# The Nuts And Bolts Of Proofs

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## The Nuts and Bolts of Proofs

Author : Antonella Cupillari
Release : 2001
ISBN : 9780121994518
Language : En, Es, Fr & De

Book Description :

This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography

## The Nuts and Bolts of Proofs

Author : Antonella Cupillari
Release : 2012
ISBN : 0123822173
Language : En, Es, Fr & De

Book Description :

The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. New chapter on proof by contradiction New updated proofs A full range of accessible proofs Symbols indicating level of difficulty help students understand whether a problem is based on calculus or linear algebra Basic terminology list with definitions at the beginning of the text

Author : Thomas P. Dence,Joseph B. Dence
Release : 2009-12-02
ISBN : 9780080959320
Language : En, Es, Fr & De

Book Description :

Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis – providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. It covers exponential function, and the development of trigonometric functions from the integral. The text is designed for a one-semester advanced calculus course for advanced undergraduates or graduate students. Appropriate rigor for a one-semester advanced calculus course Presents modern materials and nontraditional ways of stating and proving some results Includes precise historical notes throughout the book outstanding feature is the collection of exercises in each chapter Provides coverage of exponential function, and the development of trigonometric functions from the integral

## The Nuts and Bolts of Proofs 4th Edition

Author : Antonella Cupillari
Publisher : Unknown
Release : 2011
ISBN : 0987650XXX
Language : En, Es, Fr & De

Book Description :

The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. Jumps right in with the needed vocabulary-gets students thinking like mathematicians from the beginning Offers a large variety of examples and problems with solutions for students to work through on their own Includes a collection of exercises without solutions to help instructors prepare assignments Contains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics.

## Debugging by Thinking

Author : Robert C. Metzger
Publisher : Digital Press
Release : 2004
ISBN : 1555583075
Language : En, Es, Fr & De

Book Description :

Debugging by Thinking: A Multi-Disciplinary Approach is the first book to apply the wisdom of six disciplines-logic, mathematics, psychology, safety analysis, computer science, and engineering-to the problem of debugging. It uses the methods of literary detectives such as Sherlock Holmes, the techniques of mathematical problem solving, the results of research into the cognitive psychology of human error, the root cause analyses of safety experts, the compiler analyses of computer science, and the processes of modern engineering to define a systematic approach to identifying and correcting software errors. * Language Independent Methods: Examples are given in Java and C++ * Complete source code shows actual bugs, rather than contrived examples * Examples are accessible with no more knowledge than a course in Data Structures and Algorithms requires * A "thought process diary" shows how the author actually resolved the problems as they occurred

## How to Read and Do Proofs

Author : Daniel Solow
Publisher : John Wiley & Sons
Release : 2013-07-29
ISBN : 1118164024
Language : En, Es, Fr & De

Book Description :

This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.

## Understanding Mathematical Proof

Author : John Taylor,Rowan Garnier
Publisher : CRC Press
Release : 2016-04-19
ISBN : 1466514914
Language : En, Es, Fr & De

Book Description :

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs.Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techn

## Discrete Mathematics with Proof

Author : Eric Gossett
Publisher : John Wiley & Sons
Release : 2009-06-22
ISBN : 0470457937
Language : En, Es, Fr & De

Book Description :

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.

## Modern Algebra

Author : John R. Durbin
Publisher : John Wiley & Sons
Release : 2008-12-31
ISBN : 0470384433
Language : En, Es, Fr & De

Book Description :

Engineers and computer scientists who need a basic understanding of algebra will benefit from this accessible book. The sixth edition includes many carefully worked examples and proofs to guide them through abstract algebra successfully. It introduces the most important kinds of algebraic structures, and helps them improve their ability to understand and work with abstract ideas. New and revised exercise sets are integrated throughout the first four chapters. A more in-depth discussion is also included on Galois Theory. The first six chapters provide engineers and computer scientists with the core of the subject and then the book explores the concepts in more detail.

## The Visual Mind II

Author : Michele Emmer
Publisher : MIT Press
Release : 2005
ISBN : 9780262050760
Language : En, Es, Fr & De

Book Description :

"This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993."--BOOK JACKET.

## Green Design and Manufacturing for Sustainability

Author : Nand K. Jha
Publisher : CRC Press
Release : 2015-12-02
ISBN : 1482282380
Language : En, Es, Fr & De

Book Description :

Written by an educator with close to 40 years of experience in developing and teaching design and manufacturing courses at the graduate and undergraduate levels, Green Design and Manufacturing for Sustainability integrates green design and manufacturing within the framework of sustainability, emphasizing cost, recyclables, and reuse. It includes th

Author : Alexander Blake
Publisher : CRC Press
Release : 1986-08-29
ISBN : 9780849383793
Language : En, Es, Fr & De

Book Description :

Download What Every Engineer Should Know about Threaded Fasteners book written by Alexander Blake, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

## A Transition to Proof

Author : Neil R. Nicholson
Publisher : CRC Press
Release : 2019-03-21
ISBN : 0429522002
Language : En, Es, Fr & De

Book Description :

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

## United States Congressional Serial Set

Author : Anonim
Publisher : Unknown
Release : 1886
ISBN : 0987650XXX
Language : En, Es, Fr & De

Book Description :

Download United States Congressional Serial Set book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

## Report of the Tests of Metals and Other Materials for Industrial Purposes Made with the United States Testing Machine at Watertown Arsenal Massachusetts During the Year Ended

Author : Anonim
Publisher : Unknown
Release : 1898
ISBN : 0987650XXX
Language : En, Es, Fr & De

Book Description :

