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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.

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.

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

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
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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.

Naive Lie Theory

Naive Lie Theory Author John Stillwell
ISBN-10 038778215X
Release 2008-12-15
Pages 217
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In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

Euclids Elements of Geometry Scholar s Choice Edition

Euclids Elements of Geometry   Scholar s Choice Edition Author Euclid Euclid
ISBN-10 1295988755
Release 2015-02-12
Pages 534
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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

All the Mathematics You Missed

All the Mathematics You Missed Author Thomas A. Garrity
ISBN-10 0521797071
Release 2002
Pages 347
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An essential resource for advanced undergraduate and beginning graduate students in quantitative subjects who need to quickly learn some serious mathematics.

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.

Mathematics and Its History

Mathematics and Its History Author John Stillwell
ISBN-10 9781441960528
Release 2010-08-02
Pages 662
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From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Elements of Algebra

Elements of Algebra Author Leonhard Euler
ISBN-10 PRNC:32101071982514
Release 1810
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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.

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.

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.

Burn Math Class

Burn Math Class Author Jason Wilkes
ISBN-10 9780465073818
Release 2016-03-22
Pages 400
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Forget everything you’ve been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to mathematics education—with its unwelcoming textbooks, unexplained rules, and authoritarian assertions—and sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically—and it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various “advanced” topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you’ve ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

Geometry Revealed

Geometry Revealed Author Marcel Berger
ISBN-10 3540709975
Release 2010-07-23
Pages 831
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Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.

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.

Architecture as Metaphor

Architecture as Metaphor Author Kōjin Karatani
ISBN-10 UOM:39015036063884
Release 1995
Pages 199
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In Architecture as Metaphor, Kojin Karatani detects a recurrent "will to architecture" that he argues is the foundation of all Western thinking, traversing architecture, philosophy, literature, linguistics, city planning, anthropology, political economics, psychoanalysis, and mathematics. Kojin Karatani, Japan's leading literary critic, is perhaps best known for his imaginative readings of Shakespeare, Soseki, Marx, Wittgenstein, and most recently Kant. His works, of which Origins of Modern Japanese Literature is the only one previously translated into English, are the generic equivalent to what in America is called "theory." Karatani's writings are important not only for the insights they offer on the various topics under discussion, but also as an example of a distinctly non-Western critical intervention. In Architecture as Metaphor, Karatani detects a recurrent "will to architecture" that he argues is the foundation of all Western thinking, traversing architecture, philosophy, literature, linguistics, city planning, anthropology, political economics, psychoanalysis, and mathematics. In the three parts of the book, he analyzes the complex bonds between construction and deconstruction, thereby pointing to an alternative model of "secular criticism," but in the domain of philosophy rather than literary or cultural criticism. As Karatani claims in his introduction, because the will to architecture is practically nonoexistent in Japan, he must first assume a dual role: one that affirms the architectonic (by scrutinizing the suppressed function of form) and one that pushes formalism to its collapse (by invoking Kurt Godel's incompleteness theorem). His subsequent discussions trace a path through the work of Christopher Alexander, Jane Jacobs, Gilles Deleuze, and others. Finally, amidst the drive that motivates all formalization, he confronts an unbridgeable gap, an uncontrollable event encountered in the exchange with the other; thus his speculation turns toward global capital movement. While in the present volume he mainly analyzes familiar Western texts, it is precisely for this reason that his voice discloses a distance that will add a new dimension to our English-language discourse.

Philosophy of Mathematics and Natural Science

Philosophy of Mathematics and Natural Science Author Hermann Weyl
ISBN-10 0691141207
Release 2009
Pages 311
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History of mathematics.