Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Download or read book Proof Theory written by Wolfram Pohlers and published by Springer. This book was released on 2009-06-10 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.
Download or read book A General Theory of Evidence and Proof written by Kevin M. Clermont and published by Springer Nature. This book was released on with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mechanizing Proof written by Donald MacKenzie and published by MIT Press. This book was released on 2004-01-30 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.
Download or read book How to Prove It written by Daniel J. Velleman and published by Cambridge University Press. This book was released on 2006-01-16 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Transition to Proof written by Neil R. Nicholson and published by CRC Press. This book was released on 2019-03-21 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology
Download or read book Miracles essential to the proof of a Divine Commission Two discourses preached Dec 30 1838 written by Joseph HUTTON (LL.D.) and published by . This book was released on 1839 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Encyclop dia of Evidence written by Edgar Whittlesey Camp and published by . This book was released on 1905 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proof and Other Dilemmas written by Bonnie Gold and published by MAA. This book was released on 2008 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Download or read book Type Theory and Formal Proof written by Rob Nederpelt and published by Cambridge University Press. This book was released on 2014-11-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.
Download or read book Handbook of Proof Theory written by S.R. Buss and published by Elsevier. This book was released on 1998-07-09 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
Download or read book The Unitary Proof of Allah Under the Light of the Quran 6th Edition written by Ender Tosun and published by ENDER TOSUN. This book was released on 2023-10-28 with total page 1702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed, consistent, complete, empirical, logical, and unitary proof of Allah by the teaching of the Quran. For the latest version of the book see: https://tinyurl.com/AAAISLAMZZZ
Download or read book Evidence and Proof in Ancient Greece written by Chris Carey and published by Cambridge Scholars Publishing. This book was released on 2024-03-26 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whether in the courts, Parliament or the pub, to persuade you need proof, be that argument- or evidence-based. But what counts as proof, and as satisfactory proof, varies from culture to culture and from context to context. This volume assembles a range of experts in ancient Greek literature to address the theme of proof from different angles and in the works of different authors and contexts. Much of the focus is on the Athenian orators, who discussed the nature and kinds of proof from at least the fourth century BC and are still the subject of lively debate. But demonstration through evidence and argument and the language of proof are not limited to the lawcourts. They have a place in other literary forms, prose and verse, including drama and historiography, and these too feature in the collection. The book will be of interest to students and professional scholars in the fields of Greek literature and law, and Greek social and political history.
Download or read book Unitary Proof of Allah Under the Light of the Quran 2nd Edition written by Ender Tosun and published by ENDER TOSUN. This book was released on 2023-08-15 with total page 1643 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a proof of Allah based on empirical and logical evidences.
Download or read book The Northeastern Reporter written by and published by . This book was released on 1914 with total page 1264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes the decisions of the Supreme Courts of Massachusetts, Ohio, Indiana, and Illinois, and Court of Appeals of New York; May/July 1891-Mar./Apr. 1936, Appellate Court of Indiana; Dec. 1926/Feb. 1927-Mar./Apr. 1936, Courts of Appeals of Ohio.
Download or read book A Preliminary Treatise on Evidence at the Common Law written by James Bradley Thayer and published by . This book was released on 1898 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proof Technology in Mathematics Research and Teaching written by Gila Hanna and published by Springer Nature. This book was released on 2019-10-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field.
