Mathematics, Computer Science and Logic - A Never Ending Story

The Bruno Buchberger Festschrift
Author: Peter Paule
Publisher: Springer Science & Business Media
ISBN: 3319009664
Category: Computers
Page: 113
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This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director. More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic. Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger’s successor as director of the Research Institute for Symbolic Computation.

Turing's Legacy

Developments from Turing's Ideas in Logic
Author: Rod Downey
Publisher: Cambridge University Press
ISBN: 1107043484
Category: Computers
Page: 539
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A collection of essays celebrating the influence of Alan Turing's work in logic, computer science and related areas.

The Outer Limits of Reason

What Science, Mathematics, and Logic Cannot Tell Us
Author: Noson S. Yanofsky
Publisher: MIT Press
ISBN: 0262316781
Category: Science
Page: 424
View: 4514

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Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Mathematics for Computer Science


Author: Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher: N.A
ISBN: 9789888407064
Category:
Page: 979
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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.

Program Development in Computational Logic

A Decade of Research Advances in Logic-Based Program Development
Author: Maurice Bruynooghe,Kung-Kiu Lau
Publisher: Springer Science & Business Media
ISBN: 3540221522
Category: Computers
Page: 539
View: 3940

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1 The tenth anniversary of the LOPSTR symposium provided the incentive for this volume. LOPSTR started in 1991 as a workshop on logic program synthesis and transformation, but later it broadened its scope to logic-based program development in general, that is, program development in computational logic, and hence the title of this volume. The motivating force behind LOPSTR has been the belief that declarative paradigms such as logic programming are better suited to program development tasks than traditional non-declarative ones such as the imperative paradigm. Speci?cation, synthesis, transformation or specialization, analysis, debugging and veri?cation can all be given logical foundations, thus providing a unifying framework for the whole development process. In the past 10 years or so, such a theoretical framework has indeed begun to emerge. Even tools have been implemented for analysis, veri?cation and speci- ization. However,itisfairtosaythatsofarthefocushaslargelybeenonprogrammi- in-the-small. So the future challenge is to apply or extend these techniques to programming-in-the-large, in order to tackle software engineering in the real world. Returning to this volume, our aim is to present a collection of papers that re?ect signi?cant research e?orts over the past 10 years. These papers cover the wholedevelopmentprocess:speci?cation,synthesis,analysis,transformationand specialization, as well as semantics and systems.

Principia Mathematica


Author: Alfred North Whitehead,Bertrand Russell
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: N.A
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1089 and All that : a Journey Into Mathematics


Author: D. J. Acheson
Publisher: Oxford University Press, USA
ISBN: 9780198516231
Category: Mathematics
Page: 178
View: 6792

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This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famous cartoonists. This unusual book is one of the most readable explanations of mathematics available.

Concrete Mathematics

A Foundation for Computer Science
Author: Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik
Publisher: Addison-Wesley Professional
ISBN: 9780201558029
Category: Computers
Page: 657
View: 1048

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This book, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every discipline.

Logic as Algebra


Author: Paul Halmos,Steven Givant
Publisher: Cambridge University Press
ISBN: 9780883853276
Category: Mathematics
Page: 141
View: 8938

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An introduction to logic from the perspective of algebra.

Logic in Computer Science

Modelling and Reasoning about Systems
Author: Michael Huth,Mark Ryan
Publisher: Cambridge University Press
ISBN: 113945305X
Category: Computers
Page: N.A
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Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements to the first edition have been made throughout, with extra and expanded sections on SAT solvers, existential/universal second-order logic, micro-models, programming by contract and total correctness. The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers, and model solutions to some exercises for students.

Pythagoras' Revenge

A Mathematical Mystery
Author: Arturo Sangalli
Publisher: Princeton University Press
ISBN: 9780691049557
Category: Fiction
Page: 183
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The celebrated mathematician and philosopher Pythagoras left no writings. But what if he had and the manuscript had never been found? Where would it be located? Two mathematicians, one American, one British, set out, unbeknownst to each other, to find the missing manuscript.

Math Girls


Author: Hiroshi Yuki
Publisher: Bento Books Inc
ISBN: 0983951306
Category: Fiction
Page: 288
View: 4326

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"Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks."--Front flap.

Infinitesimal


Author: Amir Alexander
Publisher: Oneworld Publications
ISBN: 1780745338
Category: Science
Page: 368
View: 5796

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On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.

