Proofs From The Book

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Proofs from THE BOOK

Download Proofs From The Book Book or Ebook File with PDF Epub Audio and Full format File

Author by : Martin Aigner, Günter M. Ziegler
Languange Used : English, France, Spanish, Italia and chinese
Page : 326
Isbn : 3662572656
Identifier : 9783662572658
Release : 2018-06-14
Publisher by : Springer
Category : Mathematics
Total Download : 3959561
Total Read : 8880006
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Description : Read Now Proofs From The Book by Martin Aigner, Günter M. Ziegler and you can download with pub, pdf, txt, doc, and more file format with free account. this revised and enlarged sixth edition of proofs from the book features an entirely new chapter on van der waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. from the citation on the occasion of the 2018 "steele prize for mathematical exposition" “... it is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet aigner and ziegler accomplish this feat of exposition with virtuoso style. [...] this book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.” from the reviews "... 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. there is vast wealth within its pages, one gem after another. ... aigner and ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." i do. ... " notices of the ams, august 1999 "... this book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... it is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." lms newsletter, january 1999 "martin aigner and günter ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the book of erdös. the theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " sigact news, december 2011

Proofs from THE BOOK

Download Proofs From The Book Book or Ebook File with PDF Epub Audio and Full format File

Author by : Martin Aigner, Günter M. Ziegler
Languange Used : English, France, Spanish, Italia and chinese
Page : 308
Isbn : 3662442051
Identifier : 9783662442050
Release : 2014-08-06
Publisher by : Springer
Category : Mathematics
Total Download : 2311076
Total Read : 2010030
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Description : Read Now Proofs From The Book by Martin Aigner, Günter M. Ziegler and you can download with pub, pdf, txt, doc, and more file format with free account. this revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the borromean rings and other surprises. from the reviews "... 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. there is vast wealth within its pages, one gem after another. ... aigner and ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." i do. ... " notices of the ams, august 1999 "... this book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... it is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." lms newsletter, january 1999 "martin aigner and günter ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the book of erdös. the theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " sigact news, december 2011.

Proofs from THE BOOK

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Author by : Martin Aigner, Günter M. Ziegler
Languange Used : English, France, Spanish, Italia and chinese
Page : 274
Isbn : 3642008569
Identifier : 9783642008566
Release : 2010-01-08
Publisher by : Springer Science & Business Media
Category : Mathematics
Total Download : 2360526
Total Read : 8705073
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Description : Read Now Proofs From The Book by Martin Aigner, Günter M. Ziegler and you can download with pub, pdf, txt, doc, and more file format with free account. paulerdos ? likedtotalkaboutthebook,inwhichgodmaintainstheperfect proofsformathematicaltheorems,followingthedictumofg. h. hardythat there is no permanent place for ugly mathematics. erdos ? also said that you need not believe in god but, as a mathematician, you should believe in the book. a few years ago, we suggested to him to write up a ?rst (and very modest) approximation to the book. he was enthusiastic about the idea and, characteristically, went to work immediately, ?lling page after page with his suggestions. our book was supposed to appear in march 1998 as a present to erdos ? ’ 85th birthday. with paul’s unfortunate death in the summer of 1996, he is not listed as a co-author. instead this book is dedicated to his memory. ? paul erdos we have no de?nition or characterization of what constitutes a proof from the book: all we offer here is the examples that we have selected, h- ing that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations. we also hope that our readers will enjoy this despite the imperfections of our exposition. the selection is to a ? great extent in?uencedby paul erdos himself. a largenumberof the topics were suggested by him, and many of the proofs trace directly back to him, or were initiated by his supreme insight in asking the right question or in makingthe rightconjecture. so to a largeextentthisbookre?ectstheviews of paul erdos ? as to what should be considered a proof from the book.

