Where S The Proof
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Proofs From The Book
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Proofs From The Book written by Martin Aigner 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 2013-06-29 with Mathematics categories.
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Logical Foundations Of Proof Complexity
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Author : Stephen Cook
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-25
Logical Foundations Of Proof Complexity written by Stephen Cook 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 2010-01-25 with Mathematics categories.
This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. The result is a uniform treatment of many systems in the literature.
Intuitionistic Proof Versus Classical Truth
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Author : Enrico Martino
language : en
Publisher: Springer
Release Date : 2018-02-23
Intuitionistic Proof Versus Classical Truth written by Enrico Martino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.
The Proof
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Author : Frederick Schauer
language : en
Publisher: Harvard University Press
Release Date : 2022-05-31
The Proof written by Frederick Schauer and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Law categories.
Winner of the Scribes Book Award “Displays a level of intellectual honesty one rarely encounters these days...This is delightful stuff.” —Barton Swaim, Wall Street Journal “At a time when the concept of truth itself is in trouble, this lively and accessible account provides vivid and deep analysis of the practices addressing what is reliably true in law, science, history, and ordinary life. The Proof offers both timely and enduring insights.” —Martha Minow, former Dean of Harvard Law School “His essential argument is that in assessing evidence, we need, first of all, to recognize that evidence comes in degrees...and that probability, the likelihood that the evidence or testimony is accurate, matters.” —Steven Mintz, Inside Higher Education “I would make Proof one of a handful of books that all incoming law students should read...Essential and timely.” —Emily R. D. Murphy, Law and Society Review In the age of fake news, trust and truth are hard to come by. Blatantly and shamelessly, public figures deceive us by abusing what sounds like evidence. To help us navigate this polarized world awash in misinformation, preeminent legal theorist Frederick Schauer proposes a much-needed corrective. How we know what we think we know is largely a matter of how we weigh the evidence. But evidence is no simple thing. Law, science, public and private decision making—all rely on different standards of evidence. From vaccine and food safety to claims of election-fraud, the reliability of experts and eyewitnesses to climate science, The Proof develops fresh insights into the challenge of reaching the truth. Schauer reveals how to reason more effectively in everyday life, shows why people often reason poorly, and makes the case that evidence is not just a matter of legal rules, it is the cornerstone of judgment.
Proof Theory
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Author : Gaisi Takeuti
language : en
Publisher: Courier Corporation
Release Date : 2013-01-01
Proof Theory written by Gaisi Takeuti and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics. The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
Proof And System Reliability
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Author : Helmut Schwichtenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Proof And System Reliability 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 Mathematics categories.
As society comes to rely increasingly on software for its welfare and prosperity there is an urgent need to create systems in which it can trust. Experience has shown that confidence can only come from a more profound understanding of the issues, which in turn can come only if it is based on logically sound foundations. This volume contains contributions from leading researchers in the critical disciplines of computing and information science, mathematics, logic, and complexity. All contributions are self-contained, aiming at comprehensibility as well as comprehensiveness. The volume also contains introductory hints to technical issues, concise surveys, introductions, and various fresh results and new perspectives.
Proof And Proving In Mathematics Education
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-14
Proof And Proving In Mathematics Education written by Gila Hanna 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 2012-06-14 with Education categories.
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Proof Methods For Modal And Intuitionistic Logics
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Author : M. Fitting
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Proof Methods For Modal And Intuitionistic Logics written by M. Fitting 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 2013-04-18 with Philosophy categories.
"Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.
Formal Semantics And Proof Techniques For Optimizing Vhdl Models
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Author : Kothanda Umamageswaran
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Formal Semantics And Proof Techniques For Optimizing Vhdl Models written by Kothanda Umamageswaran 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 Technology & Engineering categories.
Written expressly for hardware designers, this book presents a formal model of VHDL clearly specifying both the static and dynamic semantics of VHDL. It provides a mathematical framework for representing VHDL constructs and shows how those constructs can be formally manipulated to reason about VHDL.
An Introduction To Proof Through Real Analysis
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Author : Daniel J. Madden
language : en
Publisher: John Wiley & Sons
Release Date : 2017-09-12
An Introduction To Proof Through Real Analysis written by Daniel J. Madden and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-12 with Education categories.
An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.