Building Proofs
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Building Proofs A Practical Guide
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Author : David Stewart
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-06-10
Building Proofs A Practical Guide written by David Stewart and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-10 with Mathematics categories.
This book introduces students to the art and craft of writing proofs, beginning with the basics of writing proofs and logic, and continuing on with more in-depth issues and examples of creating proofs in different parts of mathematics, as well as introducing proofs-of-correctness for algorithms. The creation of proofs is covered for theorems in both discrete and continuous mathematics, and in difficulty ranging from elementary to beginning graduate level.Just beyond the standard introductory courses on calculus, theorems and proofs become central to mathematics. Students often find this emphasis difficult and new. This book is a guide to understanding and creating proofs. It explains the standard “moves” in mathematical proofs: direct computation, expanding definitions, proof by contradiction, proof by induction, as well as choosing notation and strategies.
Types For Proofs And Programs
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Author : Stefano Berardi
language : en
Publisher: Springer
Release Date : 2009-06-07
Types For Proofs And Programs written by Stefano Berardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-07 with Computers categories.
These proceedings contain a selection of refereed papers presented at or - lated to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held during March 26–29, 2008 in Turin, Italy. The topic of this workshop, and of all previous workshops of the same project, was f- mal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certi?ed software, mobile code, formali- tion of mathematics, mathematics education. The workshop was attended by more than 100 researchers and included more than 40 presentations. We also had three invited lectures, from A. Asperti (University of Bologna), G. Dowek (LIX, Ecole polytechnique, France) and J. W. Klop (Vrije Universiteit, A- terdam, The Netherlands). From 27 submitted papers, 19 were selected after a reviewing process. Each submitted paper was reviewed by three referees; the ?nal decisions were made by the editors. This workshop is the last of a series of meetings of the TYPES working group funded by the European Union (IST project 29001, ESPRIT Working Group 21900, ESPRIT BRA 6435).
Types For Proofs And Programs
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Author : Hendrik Pieter Barendregt
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-05-20
Types For Proofs And Programs written by Hendrik Pieter Barendregt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-20 with Computers categories.
This volume contains thoroughly refereed and revised full papers selected from the presentations at the first workshop held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs in Nijmegen, The Netherlands, in May 1993. As the whole ESPRIT BRA 6453, this volume is devoted to the theoretical foundations, design and applications of systems for theory development. Such systems help in designing mathematical axiomatisation, performing computer-aided logical reasoning, and managing databases of mathematical facts; they are also known as proof assistants or proof checkers.
Tests And Proofs
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Author : Achim Brucker
language : en
Publisher: Springer
Release Date : 2012-05-26
Tests And Proofs written by Achim Brucker and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-26 with Computers categories.
This book constitutes the refereed proceedings of the 6th International Conference on Test and Proofs, TAP 2012, held in Prague, Czech Republic, in May/June 2012, as part of the TOOLS 2012 Federated Conferences. The 9 revised full papers presented together with 2 invited papers, 4 short papers and one tutorial were carefully reviewed and selected from 29 submissions. The papers are devoted to the convergence of tests and proofs for developing novel techniques and application that support engineers in building secure, safe, and reliable systems. Among the topics covered are model-based testing; scenario-based testing; complex data structure generation; and the validation of protocols and libraries.
Automated Model Building
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Author : Ricardo Caferra
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Automated Model Building written by Ricardo Caferra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Philosophy categories.
On the history of the book: In the early 1990s several new methods and perspectives in au- mated deduction emerged. We just mention the superposition calculus, meta-term inference and schematization, deductive decision procedures, and automated model building. It was this last ?eld which brought the authors of this book together. In 1994 they met at the Conference on Automated Deduction (CADE-12) in Nancy and agreed upon the general point of view, that semantics and, in particular, construction of models should play a central role in the ?eld of automated deduction. In the following years the deduction groups of the laboratory LEIBNIZ at IMAG Grenoble and the University of Technology in Vienna organized several bilateral projects promoting this topic. This book emerged as a main result of this cooperation. The authors are aware of the fact, that the book does not cover all relevant methods of automated model building (also called model construction or model generation); instead the book focuses on deduction-based symbolic methods for the construction of Herbrand models developed in the last 12 years. Other methods of automated model building, in particular also ?nite model building, are mainly treated in the ?nal chapter; this chapter is less formal and detailed but gives a broader view on the topic and a comparison of di?erent approaches. Howtoreadthisbook: In the introduction we give an overview of automated deduction in a historical context, taking into account its relationship with the human views on formal and informal proofs.
Proof And Computation
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Author : Helmut Schwichtenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Proof And Computation written by Helmut Schwichtenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Logical concepts and methods are of growing importance in many areas of computer science. The proofs-as-programs paradigm and the wide acceptance of Prolog show this clearly. The logical notion of a formal proof in various constructive systems can be viewed as a very explicit way to describe a computation procedure. Also conversely, the development of logical systems has been influenced by accumulating knowledge on rewriting and unification techniques. This volume contains a series of lectures by leading researchers giving a presentation of new ideas on the impact of the concept of a formal proof on computation theory. The subjects covered are: specification and abstract data types, proving techniques, constructive methods, linear logic, and concurrency and logic.
Human Interactive Proofs
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Author : Henry S. Baird
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-12
Human Interactive Proofs written by Henry S. Baird and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-12 with Computers categories.
This book constitutes the refereed proceedings of the Second International Workshop on Human Interactive Proofs, HIP 2005, held in Bethlehem, PA, USA in May 2005. The 9 revised full papers presented were carefully reviewed and selected for presentation. This book is the first archival publication devoted to the new class of security protocols called human interactive proofs. The variant of HIPs being used in e-commerce and Web services today is completely automatic public Turing tests to tell computers and humans apart, CAPTCHAs. The papers in this book are organized in topical sections on CAPTCHAs and performance analysis, HIP architectures, HIP as security systems components.
Machine Proofs In Geometry Automated Production Of Readable Proofs For Geometry Theorems
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Author : Shang-ching Chou
language : en
Publisher: World Scientific
Release Date : 1994-04-06
Machine Proofs In Geometry Automated Production Of Readable Proofs For Geometry Theorems written by Shang-ching Chou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-06 with Mathematics categories.
This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16
How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Proof Technology And Computation
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Author : Helmut Schwichtenberg
language : en
Publisher: IOS Press
Release Date : 2006
Proof Technology And Computation written by Helmut Schwichtenberg and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
Proof technology aims at integrating proof processing into industrial design and verifications tools. The chapters in this book deal with: the benefits and technical challenges of sharing formal mathematics among interactive theorem provers; proof normalization for various axiomatic theories; and more.