Algorithms Unlocked


Author: Thomas H. Cormen
Publisher: MIT Press
ISBN: 0262313235
Category: Computers
Page: 240
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Have you ever wondered how your GPS can find the fastest way to your destination, selecting one route from seemingly countless possibilities in mere seconds? How your credit card account number is protected when you make a purchase over the Internet? The answer is algorithms. And how do these mathematical formulations translate themselves into your GPS, your laptop, or your smart phone? This book offers an engagingly written guide to the basics of computer algorithms. In Algorithms Unlocked, Thomas Cormen -- coauthor of the leading college textbook on the subject -- provides a general explanation, with limited mathematics, of how algorithms enable computers to solve problems. Readers will learn what computer algorithms are, how to describe them, and how to evaluate them. They will discover simple ways to search for information in a computer; methods for rearranging information in a computer into a prescribed order ("sorting"); how to solve basic problems that can be modeled in a computer with a mathematical structure called a "graph" (useful for modeling road networks, dependencies among tasks, and financial relationships); how to solve problems that ask questions about strings of characters such as DNA structures; the basic principles behind cryptography; fundamentals of data compression; and even that there are some problems that no one has figured out how to solve on a computer in a reasonable amount of time.

PPDP ...


Author: ACM Special Interest Group on Programming Languages
Publisher: N.A
ISBN: N.A
Category: Declarative programming
Page: N.A
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Logic-Based Program Synthesis and Transformation

8th International Workshop, LOPSTR'98, Manchester, UK, June 15-19, 1998, Selected Papers
Author: Pierre Flener
Publisher: Springer
ISBN: N.A
Category: Computers
Page: 331
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This book presents the thoroughly refereed post-workshop proceedings of the 8th International Workshop on Logic-Based Program Synthesis and Transformation, LOPSTR'98 held in Manchester, UK in June 1998. The 16 revised full papers presented were carefully reviewed and selected during three rounds of inspection from a total of initially 36 extended abstracts submitted. Also included are eight short papers. Among the topics covered are logic specification, mathematical program construction, logic programming, computational logics, inductive program synthesis, constraint logic programs, and mathematical foundations.

Logic Based Program Synthesis and Transformation

10th International Workshop, LOPSTR 2000 London, UK, July 24-28, 2000 Selected Papers
Author: Kung-Kiu Lau
Publisher: Springer
ISBN: N.A
Category: Logic programming
Page: 183
View: 6547

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This book presents revised full papers from the 10th International Workshop on Logic-Based Program Synthesis and Transformation, LOPSTR 2000, held in London, UK, in July 2000 as part of the International Conference on Computational Logic. The 10 revised full papers presented have gone through two rounds of reviewing, selection and revision. The book is divided in topical sections on synthesis, transformation, analysis, specialization, and abstract interpretation.

Logic for Programming and Automated Reasoning

7th International Conference, LPAR 2000 Reunion Island, France, November 6-10, 2000 Proceedings
Author: Michel Parigot,Andrei Voronkov
Publisher: Springer
ISBN: 9783540412854
Category: Mathematics
Page: 490
View: 4863

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This volumecontains the papers presentedatthe SeventhInternationalC- ference on Logicfor Programmingand Automated Reasoning (LPAR 2000)held onReunionIsland,France,6–10November2000,followedbythe ReunionWo- shop on Implementation of Logic. Sixty-?ve papers were submitted to LPAR 2000 of which twenty-six papers were accepted. Submissions by the program committee members were not - lowed. There was a special category of experimental papers intended to describe implementations of systems, to report experiments with implemented systems, orto compareimplementedsystems.Eachof thesubmissionswasreviewedbyat least three program committee members and an electronic program committee meeting was held via the Internet. In addition to the refereed papers, this volume contains full papers by two of the four invited speakers, Georg Gottlob and Micha ̈ el Rusinowitch, along with an extended abstract of Bruno Courcelle’s invited lecture and an abstract of Erich Gr ̈ adel’s invited lecture. WewouldliketothankthemanypeoplewhohavemadeLPAR2000possible. We are grateful to the following groups and individuals: the program and or- nizing committees; the additional referees; the local arrangements chair Teodor Knapik; PascalManoury, who was in chargeof accommodation; Konstantin - rovin,whomaintainedthe programcommittee Webpage;andBillMcCune,who implemented the program committee management software.

Objectivity and Diversity

Another Logic of Scientific Research
Author: Sandra Harding
Publisher: University of Chicago Press
ISBN: 022624153X
Category: Philosophy
Page: 232
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Worries about scientific objectivity seem never-ending. Social critics and philosophers of science have argued that invocations of objectivity are often little more than attempts to boost the status of a claim, while calls for value neutrality may be used to suppress otherwise valid dissenting positions. Objectivity is used sometimes to advance democratic agendas, at other times to block them; sometimes for increasing the growth of knowledge, at others to resist it. Sandra Harding is not ready to throw out objectivity quite yet. For all of its problems, she contends that objectivity is too powerful a concept simply to abandon. In Objectivity and Diversity, Harding calls for a science that is both more epistemically adequate and socially just, a science that would ask: How are the lives of the most economically and politically vulnerable groups affected by a particular piece of research? Do they have a say in whether and how the research is done? Should empirically reliable systems of indigenous knowledge count as "real science"? Ultimately, Harding argues for a shift from the ideal of a neutral, disinterested science to one that prizes fairness and responsibility.