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Geometry & Topology


Sacred Geometry: Philosophy & Practice (Art and Imagination)

Sacred Geometry: Philosophy & Practice (Art and Imagination) Lowest new price: $9.33
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Author: Robert Lawlor
Brand: Thames & Hudson

An introduction to the geometry which, as modern science now confirms, underlies the structure of the universe.

The thinkers of ancient Egypt, Greece and India recognized that numbers governed much of what they saw in their world and hence provided an approach to its divine creator. Robert Lawlor sets out the system that determines the dimension and the form of both man-made and natural structures, from Gothic cathedrals to flowers, from music to the human body. By also involving the reader in practical experiments, he leads with ease from simple principles to a grasp of the logarithmic spiral, the Golden Proportion, the squaring of the circle and other ubiquitous ratios and proportions.

Art and Imagination: These large-format, gloriously-illustrated paperbacks cover Eastern and Western religion and philosophy, including myth and magic, alchemy and astrology. The distinguished authors bring a wealth of knowledge, visionary thinking and accessible writing to each intriguing subject. 202 illustrations and diagrams, 56 in two colors

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Byrne: Six Books of Euclid

Byrne: Six Books of Euclid Lowest new price: $14.94
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Author: Werner Oechslin
Brand: Oechslin Werner

Elemental
Ancient Greek mathematics meet modernist design

Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th-century mathematician Oliver Byrne employed the color scheme for his 1847 edition of Euclid’s mathematical and geometric treatise Elements. Byrne’s idea was to use color to make learning easier and “diffuse permanent knowledge.” The result has been described as one of the oddest and most beautiful books of the 19th century.

The facsimile of Byrne’s vivid publication is now available as part of TASCHEN’s Bibliotheca Universalis series. A masterwork of art and science, it is as beautiful in the boldness of its red, yellow, and blue figures and diagrams as it is in the mathematical precision of its theories. In the simplicity of forms and colors, the pages anticipate the vigor of De Stijl and Bauhaus design. In making complex information at once accessible and aesthetically engaging, this work is a forerunner to the information graphics that today define much of our data consumption.

Text in English, French, and German

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Sacred Geometry: Deciphering the Code

Sacred Geometry: Deciphering the Code Lowest new price: $10.00
Lowest used price: $7.89
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Author: Stephen Skinner
Brand: Sterling Publishing

A fascinating and inspirational look at the vital link between the hidden geometrical order of the universe, geometry in nature, and the geometry of the man-made world.

The Da Vinci Code has awakened the public to the powerful and very ancient idea that religious truths and mathematical principles are intimately intertwined. Sacred Geometry offers an accessible way of understanding how that connection is revealed in nature and the arts. Over the centuries, temple builders have relied on magic numbers to shape sacred spaces, astronomers have used geometry to calculate holy seasons, and philosophers have observed the harmony of the universe in the numerical properties of music. By showing how the discoveries of mathematics are manifested over and over again in biology and physics, and how they have inspired the greatest works of art, this illuminating study reveals the universal principles that link us to the infinite.

 

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Topology (Classic Version) (2nd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Topology (Classic Version) (2nd Edition) (Pearson Modern Classics for Advanced Mathematics Series) Lowest new price: $90.95
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Author: James Munkres

For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately.


This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles.


This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.

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Algebraic Topology

Algebraic Topology Lowest new price: $39.18
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Author: Allen Hatcher
Brand: Brand: Cambridge University Press

In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

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E-Z Geometry (Barron's E-Z Series)

E-Z Geometry (Barron's E-Z Series) Lowest new price: $4.45
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Author: Lawrence S. Leff
Brand: Brand: Barron's Educational Series

Known for many years as Barron’s Easy Way Series, the new editions of these popular self-teaching titles are now Barron’s E-Z Series. Brand-new cover designs reflect all new page layouts, which feature extensive two-color treatment, a fresh, modern typeface, and more graphic material than ever— charts, graphs, diagrams, instructive line illustrations, and where appropriate, amusing cartoons. Meanwhile, the quality of the books’ contents remains at least as high as ever. Barron’s E-Z books are self-help manuals focused to improve students’ grades in a wide variety of academic and practical subjects. For most subjects, the level of difficulty ranges between high school and college-101 standards. Although primarily designed as self-teaching manuals, these books are also preferred by many teachers as classroom supplements—and for some courses, as main textbooks. E-Z books review their subjects in detail, and feature both short quizzes and longer tests with answers to help students gauge their learning progress. Subject heads and key phrases are set in a second color as an easy reference aid. Barron’s E-Z Geometry covers the "how" and "why" of geometry, with examples, exercises, and solutions throughout, plus hundreds of drawings, graphs, and tables.

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Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)

Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218) Lowest new price: $69.99
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Author: John Lee
Brand: Brand: Springer

This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.

This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.

Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.

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Geometry (Translations of Mathematical Monographs)

Geometry (Translations of Mathematical Monographs) Lowest new price: $88.00
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Author: V. V. Prasolov

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.


Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Lowest new price: $9.99
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Author: John Derbyshire
Brand: John Derbyshire

In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.”  Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae.

In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. --Therese Littleton

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Geometry Part 1 (Quickstudy Reference Guides - Academic)

Geometry Part 1 (Quickstudy Reference Guides - Academic) Lowest new price: $4.95
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Author: Inc. BarCharts
Brand: QuickStudy

Coverage of the fundamental structure of geometry.

Part 1 of two guides on geometry.

 

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