classes and sets, functions, natural and cardinal numbers, arithmetic of ordinal numbers, and more. 1971 edition with new material by author.
Author : Frederick Goodman
Publisher : SemiSimple Press (Frederick Goodman)
Page : 586 pages
File Size : 47,6 Mb
Release : 2014-01-10
Category : Mathematics
ISBN : 9780979914218
This text provides a thorough introduction to “modern” or “abstract” algebra at a level suitable for upper-level undergraduates and beginning graduate students. The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme. This subject matter is central and ubiquitous in modern mathematics and in applications ranging from quantum physics to digital communications. The most important goal of this book is to engage students in the ac- tive practice of mathematics.