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Building Proofs A Practical Guide
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Book Synopsis Building Proofs: A Practical Guide by : David Stewart
Download or read book Building Proofs: A Practical Guide written by David Stewart and published by World Scientific Publishing Company. This book was released on 2015-06-10 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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.
Download or read book Good Math written by Mark C. Chu-Carroll and published by Pragmatic Bookshelf. This book was released on 2013-07-18 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.
Book Synopsis The Builder's Guide: a Practical Manual for the Use of Builders, Clerks of Works, Professional Students, and Others, Engaged in Designing Or Superintending the Construction of Buildings. Comprising a Concise and Arranged Description of Materials, and Details of Parts, with Rules and Data for Calculating Strengths, and Determining Scantlings and Dimensions; Also, Tables of Weights, Lists of Prices, Etc., Etc. With 165 Illustrations by : George Drysdale DEMPSEY
Download or read book The Builder's Guide: a Practical Manual for the Use of Builders, Clerks of Works, Professional Students, and Others, Engaged in Designing Or Superintending the Construction of Buildings. Comprising a Concise and Arranged Description of Materials, and Details of Parts, with Rules and Data for Calculating Strengths, and Determining Scantlings and Dimensions; Also, Tables of Weights, Lists of Prices, Etc., Etc. With 165 Illustrations written by George Drysdale DEMPSEY and published by . This book was released on 1851 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Mathematician’s Practical Guide to Mentoring Undergraduate Research by : Michael Dorff
Download or read book A Mathematician’s Practical Guide to Mentoring Undergraduate Research written by Michael Dorff and published by American Mathematical Soc.. This book was released on 2019-09-16 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematician's Practical Guide to Mentoring Undergraduate Research is a complete how-to manual on starting an undergraduate research program. Readers will find advice on setting appropriate problems, directing student progress, managing group dynamics, obtaining external funding, publishing student results, and a myriad of other relevant issues. The authors have decades of experience and have accumulated knowledge that other mathematicians will find extremely useful.
Book Synopsis Practical Guide to the Unit Area Method of Property Tax by : H K Dhawan
Download or read book Practical Guide to the Unit Area Method of Property Tax written by H K Dhawan and published by Allied Publishers. This book was released on with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Practical Guide to Construction Adjudication by : James Pickavance
Download or read book A Practical Guide to Construction Adjudication written by James Pickavance and published by John Wiley & Sons. This book was released on 2015-10-22 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the United Kingdom, adjudication is available as a right for parties to a construction contract, following the enactment of the Housing Grants Construction and Regeneration Act 1996. In general, within a comparatively short period of time, parties in dispute will have a decision from an adjudicator, which, except in limited circumstances, the courts will enforce. Adjudication has become the number one method of dispute resolution in the construction industry. The short timescale means that a party needs to know what to do, when to do it and be able to check that the other party and the adjudicator are following the right steps. A Practical Guide to Construction Adjudication gives parties the necessary information to achieve this. It provides a straightforward overview of the process and procedure of adjudication by reference to legislation and case law, augmented with practical guidance including suggestions on what to do or not to do, drafting tips and checklists. Separate chapters for Scotland and Northern Ireland identify and explain the differences in procedure and judicial interpretation between those jurisdictions and England and Wales, and further detailed explanations of the adjudication regimes in Australia, Ireland, Malaysia, New Zealand and Singapore are included. Each of the chapters on jurisdictions outside England and Wales has been written by senior experts in those jurisdictions to ensure the content is accurate and insightful. There are a range of helpful appendices including a bank of model form adjudication documents and tabulated detailed comparisons of the Scheme for Construction Contracts, the other major adjudication rules, the major adjudicator nominating bodies and the UK and international regimes. Readers will particularly appreciate the most comprehensive index of adjudication cases available, sorted into 260 subject headings providing immediate access to all the reported cases on any adjudication topic.
Book Synopsis Abstract State Machines, Alloy, B and Z by : Marc Frappier
Download or read book Abstract State Machines, Alloy, B and Z written by Marc Frappier and published by Springer Science & Business Media. This book was released on 2010-03-02 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the Second International Conference on Abstract State Machines, B and Z, which took place in Orford, QC, Canada, in February 2010. The 26 full papers presented were carefully reviewed and selected from 60 submissions. The book also contains two invited talks and abstracts of 18 short papers which address work in progress, industrial experience reports and tool descriptions. The papers cover recent advances in four equally rigorous methods for software and hardware development: abstract state machines (ASM), Alloy, B and Z. They share a common conceptual framework, centered around the notions of state and operation, and promote mathematical precision in the modeling, verification and construction of highly dependable systems.
Book Synopsis Building a Writing Community by : Marcia Sheehan Freeman
Download or read book Building a Writing Community written by Marcia Sheehan Freeman and published by Maupin House Publishing, Inc.. This book was released on 1995 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains how to create the philosophical and physical environment needed to develop successful writing communities in which students learn, practice, and apply writing-craft skills.
