Proofs from THE BOOK

Proofs from THE BOOK
Title Proofs from THE BOOK PDF eBook
Author Martin Aigner
Publisher Springer
Pages 308
Release 2014-08-06
Genre Mathematics
ISBN 3662442051

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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

Proofs from the Book
Title Proofs from the Book PDF eBook
Author Martin Aigner
Publisher Springer
Pages 265
Release 2010
Genre Analysis
ISBN 3642010377

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This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". 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. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ... 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. Moreover, the exposition makes them transparent. ..." LMS Newsletter, January 1999.

Proofs from THE BOOK

Proofs from THE BOOK
Title Proofs from THE BOOK PDF eBook
Author Martin Aigner
Publisher Springer Science & Business Media
Pages 256
Release 2004
Genre Computers
ISBN 9783540404606

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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.

Proofs from THE BOOK

Proofs from THE BOOK
Title Proofs from THE BOOK PDF eBook
Author Martin Aigner
Publisher Springer Science & Business Media
Pages 234
Release 2013-03-14
Genre Mathematics
ISBN 3662054124

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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

Proofs
Title Proofs PDF eBook
Author Jay Cummings
Publisher
Pages 511
Release 2021-01-19
Genre
ISBN

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This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own.This book covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions and relations. The text aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and conversational, and includes periodic attempts at humor.This text is also an introduction to higher mathematics. This is done in-part through the chosen examples and theorems. Furthermore, following every chapter is an introduction to an area of math. These include Ramsey theory, number theory, topology, sequences, real analysis, big data, game theory, cardinality and group theory.After every chapter are "pro-tips," which are short thoughts on things I wish I had known when I took my intro-to-proofs class. They include finer comments on the material, study tips, historical notes, comments on mathematical culture, and more. Also, after each chapter's exercises is an introduction to an unsolved problem in mathematics.In the first appendix we discuss some further proof methods, the second appendix is a collection of particularly beautiful proofs, and the third is some writing advice.

Book of Proof

Book of Proof
Title Book of Proof PDF eBook
Author Richard H. Hammack
Publisher Virginia Commonwealth University Mathematics
Pages 312
Release 2009
Genre Mathematics
ISBN

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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. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

The 1920 Edition of the Book of Mormon

The 1920 Edition of the Book of Mormon
Title The 1920 Edition of the Book of Mormon PDF eBook
Author Richard L. Saunders
Publisher Greg Kofford Books
Pages 292
Release 2022-01-25
Genre Religion
ISBN

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Members of The Church of Jesus Christ of Latter-day Saints tend to see the Book of Mormon through the lens of personal use, as a single textual and scriptural monolith—the Book of Mormon. That is somewhat natural, since we tend to have at hand and in-use, only the copy or version in our language needed to study it for inspiration. In the process, the point tends to get overlooked that while we may accept the text as inspired, the physical embodiment of that text—the Book of Mormon—is a mortal reality. The Book of Mormon, while it has a “spirit,” also has a mortal “body” (or rather, bodies) existing in space and time. As such, it has a history—and because it comes to us in the form of a book, it also has a book history. This study is divided into three parts. The first part is a straightforward history of the edition’s editing, production, and manufacturing processes. It examines key points in the reprint history of the book, following important factors in the subsequent impressions of the work across nearly thirty years of re-impressions, corrections, transfers, and one new format. The narrative crowded into chapters one through four together leave Part II to catalogue the bibliographic minutia that is the beating heart of analytic book history and which provides entertainment for true-blooded bibliophiles. The details contained in the production and manufacturing contracts and coupled to the typographical evidence explained in Part III, together resolve once and for all the question of what constitutes the 1920 edition and what does not.