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Author: David Stewart Publisher: World Scientific Publishing Company ISBN: 9814641324 Category : Mathematics Languages : en Pages : 175
Book Description
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.
Author: David Stewart Publisher: World Scientific Publishing Company ISBN: 9814641324 Category : Mathematics Languages : en Pages : 175
Book Description
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.
Author: Daniel J. Velleman Publisher: Cambridge University Press ISBN: 0521861241 Category : Mathematics Languages : en Pages : 401
Book Description
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.
Author: Martin Aigner Publisher: Springer Science & Business Media ISBN: 3662223430 Category : Mathematics Languages : en Pages : 194
Book Description
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.
Author: Richard H. Hammack Publisher: ISBN: 9780989472111 Category : Mathematics Languages : en Pages : 314
Book Description
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.
Author: Mark C. Chu-Carroll Publisher: Pragmatic Bookshelf ISBN: 168050360X Category : Computers Languages : en Pages : 261
Book Description
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.
Author: Michael Dorff Publisher: American Mathematical Soc. ISBN: 147044934X Category : Education Languages : en Pages : 232
Book Description
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.
Author: James Pickavance Publisher: John Wiley & Sons ISBN: 1118717937 Category : Law Languages : en Pages : 768
Book Description
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.
Author: Marc Frappier Publisher: Springer Science & Business Media ISBN: 3642118100 Category : Computers Languages : en Pages : 429
Book Description
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.
Author: David Stewart
Author: David Stewart
Author: Daniel J. Velleman
Author: Martin Aigner
Author: Richard H. Hammack
Author: Mark C. Chu-Carroll
Author: George Drysdale DEMPSEY
Author: Michael Dorff
Author: H K Dhawan
Author: James Pickavance
Author: Marc Frappier