Download Report of the Tests of Metals and Other Materials for Industrial Purposes Made with the United States Testing Machine at Watertown Arsenal Massachusetts During the Year Ended book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

## Absolute Proof

Author : Peter James
Publisher : Pan Macmillan
Release : 2018-10-04
ISBN : 023077220X
Language : En, Es, Fr & De

Book Description :

'Sensational – the best what-if thriller since The Da Vinci Code' - Lee Child, author of Killing Floor. From the number one bestselling author, Peter James, comes an explosive standalone thriller for fans of Dan Brown that will grip you and won't let go until the very last page. Investigative reporter Ross Hunter nearly didn’t answer the phone call that would change his life – and possibly the world – for ever. ‘I know this is going to sound strange, but I’ve recently been given absolute proof of God’s existence – and I’ve been advised there is a writer, a respected journalist called Ross Hunter, who could help me to get taken seriously.’ What would it take to prove the existence of God? And what would be the consequences? This question and its answer lie at the heart of Absolute Proof. The false faith of a billionaire evangelist, the life’s work of a famous atheist, and the credibility of each of the world’s major religions are all under threat. If Ross Hunter can survive long enough to present the evidence . . .

## The Complete Idiot s Guide to Recession Proof Careers

Author : Jeff Cohen
Publisher : Penguin
Release : 2010-02-02
ISBN : 110119524X
Language : En, Es, Fr & De

Book Description :

Keeping your job is job one. In these uncertain economic times, secure employment is more important than ever. 'The Complete Idiot's Guide® to Recession-Proof Careers', presents all of the information needed to make an informed decision about choosing a career that ensures your continued employability. - Wide range of career fields presents a plethora of ideas for career paths - Each career is described in detail so that the reader has a clear picture of the job requirements, salary, and experience and schooling needed - Handy appendices outline the best careers by growth, salary, and geography as well as resources for job sites, fairs and organizations

## Handbook of Bolts and Bolted Joints

Author : John Bickford
Publisher : CRC Press
Release : 1998-04-28
ISBN : 9780824799779
Language : En, Es, Fr & De

Book Description :

Presenting time-tested standard as well as reliable emerging knowledge on threaded fasteners and joints, this book covers how to select parts and materials, predict behavior, control assembly processes, and solve on-the-job problems. It examines key issues affecting bolting in the automotive, pressure vessel, petrochemical, aerospace, and structural steel industries. The editors have successfully created a useful rather than scholarly handbook with chapters written in a straightforward, how-to-do-it manner. Theory is discussed only when necessary and the handbook's logical organization and thorough index enhances its usefulness.

## Introduction to the Design and Behavior of Bolted Joints Fourth Edition

Author : John H. Bickford
Publisher : CRC Press
Release : 2007-08-24
ISBN : 9780849381874
Language : En, Es, Fr & De

Book Description :

Redesigned for increased accessibility, this fourth edition of the bestselling Introduction to the Design and Behavior of Bolted Joints has been divided into two separate but complementary volumes. Each volume contains the basic information useful to bolting experts in any industry, but because the two volumes are more clearly focused, they are easier and more efficient to use. The first volume, Non-Gasketed Joints, describes the design, behavior, misbehavior, failure modes, and analysis of the bolts and bolted joints that play a large, even ubiquitous, role in the myriad machines and structures that form our world. The author elucidates why proper bolt tension - often called preload - is critical to the safety and reliability of an assembled joint. He introduces many ways to create that preload as well as ways to measure or inspect for it, then covers how to design joints that are less apt to misbehave or fail, using the guidelines, procedures, and simple algebraic mathematics included in the text. The book provides numerous tables, charts, graphs, and appendices, giving you all the information and data required to design and use non-gasketed bolted joints. Now leaner and meaner, this new edition is better suited for classrooms as well as the practicing engineer.

## Linear Optimization and Duality

Author : Craig A. Tovey
Publisher : CRC Press
Release : 2020-12-15
ISBN : 1439887470
Language : En, Es, Fr & De

Book Description :

Linear Optimization and Dualiyy: A Modern Exposition departs from convention in significant ways. Standard linear programming textbooks present the material in the order in which it was discovered. Duality is treated as a difficult add-on after coverage of formulation, the simplex method, and polyhedral theory. Students end up without knowing duality in their bones. This text brings in duality in Chapter 1 and carries duality all the way through the exposition. Chapter 1 gives a general definition of duality that shows the dual aspects of a matrix as a column of rows and a row of columns. The proof of weak duality in Chapter 2 is shown via the Lagrangian, which relies on matrix duality. The first three LP formulation examples in Chapter 3 are classic primal-dual pairs including the diet problem and 2-person zero sum games. For many engineering students, optimization is their first immersion in rigorous mathematics. Conventional texts assume a level of mathematical sophistication they don’t have. This text embeds dozens of reading tips and hundreds of answered questions to guide such students. Features Emphasis on duality throughout Practical tips for modeling and computation Coverage of computational complexity and data structures Exercises and problems based on the learning theory concept of the zone of proximal development Guidance for the mathematically unsophisticated reader About the Author Craig A. Tovey is a professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Dr. Tovey received an AB from Harvard College, an MS in computer science and a PhD in operations research from Stanford University. His principal activities are in operations research and its interdisciplinary applications. He received a Presidential Young Investigator Award and the Jacob Wolfowitz Prize for research in heuristics. He was named an Institute Fellow at Georgia Tech, and was recognized by the ACM Special Interest Group on Electronic Commerce with the Test of Time Award. Dr. Tovey received the 2016 Golden Goose Award for his research on bee foraging behavior leading to the development of the Honey Bee Algorithm.