Proving Possibility Properties

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How to Prove It

Author : Daniel J. Velleman
Publisher : Cambridge University Press
ISBN 13 : 0521861241
Total Pages : 401 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis How to Prove It by : Daniel J. Velleman

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.

Book of Proof

Author : Richard H. Hammack
Publisher :
ISBN 13 : 9780989472111
Total Pages : 314 pages
Book Rating : 4.4/5 (721 download)

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Book Synopsis Book of Proof by : Richard H. Hammack

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.

Discrete Mathematics

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781534970748
Total Pages : 342 pages
Book Rating : 4.9/5 (77 download)

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Book Synopsis Discrete Mathematics by : Oscar Levin

Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2016-08-16 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.

Proofs from THE BOOK

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3662223430
Total Pages : 194 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Proofs from THE BOOK by : Martin Aigner

Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Formalized Probability Theory and Applications Using Theorem Proving

Author : Hasan, Osman
Publisher : IGI Global
ISBN 13 : 1466683163
Total Pages : 310 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Formalized Probability Theory and Applications Using Theorem Proving by : Hasan, Osman

Download or read book Formalized Probability Theory and Applications Using Theorem Proving written by Hasan, Osman and published by IGI Global. This book was released on 2015-03-31 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists and engineers often have to deal with systems that exhibit random or unpredictable elements and must effectively evaluate probabilities in each situation. Computer simulations, while the traditional tool used to solve such problems, are limited in the scale and complexity of the problems they can solve. Formalized Probability Theory and Applications Using Theorem Proving discusses some of the limitations inherent in computer systems when applied to problems of probabilistic analysis, and presents a novel solution to these limitations, combining higher-order logic with computer-based theorem proving. Combining practical application with theoretical discussion, this book is an important reference tool for mathematicians, scientists, engineers, and researchers in all STEM fields.

A Practical Theory of Reactive Systems

Author : R. Kurki-Suonio
Publisher : Springer Science & Business Media
ISBN 13 : 3540273484
Total Pages : 428 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis A Practical Theory of Reactive Systems by : R. Kurki-Suonio

Download or read book A Practical Theory of Reactive Systems written by R. Kurki-Suonio and published by Springer Science & Business Media. This book was released on 2005-07-20 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A man may imagine he understands something, but still not understand anything in the way that he ought to. (Paul of Tarsus, 1 Corinthians 8:2) Calling this a ‘practical theory’ may require some explanation. Theory and practice are often thought of as two di?erent worlds, governed bydi?erentideals,principles, andlaws.DavidLorgeParnas, forinstance,who hascontributedmuchtoourtheoreticalunderstandingofsoftwareengineering and also to sound use of theory in the practice of it, likes to point out that ‘theoretically’ is synonymous to ‘not really’. In applied mathematics the goal is to discover useful connections between these two worlds. My thesis is that in software engineering this two-world view is inadequate, and a more intimate interplay is required between theory and practice. That is, both theoretical and practical components should be integrated into a practical theory. It should beclearfrom theabovethattheintended readership of this book is not theoreticians. They would probably have di?culties in appreciating a book on theory where the presentation does not proceed in a logical sequence from basic de?nitions to theorems and mathematical proofs, followed by - plication examples. In fact, all this would not constitute what I understand by a practical theory in this context.

Probability

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Probability by : Rick Durrett

Download or read book Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Interactive Theorem Proving

Author : Marko Van Eekelen
Publisher : Springer
ISBN 13 : 3642228631
Total Pages : 394 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Interactive Theorem Proving by : Marko Van Eekelen

Download or read book Interactive Theorem Proving written by Marko Van Eekelen and published by Springer. This book was released on 2011-08-02 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Interactive Theorem proving, ITP 2011, held in Berg en Dal, The Netherlands, in August 2011. The 25 revised full papers presented were carefully reviewed and selected from 50 submissions. Among the topics covered are counterexample generation, verification, validation, term rewriting, theorem proving, computability theory, translations from one formalism to another, and cooperation between tools. Several verification case studies were presented, with applications to computational geometry, unification, real analysis, etc.