Reverse Mathematics Proofs from the Inside Out

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Author by : John Stillwell
Languange Used : English, France, Spanish, Italia and chinese
Page : 200
Isbn : 1400889030
Identifier : 9781400889037
Release : 2018-01-02
Publisher by : Princeton University Press
Category : Mathematics
Total Download : 9939755
Total Read : 2855095
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Description : Read Now Reverse Mathematics by John Stillwell and you can download with pub, pdf, txt, doc, and more file format with free account. this book presents reverse mathematics to a general mathematical audience for the first time. reverse mathematics is a new field that answers some old questions. in the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. in reverse mathematics, john stillwell gives a representative view of this field, emphasizing basic analysis—finding the “right axioms” to prove fundamental theorems—and giving a novel approach to logic. stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. the first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. the second was the twentieth-century arithmetization of logic and computation. thus arithmetic in some sense underlies analysis, logic, and computation. reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, stillwell finds the “right axiom” to prove it. by using a minimum of mathematical logic in a well-motivated way, reverse mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

Book of Proof

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Author by : Richard H Hammack
Languange Used : English, France, Spanish, Italia and chinese
Page : 382
Isbn : 9780989472128
Identifier : 0989472124
Release : 2018-10
Publisher by :
Category : Mathematics
Total Download : 1434977
Total Read : 108522
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Description : Read Now Book Of Proof by Richard H Hammack and you can download with pub, pdf, txt, doc, and more file format with free account. this book is an introduction to the language and standard proof methods of mathematics. it is a bridge from the computational courses 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.

How to Prove It A Structured Approach

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Author by : Daniel J. Velleman
Languange Used : English, France, Spanish, Italia and chinese
Page :
Isbn : 1139450972
Identifier : 9781139450973
Release : 2006-01-16
Publisher by : Cambridge University Press
Category : Mathematics
Total Download : 8647183
Total Read : 4596640
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Description : Read Now How To Prove It by Daniel J. Velleman and you can download with pub, pdf, txt, doc, and more file format with free account. 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.

Journey into Mathematics An Introduction to Proofs

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Author by : Joseph J. Rotman
Languange Used : English, France, Spanish, Italia and chinese
Page : 256
Isbn : 0486151689
Identifier : 9780486151687
Release : 2013-01-18
Publisher by : Courier Corporation
Category : Mathematics
Total Download : 7788180
Total Read : 5841650
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Description : Read Now Journey Into Mathematics by Joseph J. Rotman and you can download with pub, pdf, txt, doc, and more file format with free account. this treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

Introduction to Proof in Abstract Mathematics

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Author by : Andrew Wohlgemuth
Languange Used : English, France, Spanish, Italia and chinese
Page : 384
Isbn : 0486141683
Identifier : 9780486141688
Release : 2014-06-10
Publisher by : Courier Corporation
Category : Mathematics
Total Download : 5012944
Total Read : 5502766
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Description : Read Now Introduction To Proof In Abstract Mathematics by Andrew Wohlgemuth and you can download with pub, pdf, txt, doc, and more file format with free account. this undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.

Proofs Without Words Exercises in Visual Thinking

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Author by : Malcolm Scott MacKenzie, Roger B. Nelsen
Languange Used : English, France, Spanish, Italia and chinese
Page : 140
Isbn : 9780883857007
Identifier : 0883857006
Release : 1993
Publisher by : MAA
Category : Mathematics
Total Download : 6087699
Total Read : 5316444
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Description : Read Now Proofs Without Words by Malcolm Scott MacKenzie, Roger B. Nelsen and you can download with pub, pdf, txt, doc, and more file format with free account. proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. while in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. the proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integer sums; and sequences and series. teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

Proof in Geometry With "Mistakes in Geometric Proofs"

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Author by : A. I. Fetisov, Ya. S. Dubnov
Languange Used : English, France, Spanish, Italia and chinese
Page : 128
Isbn : 0486154920
Identifier : 9780486154923
Release : 2012-06-11
Publisher by : Courier Corporation
Category : Mathematics
Total Download : 6561021
Total Read : 1500139
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Description : Read Now Proof In Geometry by A. I. Fetisov, Ya. S. Dubnov and you can download with pub, pdf, txt, doc, and more file format with free account. 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.