Book Synopsis Proofs and Fundamentals by : Ethan D. Bloch
Download or read book Proofs and Fundamentals written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2011-02-15 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis. This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. New to the second edition: 1) A new section about the foundations of set theory has been added at the end of the chapter about sets. This section includes a very informal discussion of the Zermelo– Fraenkel Axioms for set theory. We do not make use of these axioms subsequently in the text, but it is valuable for any mathematician to be aware that an axiomatic basis for set theory exists. Also included in this new section is a slightly expanded discussion of the Axiom of Choice, and new discussion of Zorn's Lemma, which is used later in the text. 2) The chapter about the cardinality of sets has been rearranged and expanded. There is a new section at the start of the chapter that summarizes various properties of the set of natural numbers; these properties play important roles subsequently in the chapter. The sections on induction and recursion have been slightly expanded, and have been relocated to an earlier place in the chapter (following the new section), both because they are more concrete than the material found in the other sections of the chapter, and because ideas from the sections on induction and recursion are used in the other sections. Next comes the section on the cardinality of sets (which was originally the first section of the chapter); this section gained proofs of the Schroeder–Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets. The chapter concludes with the section on the cardinality of the number systems. 3) The chapter on the construction of the natural numbers, integers and rational numbers from the Peano Postulates was removed entirely. That material was originally included to provide the needed background about the number systems, particularly for the discussion of the cardinality of sets, but it was always somewhat out of place given the level and scope of this text. The background material about the natural numbers needed for the cardinality of sets has now been summarized in a new section at the start of that chapter, making the chapter both self-contained and more accessible than it previously was. 4) The section on families of sets has been thoroughly revised, with the focus being on families of sets in general, not necessarily thought of as indexed. 5) A new section about the convergence of sequences has been added to the chapter on selected topics. This new section, which treats a topic from real analysis, adds some diversity to the chapter, which had hitherto contained selected topics of only an algebraic or combinatorial nature. 6) A new section called ``You Are the Professor'' has been added to the end of the last chapter. This new section, which includes a number of attempted proofs taken from actual homework exercises submitted by students, offers the reader the opportunity to solidify her facility for writing proofs by critiquing these submissions as if she were the instructor for the course. 7) All known errors have been corrected. 8) Many minor adjustments of wording have been made throughout the text, with the hope of improving the exposition.
Book Synopsis Discrete Mathematics with Proof by : Eric Gossett
Download or read book Discrete Mathematics with Proof written by Eric Gossett and published by John Wiley & Sons. This book was released on 2009-06-22 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.
Book Synopsis Computational Complexity by : Sanjeev Arora
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Book Synopsis Interactive Theorem Proving and Program Development by : Yves Bertot
Download or read book Interactive Theorem Proving and Program Development written by Yves Bertot and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.
Book Synopsis Practical Discrete Mathematics by : Ryan T. White
Download or read book Practical Discrete Mathematics written by Ryan T. White and published by Packt Publishing Ltd. This book was released on 2021-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science Key FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook Description Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning. What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is for This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.
Download or read book Mastering Agda written by Robert Johnson and published by HiTeX Press. This book was released on 2024-10-19 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mastering Agda: A Practical Guide to Dependently Typed Programming and Formal Verification" serves as an essential resource for developers and researchers looking to harness the full potential of Agda's advanced type system. This book meticulously covers the foundations of dependently typed programming, introducing readers to Agda's unique capabilities as both a programming language and a proof assistant. Through detailed chapters, it guides learners from basic installations to crafting complex, verified programs, emphasizing Agda’s strength in providing robust guarantees about code correctness. With a structured approach, the book delves into the core components of Agda, including inductive types, pattern matching, and dependent types, while also exploring interfacing with other languages for broader applicability. Practical examples and case studies demonstrate Agda's application in fields like cryptography, formal algorithm verification, and industrial software development. By combining theoretical insights with real-world applications, "Mastering Agda" equips readers with the knowledge and skills to improve software reliability and explore innovative programming paradigms through formal methods.
Book Synopsis Build Your Own Blockchain by : Daniel Hellwig
Download or read book Build Your Own Blockchain written by Daniel Hellwig and published by Springer Nature. This book was released on 2020-05-02 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to blockchain and distributed ledger technology. Intended as an applied guide for hands-on practitioners, the book includes detailed examples and in-depth explanations of how to build and run a blockchain from scratch. Through its conceptual background and hands-on exercises, this book allows students, teachers and crypto enthusiasts to launch their first blockchain while assuming prior knowledge of the underlying technology. How do I build a blockchain? How do I mint a cryptocurrency? How do I write a smart contract? How do I launch an initial coin offering (ICO)? These are some of questions this book answers. Starting by outlining the beginnings and development of early cryptocurrencies, it provides the conceptual foundations required to engineer secure software that interacts with both public and private ledgers. The topics covered include consensus algorithms, mining and decentralization, and many more. “This is a one-of-a-kind book on Blockchain technology. The authors achieved the perfect balance between the breadth of topics and the depth of technical discussion. But the real gem is the set of carefully curated hands-on exercises that guide the reader through the process of building a Blockchain right from Chapter 1.” Volodymyr Babich, Professor of Operations and Information Management, McDonough School of Business, Georgetown University "An excellent introduction of DLT technology for a non-technical audience. The book is replete with examples and exercises, which greatly facilitate the learning of the underlying processes of blockchain technology for all, from students to entrepreneurs.” Serguei Netessine, Dhirubhai Ambani Professor of Innovation and Entrepreneurship, The Wharton School, University of Pennsylvania "Whether you want to start from scratch or deepen your blockchain knowledge about the latest developments, this book is an essential reference. Through clear explanations and practical code examples, the authors take you on a progressive journey to discover the technology foundations and build your own blockchain. From an operations perspective, you can learn the principles behind the distributed ledger technology relevant for transitioning towards blockchain-enabled supply chains. Reading this book, you'll get inspired, be able to assess the applicability of blockchain to supply chain operations, and learn from best practices recognized in real-world examples." Ralf W. Seifert, Professor of Technology and Operations Management at EPFL and Professor of Operations Management at IMD
