Proofs From The Book
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Proofs From The Book
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Proofs From The Book written by Martin Aigner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The mathematical heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background.
Proofs From The Book
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Proofs From The Book written by Martin Aigner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Proofs From The Book
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
Proofs From The Book written by Martin Aigner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
Inside PFTB ("Proofs from The Book") is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. Some of the proofs are classics, but many are new and brilliant proofs of classical results--"Notices of the AMS," August 1999.
Book Of Proof
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Author : Richard H. Hammack
language : en
Publisher:
Release Date : 2016-01-01
Book Of Proof written by Richard H. Hammack and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-01 with Mathematics categories.
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.
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.
Why Prove It Again
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Author : John W. Dawson, Jr.
language : en
Publisher: Birkhäuser
Release Date : 2015-07-15
Why Prove It Again written by John W. Dawson, Jr. and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16
How To Prove It written by Daniel J. Velleman 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 2006-01-16 with Mathematics categories.
This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
Formal Proofs In Maths
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Author : Chris Lavranos
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2015-07-15
Formal Proofs In Maths written by Chris Lavranos and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with categories.
The scope of Formal Proofs in Maths is to teach students between higher school classes and University undergraduate or postgraduate studies, how to write a formal proof with the true meaning of the concept, of simple theorems in Algebra, particulary in identities concerning equalities, equations and inequalities. This is accomplished by writing four different types of proof namely type(A), type(B), type(C) and type(D) for each theorem or exercise. In TYPE(A) ordinary proofs will be cited in the usual narrative style used by experienced mathematicians. In TYPE(B) a rigorous proof in steps will be introduced to the reader. Each line of that proof will be justified by an appropriate axiom, theorem or definition. In TYPE(C) we will try for a smooth transition from a rigorous proof to a formal proof exposing the way that the laws of logic apply on one or more statements of the proof. In TYPE(D) we will simply write in tabular stepwise form, the results of TYPE(C) mentioning both: 1) Axioms, theorems or definitions. 2) The laws of logic. Hence, finally producing a formal proof according to the definition given in the preface note of the book.
Proof In Geometry
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Author : A. I. Fetisov
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11
Proof In Geometry written by A. I. Fetisov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Mathematics categories.
This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Introduction To Proof In Abstract Mathematics
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Author : Andrew Wohlgemuth
language : en
Publisher: Courier Corporation
Release Date : 2014-06-10
Introduction To Proof In Abstract Mathematics written by Andrew Wohlgemuth and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-10 with Mathematics categories.
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.