How to Read and Do Proofs An Introduction to Mathematical Thought Processes

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Author by : Daniel Solow
Languange Used : English, France, Spanish, Italia and chinese
Page : 336
Isbn : 9781118164020
Identifier : 1118164024
Release : 2013-07-29
Publisher by : John Wiley & Sons
Category : Mathematics
Total Download : 4064951
Total Read : 3438810
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Description : Read Now How To Read And Do Proofs by Daniel Solow and you can download with pub, pdf, txt, doc, and more file format with free account. the inclusion in practically every chapter of new material on how to read and understand proofs as they are typically presented in class lectures, textbooks, and other mathematical literature. the goal is to provide sufficient examples (and exercises) to give students the ability to learn mathematics on their own.

Problems and Proofs in Numbers and Algebra

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Author by : Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn
Languange Used : English, France, Spanish, Italia and chinese
Page : 223
Isbn : 3319144278
Identifier : 9783319144276
Release : 2015-02-09
Publisher by : Springer
Category : Mathematics
Total Download : 6213541
Total Read : 688330
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Description : Read Now Problems And Proofs In Numbers And Algebra by Richard S. Millman, Peter J. Shiue, Eric Brendan Kahn and you can download with pub, pdf, txt, doc, and more file format with free account. focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. the benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. this book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. to achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. the problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. in the past, pna has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. pna is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.

Writing Proofs in Analysis

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Author by : Jonathan M. Kane
Languange Used : English, France, Spanish, Italia and chinese
Page : 347
Isbn : 3319309676
Identifier : 9783319309675
Release : 2016-05-28
Publisher by : Springer
Category : Mathematics
Total Download : 4652344
Total Read : 9903457
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Description : Read Now Writing Proofs In Analysis by Jonathan M. Kane and you can download with pub, pdf, txt, doc, and more file format with free account. 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.

A = B

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Author by : Marko Petkovsek, Herbert S Wilf, Doron Zeilberger
Languange Used : English, France, Spanish, Italia and chinese
Page : 224
Isbn : 1439864500
Identifier : 9781439864500
Release : 1996-01-01
Publisher by : CRC Press
Category : Mathematics
Total Download : 7648055
Total Read : 7677796
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Description : Read Now A = B by Marko Petkovsek, Herbert S Wilf, Doron Zeilberger and you can download with pub, pdf, txt, doc, and more file format with free account. this book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. it presents a breakthrough method for analyzing complex summations. beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics. from the table of contents: * proof machines * tightening the target * the hypergeometric database * the five basic algorithms: sister celine's method, gosper&'s algorithm, zeilberger's algorithm, the wz phenomenon, algorithm hyper * epilogue: an operator algebra viewpoint * the www sites and the software (maple and mathematica) each chapter contains an introduction to the subject and ends with a set of exercises.

Certified Programming with Dependent Types A Pragmatic Introduction to the Coq Proof Assistant

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Author by : Adam Chlipala
Languange Used : English, France, Spanish, Italia and chinese
Page : 424
Isbn : 0262026651
Identifier : 9780262026659
Release : 2013-12-06
Publisher by : MIT Press
Category : Computers
Total Download : 6855645
Total Read : 9271438
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Description : Read Now Certified Programming With Dependent Types by Adam Chlipala and you can download with pub, pdf, txt, doc, and more file format with free account. a handbook to the coq software for writing and checking mathematical proofs, with a practical engineering focus.

Charming Proofs A Journey Into Elegant Mathematics

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Author by : Claudi Alsina, Roger B. Nelsen
Languange Used : English, France, Spanish, Italia and chinese
Page : 295
Isbn : 0883853485
Identifier : 9780883853481
Release : 2010
Publisher by : MAA
Category : Mathematics
Total Download : 9540492
Total Read : 2878909
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Description : Read Now Charming Proofs by Claudi Alsina, Roger B. Nelsen and you can download with pub, pdf, txt, doc, and more file format with free account. a collection of remarkable proofs that are exceptionally elegant, and thus invite the reader to enjoy the beauty of mathematics.