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Elements of Mathematics

Elements of Mathematics Author John Stillwell
ISBN-10 9781400880560
Release 2016-05-31
Pages 440
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Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.



The Elements of Euclid

The Elements of Euclid Author Euclid
ISBN-10 HARVARD:32044020122263
Release 1838
Pages 416
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The Elements of Euclid has been writing in one form or another for most of life. You can find so many inspiration from The Elements of Euclid also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Elements of Euclid book for free.



Euclid s Elements

Euclid s Elements Author Euclid
ISBN-10 CORNELL:31924096124197
Release 2002-08-20
Pages 499
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The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy sewn hardcover student and teacher edition in one volume, with minimal notes and a new index/glossary.



Euclid s Elements of Geometry Book 1 6 11 12 demonstrated by E Stone

Euclid s Elements of Geometry  Book 1 6  11  12       demonstrated by E  Stone Author
ISBN-10 BL:A0018130820
Release 1728
Pages
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Euclid s Elements of Geometry Book 1 6 11 12 demonstrated by E Stone has been writing in one form or another for most of life. You can find so many inspiration from Euclid s Elements of Geometry Book 1 6 11 12 demonstrated by E Stone also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Euclid s Elements of Geometry Book 1 6 11 12 demonstrated by E Stone book for free.



G del Escher Bach

G  del  Escher  Bach Author Douglas R. Hofstadter
ISBN-10 0140179976
Release 1979
Pages 777
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G del Escher Bach has been writing in one form or another for most of life. You can find so many inspiration from G del Escher Bach also informative, and entertaining. Click DOWNLOAD or Read Online button to get full G del Escher Bach book for free.



Euclid s Elements

Euclid s Elements Author Richard Fitzpatrick
ISBN-10 9780615179841
Release 2007-12-01
Pages 548
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Euclid's Elements of Geometry, with Greek and English texts in side-by-side columns.



The Four Pillars of Geometry

The Four Pillars of Geometry Author John Stillwell
ISBN-10 9780387255309
Release 2005-08-09
Pages 228
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This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises



Elements of Number Theory

Elements of Number Theory Author John Stillwell
ISBN-10 9780387217352
Release 2012-11-12
Pages 256
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Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.



Elements of Algebra

Elements of Algebra Author Leonhard Euler
ISBN-10 PRNC:32101071982514
Release 1810
Pages
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Elements of Algebra has been writing in one form or another for most of life. You can find so many inspiration from Elements of Algebra also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Elements of Algebra book for free.



All the Mathematics You Missed

All the Mathematics You Missed Author
ISBN-10 7302090858
Release 2002
Pages 347
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All the Mathematics You Missed has been writing in one form or another for most of life. You can find so many inspiration from All the Mathematics You Missed also informative, and entertaining. Click DOWNLOAD or Read Online button to get full All the Mathematics You Missed book for free.



Elementary Mathematics from an Advanced Standpoint

Elementary Mathematics from an Advanced Standpoint Author Felix Klein
ISBN-10 9781605209319
Release 2009-01-01
Pages 284
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When the mathematician Felix Klein first went to university, he was surprised at just how little what he had learned up to that point was relevant to his new studies. Professors had their own interests, and these they conveyed without regard for the math students of the future that these prospective secondary schoolteachers would one day instruct. Elementary Mathematics from an Advanced Standpoint was written to help remedy that problem. Though highly regarded as one of the finest mathematical minds of his day, Professor Klein took a great deal of interest in guiding teachers and "reducing the gap between the school and the university." Readers will come away impressed at the clarity of Klein's writing, and the ease with which he conveys complex mathematical ideas. Divided into three parts-arithmetic, algebra, and analysis-and covering such topics as complex numbers, real equations, and logarithmic and exponential functions, Klein's classic is essential reading for math instructors and students planning to become math instructors. German mathematician FELIX KLEIN (1849-1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Geometry and Famous Problems of Elementary Geometry.



Reverse Mathematics

Reverse Mathematics Author John Stillwell
ISBN-10 9781400889037
Release 2018-01-02
Pages 200
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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.



Mathematical Conversations

Mathematical Conversations Author Robin Wilson
ISBN-10 9781461301950
Release 2012-12-06
Pages 488
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Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.



Euclid s Elements in Greek

Euclid s Elements in Greek Author Richard Fitzpatrick
ISBN-10 9781430319740
Release 2007-08-01
Pages 368
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Euclid's Elements is the most famous mathematical work of classical antiquity, and has had a profound influence on the development of modern Mathematics and Physics. This volume contains the definitive Ancient Greek text of J.L. Heiberg (1883), together with an English translation. For ease of use, the Greek text and the corresponding English text are on facing pages. Moreover, the figures are drawn with both Greek and English symbols. Finally, a helpful Greek/English lexicon explaining Ancient Greek mathematical jargon is appended. Volume III contains Book 10, and covers incommesurable magnitudes.



The Automation of Proof

The Automation of Proof Author Donald A. MacKenzie
ISBN-10 IND:30000086894205
Release 1994
Pages 45
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The Automation of Proof has been writing in one form or another for most of life. You can find so many inspiration from The Automation of Proof also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Automation of Proof book for free.



The Joy of X

The Joy of X Author Steven Henry Strogatz
ISBN-10 9780547517650
Release 2012
Pages 316
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A comprehensive tour of leading mathematical ideas by an award-winning professor and columnist for the New York Times Opinionator series demonstrates how math intersects with philosophy, science and other aspects of everyday life. By the author of The Calculus of Friendship. 50,000 first printing.



Truth

Truth Author Felipe Fernandez-Armesto
ISBN-10 9781466852396
Release 2013-09-10
Pages 256
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Written by a renowned Oxford historian, this fascinating volume presents a global history of truth. Sharp and authoritative, Truth manages to touch every period of human experience; it leaps from truth-telling technologies of "primitive" societies to the private mental worlds of great philosophers; from spiritualism to science and from New York to New Guinea. In clear, lucid prose, this little book takes on an enormous subject and makes it understandable to anyone.