Tristan Needham's Books

Visual Differential Geometry and Forms

A Mathematical Drama in Five Acts

By: Tristan Needham

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Visual Differential Geometry and Forms

A Mathematical Drama in Five Acts

By: Tristan Needham

An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

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Page Count

530

Publisher

Princeton University Press

Published Date

ISBN 10

0691203695

ISBN 13

9780691203690

Visual Differential Geometry and Forms

A Mathematical Drama in Five Acts

By: Tristan Needham

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Visual Differential Geometry and Forms

A Mathematical Drama in Five Acts

By: Tristan Needham

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N/A

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Solve jigsaw puzzle

Age

Page Count

530

Publisher

Princeton University Press

Published Date

ISBN 10

0691203695

ISBN 13

9780691203690

Laws of the Land

Fengshui and the State in Qing Dynasty China

By: Tristan G. Brown

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Laws of the Land

Fengshui and the State in Qing Dynasty China

By: Tristan G. Brown

A groundbreaking history of fengshui’s roles in public life and law during China’s last imperial dynasty Today the term fengshui, which literally means “wind and water,” is recognized around the world. Yet few know exactly what it means, let alone its fascinating history. In Laws of the Land, Tristan Brown tells the story of the important roles—especially legal ones—played by fengshui in Chinese society during China’s last imperial dynasty, the Manchu Qing (1644–1912). Employing archives from Mainland China and Taiwan that have only recently become available, this is the first book to document fengshui’s invocations in Chinese law during the Qing dynasty. Facing a growing population, dwindling natural resources, and an overburdened rural government, judicial administrators across China grappled with disputes and petitions about fengshui in their efforts to sustain forestry, farming, mining, and city planning. Laws of the Land offers a radically new interpretation of these legal arrangements: they worked. An intelligent, considered, and sustained engagement with fengshui on the ground helped the imperial state keep the peace and maintain its legitimacy, especially during the increasingly turbulent decades of the nineteenth century. As the century came to an end, contentious debates over industrialization swept across the bureaucracy, with fengshui invoked by officials and scholars opposed to the establishment of railways, telegraphs, and foreign-owned mines. Demonstrating that the only way to understand those debates and their profound stakes is to grasp fengshui’s longstanding roles in Chinese public life, Laws of the Land rethinks key issues in the history of Chinese law, politics, science, religion, and economics.

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Page Count

360

Publisher

Princeton University Press

Published Date

ISBN 10

0691246726

ISBN 13

9780691246727

Visual Complex Analysis

By: Tristan Needham

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Visual Complex Analysis

By: Tristan Needham

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

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Page Count

620

Publisher

Oxford University Press

Published Date

ISBN 10

0198534469

ISBN 13

9780198534464

Visual Complex Analysis

25th Anniversary Edition

By: Tristan Needham

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Visual Complex Analysis

25th Anniversary Edition

By: Tristan Needham

Complex Analysis is the powerful fusion of the complex numbers (involving the 'imaginary' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years. This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality. This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new way—as a highbrow comic book!

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Page Count

720

Publisher

Oxford University Press

Published Date

ISBN 10

0192695452

ISBN 13

9780192695451

Book's by Tristan Needham

Visual Differential Geometry and Forms

Visual Differential Geometry and Forms

Visual Differential Geometry and Forms

Visual Differential Geometry and Forms

Laws of the Land

Laws of the Land

Visual Complex Analysis

Visual Complex Analysis

Visual Complex Analysis

Visual Complex Analysis

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