Proof Analysis
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Proof Analysis
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Author : Sara Negri
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29
Proof Analysis written by Sara Negri 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 2011-09-29 with Mathematics categories.
This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.
Writing Proofs In Analysis
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Author : Jonathan M. Kane
language : en
Publisher: Springer
Release Date : 2016-05-28
Writing Proofs In Analysis written by Jonathan M. Kane and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-28 with Mathematics categories.
This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.
Analysis Of Evidence
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Author : Terence Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2005-07-11
Analysis Of Evidence written by Terence Anderson 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 2005-07-11 with Law categories.
This extensively revised second edition is a rigorous introduction to the construction and criticism of arguments about questions of fact, and to the marshalling and evaluation of evidence at all stages of litigation. It covers the principles underlying the logic of proof; the uses and dangers of story-telling; standards for decision and the relationship between probabilities and proof; the chart method and other methods of analyzing and ordering evidence in fact-investigation, in preparing for trial, and in connection with other important decisions in legal processes and in criminal investigation and intelligence analysis. Most of the chapters in this new edition have been rewritten; the treatment of fact investigation, probabilities and narrative has been extended; and new examples and exercises have been added. Designed as a flexible tool for undergraduate and postgraduate courses on evidence and proof, students, practitioners and teachers alike will find this book challenging but rewarding.
On The Extraction Of Computational Content From Noneffective Convergence Proofs In Analysis
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Author : Pavol Safarik
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2014
On The Extraction Of Computational Content From Noneffective Convergence Proofs In Analysis written by Pavol Safarik and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Computers categories.
The Fields medalist, Terence Tao, recently emphasized the importance of ''hard'' (or finitary) analysis and connected the finitisation to the methods we will employ in this thesis: ... The main advantage of working in a finitary setting ... is that the underlying dynamical system becomes extremely explicit. ... In proof theory, this finitisation is known as Gödel functional interpretation ... For convergence theorems Tao calls the finitary formulation metastability and the corresponding explicit content its rate(s). In the case of the mean ergodic theorem such a rate can be used to obtain even an effective bound on the number of fluctuations. We introduce effective learnability and three other natural kinds of such finitary information and analyze the corresponding proof-theoretic conditions. Effective learnability not only provides means to know when to expect a bound on the number of fluctuations but also explains a very common pattern in the realizers for strong ergodic theorems. Moreover, we will see how a most natural example for a non-learnable convergence theorem closely relates to a notable exception to this pattern, the strong nonlinear ergodic theorem due to Wittmann. Finally, we show how can computational content be extracted in the context of non-standard analysis.
Mathematical Analysis
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Author : Bernd S. W. Schröder
language : en
Publisher: John Wiley & Sons
Release Date : 2008-01-28
Mathematical Analysis written by Bernd S. W. Schröder 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 2008-01-28 with Mathematics categories.
A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
A Probabilistic Analysis Of The Sacco And Vanzetti Evidence
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Author : Joseph B. Kadane
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-26
A Probabilistic Analysis Of The Sacco And Vanzetti Evidence written by Joseph B. Kadane 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 2011-09-26 with Mathematics categories.
A Probabilistic Analysis of the Sacco and Vanzetti Evidence is aBayesian analysis of the trial and post-trial evidence in the Saccoand Vanzetti case, based on subjectively determined probabilitiesand assumed relationships among evidential events. It applies theideas of charting evidence and probabilistic assessment to thiscase, which is perhaps the ranking cause celebre in all of Americanlegal history. Modern computation methods applied to inferencenetworks are used to show how the inferential force of evidence ina complicated case can be graded. The authors employ probabilisticassessment to obtain opinions about how influential each group ofevidential items is in reaching a conclusion about the defendants'innocence or guilt. A Probabilistic Analysis of the Sacco and Vanzetti Evidence holdsparticular interest for statisticians and probabilists in academiaand legal consulting, as well as for the legal community,historians, and behavioral scientists. It combines structural andprobabilistic ideas in the analysis of masses of evidence fromevery recognized logical species of evidence. Twenty-eight chartsshow the chains of reasoning in defense of the relevance ofevidentiary matters and a listing of trial witnesses who providedthe evidence. References include nearly 300 items drawn from thefields of probability theory, history, law, artificialintelligence, psychology, literature, and other areas.
Proofs And Refutations
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Author : Imre Lakatos
language : en
Publisher: Cambridge University Press
Release Date : 1976-01-01
Proofs And Refutations written by Imre Lakatos 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 1976-01-01 with Science categories.
Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
Trace Evidence Analysis
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Author : Max M. Houck
language : en
Publisher: Elsevier
Release Date : 2003-12-03
Trace Evidence Analysis written by Max M. Houck and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-03 with Law categories.
Trace Evidence Analysis continues and builds upon the tradition of its successful companion title Mute Witnesses (2000). The book contains nine entirely new cases, each self-contained in its own chapter, covering everything from homicides to accident reconstruction. It includes contributions from some of the premier forensic scientists in the field who provide detailed accounts of the process of collection, classification, and analysis of microscopic evidence to draw definitive conclusions that solved actual cases. The book discusses the role of evidence in solving cases and explores the legal and ethical responsibility of the forensic scientist. It examines real-world application of scientific methods and analytic principles, including evidence gathering, instrumentation, sampling methods, analysis, and interpretation; and features over 160 full-color figures that illustrate the relevant case evidence. This book is a recommended resource for forensic microscopists and trace evidence analysts, crime laboratories, crime scene technicians, criminal investigators, forensic science professionals and students, and the legal community. - Contains contributions from some of the premier forensic scientists in the field - Discusses the role of evidence in solving cases and explores the legal and ethical responsibility of the forensic scientist - Explores real-world application of scientific methods and analytic principles including evidence gathering, instrumentation, sampling methods, analysis, and interpretation - Includes over 160 full-color figures that illustrate the relevant case evidence
Tools And Algorithms For The Construction And Analysis Of Systems
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Author : Marsha Chechik
language : en
Publisher: Springer
Release Date : 2016-04-08
Tools And Algorithms For The Construction And Analysis Of Systems written by Marsha Chechik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-08 with Computers categories.
This book constitutes the proceedings of the 22nd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2016, which took place in Eindhoven, The Netherlands, in April 2016, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016. The 44 full papers presented in this volume were carefully reviewed and selected from 175 submissions. They were organized in topical sections named: abstraction and verification; probabilistic and stochastic systems; synthesis; tool papers; concurrency; tool demos; languages and automata; security; optimization; and competition on software verification – SV-COMP.
Elementary Real Analysis
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Author : Brian S. Thomson
language : en
Publisher: ClassicalRealAnalysis.com
Release Date : 2008
Elementary Real Analysis written by Brian S. Thomson and has been published by ClassicalRealAnalysis.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This is the second edition of the title originally published by Prentice Hall (Pearson) in 2001. Here is the reference information for the first edition:[TBB] Elementary Real Analysis, Brian S. Thomson, Judith B. Bruckner,Andrew M. Bruckner. Prentice-Hall, 2001, xv 735 pp. [ISBN 0-13-019075-61]The present title contains Chapters 1-8. The full version containing all of the chapters is also available as a trade paperback. A hypertexted PDF file of the entire text is available free for download on www.classicalrealanalysis.com.Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. DifferentiationChapter 8. The integral