Logic and Combinatorics
| Author | : Stephen George Simpson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 408 |
| Release | : 1987 |
| Genre | : Combinatorial analysis |
| ISBN | : 0821850520 |
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Algebra, Logic And Combinatorics
| Author | : Shaun Bullett |
| Publisher | : World Scientific |
| Total Pages | : 184 |
| Release | : 2016-04-21 |
| Genre | : Mathematics |
| ISBN | : 1786340321 |
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This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
Counting and Configurations
| Author | : Jiri Herman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 402 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475739257 |
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This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.
Logic and Discrete Mathematics
| Author | : Willem Conradie |
| Publisher | : John Wiley & Sons |
| Total Pages | : 195 |
| Release | : 2015-05-08 |
| Genre | : Mathematics |
| ISBN | : 1119000106 |
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Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.
On Sets and Graphs
| Author | : Eugenio G. Omodeo |
| Publisher | : Springer |
| Total Pages | : 283 |
| Release | : 2017-05-11 |
| Genre | : Computers |
| ISBN | : 3319549812 |
Download On Sets and Graphs Book in PDF, ePub and Kindle
This treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problems and insight panels.
Combinatorial Set Theory
| Author | : Lorenz J. Halbeisen |
| Publisher | : Springer |
| Total Pages | : 586 |
| Release | : 2017-12-20 |
| Genre | : Mathematics |
| ISBN | : 3319602314 |
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This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.
Finite and Infinite Combinatorics in Sets and Logic
| Author | : Norbert W Sauer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 452 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401120803 |
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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.
The Strange Logic of Random Graphs
| Author | : Joel Spencer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 167 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662045389 |
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The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.
Logic and Combinatorics
| Author | : |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1987-12-30 |
| Genre | : |
| ISBN | : 9780821850527 |
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Contains articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California. This work consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'.
Lambda-Calculus and Combinators
| Author | : J. Roger Hindley |
| Publisher | : Cambridge University Press |
| Total Pages | : 358 |
| Release | : 2008-07-24 |
| Genre | : Computers |
| ISBN | : 9780521898850 |
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Combinatory logic and lambda-calculus, originally devised in the 1920's, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this long-awaited new version is thoroughly revised and offers a fully up-to-date account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.
