Topology Via Logic
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Author | : Steven Vickers |
Publisher | : Cambridge University Press |
Total Pages | : 224 |
Release | : 1989 |
Genre | : Computers |
ISBN | : 9780521576512 |
Now in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.
Author | : Stephen Barr |
Publisher | : Courier Corporation |
Total Pages | : 244 |
Release | : 2012-12-04 |
Genre | : Mathematics |
ISBN | : 048615274X |
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Author | : Jorge Picado |
Publisher | : Springer Science & Business Media |
Total Pages | : 412 |
Release | : 2011-10-21 |
Genre | : Mathematics |
ISBN | : 3034801548 |
Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent. Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory. No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.
Author | : Lorenzo Adlai Sadun |
Publisher | : American Mathematical Soc. |
Total Pages | : 131 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821847279 |
"This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Author | : Peter T. Johnstone |
Publisher | : Cambridge University Press |
Total Pages | : 398 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : 9780521337793 |
A unified treatment of the corpus of mathematics that has developed out of M. H. Stone's representation theorem for Boolean algebras (1936) which has applications in almost every area of modern mathematics.
Author | : Dominique Perrin |
Publisher | : Academic Press |
Total Pages | : 560 |
Release | : 2004-02-18 |
Genre | : Computers |
ISBN | : 9780125321112 |
Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures.
Author | : Maria Manzano |
Publisher | : Cambridge University Press |
Total Pages | : 414 |
Release | : 1996-03-29 |
Genre | : Computers |
ISBN | : 9780521354356 |
An introduction to many-sorted logic as an extension of first-order logic.
Author | : Maria Cristina Pedicchio |
Publisher | : Cambridge University Press |
Total Pages | : 452 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780521834148 |
Author | : N. Shankar |
Publisher | : Cambridge University Press |
Total Pages | : 224 |
Release | : 1997-01-30 |
Genre | : Computers |
ISBN | : 9780521585330 |
Describes the use of computer programs to check several proofs in the foundations of mathematics.