Lectures on Probability Theory and Mathematical Statistics - 3rd Edition

Author : Marco Taboga
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781981369195
Total Pages : 670 pages
Book Rating : 4.3/5 (691 download)

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Book Synopsis Lectures on Probability Theory and Mathematical Statistics - 3rd Edition by : Marco Taboga

Download or read book Lectures on Probability Theory and Mathematical Statistics - 3rd Edition written by Marco Taboga and published by Createspace Independent Publishing Platform. This book was released on 2017-12-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.

Introduction to Property Testing

Author : Oded Goldreich
Publisher : Cambridge University Press
ISBN 13 : 1107194059
Total Pages : 473 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Introduction to Property Testing by : Oded Goldreich

Download or read book Introduction to Property Testing written by Oded Goldreich and published by Cambridge University Press. This book was released on 2017-11-23 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive and authoritative introduction to property testing, the study of super-fast algorithms for the structural analysis of large quantities of data in order to determine global properties. This book can be used both as a reference book and a textbook, and includes numerous exercises.

Beyond Two: Theory and Applications of Multiple-Valued Logic

Author : Melvin Fitting
Publisher : Physica
ISBN 13 : 3790817694
Total Pages : 374 pages
Book Rating : 4.7/5 (98 download)

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Book Synopsis Beyond Two: Theory and Applications of Multiple-Valued Logic by : Melvin Fitting

Download or read book Beyond Two: Theory and Applications of Multiple-Valued Logic written by Melvin Fitting and published by Physica. This book was released on 2013-06-05 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

Lectures on Embedded Systems

Author : Grzegorz Rozenberg
Publisher : Springer Science & Business Media
ISBN 13 : 9783540651932
Total Pages : 446 pages
Book Rating : 4.6/5 (519 download)

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Book Synopsis Lectures on Embedded Systems by : Grzegorz Rozenberg

Download or read book Lectures on Embedded Systems written by Grzegorz Rozenberg and published by Springer Science & Business Media. This book was released on 1998-10-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originates from the School on Embedded Systems held in Veldhoven, The Netherlands, in November 1996 as the first event organized by the European Educational Forum. Besides thoroughly reviewed and revised chapters based on lectures given during the school, additional papers have been solicited for inclusion in the present book in order to complete coverage of the relevant topics. The authors adress professionals involved in the design and management of embedded systems in industry as well as researchers and students interested in a competent survey. The book will convince the reader that many architectural and algorithmic problems in the area of embedded systems have well documented optimal or correct solutions, notably in the fields of real-time computing, distributed computing, and fault-tolerant computing.

Program = Proof

Author : Samuel Mimram
Publisher :
ISBN 13 :
Total Pages : 539 pages
Book Rating : 4.6/5 (155 download)

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Book Synopsis Program = Proof by : Samuel Mimram

Download or read book Program = Proof written by Samuel Mimram and published by . This book was released on 2020-07-03 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This course provides a first introduction to the Curry-Howard correspondence between programs and proofs, from a theoretical programmer's perspective: we want to understand the theory behind logic and programming languages, but also to write concrete programs (in OCaml) and proofs (in Agda). After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.

Introduction to Probability

Author : Joseph K. Blitzstein
Publisher : CRC Press
ISBN 13 : 1466575573
Total Pages : 599 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Introduction to Probability by : Joseph K. Blitzstein

Download or read book Introduction to Probability written by Joseph K. Blitzstein and published by CRC Press. This book was released on 2014-07-24 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Current Law

Author :
Publisher :
ISBN 13 :
Total Pages : 2422 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Current Law by :

Download or read book Current Law written by and published by . This book was released on 1911 with total page 2422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Correct Hardware Design and Verification Methods

Author : Dominique Borrione
Publisher : Springer
ISBN 13 : 354032030X
Total Pages : 423 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Correct Hardware Design and Verification Methods by : Dominique Borrione

Download or read book Correct Hardware Design and Verification Methods written by Dominique Borrione and published by Springer. This book was released on 2005-10-07 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods, CHARME 2005, held in Saarbrücken, Germany, in October 2005. The 21 revised full papers and 18 short papers presented together with 2 invited talks and one tutorial were carefully reviewed and selected from 79 submissions. The papers are organized in topical sections on functional approaches to design description, game solving approaches, abstraction, algorithms and techniques for speeding (DD-based) verification, real time and LTL model checking, evaluation of SAT-based tools, model reduction, and verification of memory hierarchy mechanisms.