Functional Differential Geometry

Gerald Jay Sussman, Jack Wisdom, Will Farr (Northwestern University)

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English

MIT Press
27 May 2025

Geometry

An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.

An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.

Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Miserables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.

The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.

By: Gerald Jay Sussman, Jack Wisdom
With: Will Farr (Northwestern University)
Imprint: MIT Press
Country of Publication: United States
Dimensions: Height: 229mm, Width: 152mm,
Weight: 369g
ISBN: 9780262052894
ISBN 10: 026205289X
Pages: 248
Publication Date: 27 May 2025
Recommended Age: From 18 years
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Inactive

Gerald Jay Sussman is Panasonic Professor of Electrical Engineering at MIT. Jack Wisdom is Professor of Planetary Science at MIT.