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| 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.
| Author | : Steven Vickers |
| Publisher | : Cambridge University Press |
| Total Pages | : 220 |
| Release | : 1996-08-22 |
| Genre | : Computers |
| ISBN | : 9780521576512 |
This advanced textbook on topology 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 author freely exploits the methods of locale theory. Third, there is substantial discussion of some computer science applications. 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 for computer scientists.
| Author | : Ernest Nagel |
| Publisher | : Lulu.com |
| Total Pages | : 132 |
| Release | : 2018-09-14 |
| Genre | : Gödel's theorem |
| ISBN | : 0359079261 |
In 1931 Kurt Gödel published his paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Gödel’s paper challenged certain basic assumptions underlying much research in mathematics and logic. However, few scholars were unable to understand Gödel’s ideas. Ernest Nagel and James Newman provide a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.
| Author | : Ernest Nagel |
| Publisher | : |
| Total Pages | : 118 |
| Release | : 1971 |
| Genre | : |
| ISBN | : |
| Author | : Gregory J. Chaitin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 148 |
| Release | : 1999-07-01 |
| Genre | : Mathematics |
| ISBN | : 9789814021722 |
This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER
| Author | : Rebecca Goldstein |
| Publisher | : W. W. Norton & Company |
| Total Pages | : 299 |
| Release | : 2006-01-31 |
| Genre | : Biography & Autobiography |
| ISBN | : 0393327604 |
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
| Author | : Roman Murawski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 416 |
| Release | : 2013-03-14 |
| Genre | : Philosophy |
| ISBN | : 9401728666 |
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
| Author | : Mark C. Chu-Carroll |
| Publisher | : Pragmatic Bookshelf |
| Total Pages | : 261 |
| Release | : 2013-07-18 |
| Genre | : Computers |
| ISBN | : 168050360X |
Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.
| Author | : Petr Hájek |
| Publisher | : Cambridge University Press |
| Total Pages | : 475 |
| Release | : 2017-03-02 |
| Genre | : Mathematics |
| ISBN | : 1107168414 |
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
| Author | : Dov M. Gabbay |
| Publisher | : Newnes |
| Total Pages | : 737 |
| Release | : 2014-12-09 |
| Genre | : Mathematics |
| ISBN | : 0080930670 |
Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: “Calculemus . The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications. Chapters by leading authorities in the field Provides a forum where philosophers and scientists interact Comprehensive reference source on the history of logic
