Functional Differential Geometry (The MIT Press) by Gerald Jay Sussman (PDF)

Description

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 Misérables 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.

User’s Reviews

Editorial Reviews: Review Another gem in the tradition of Structure and Interpretation of Computer Programs and Structure and Interpretation of Classical Mechanics, providing for applied mathematics what the previous two books did for computer science and physics.―Piet Hut, Institute for Advanced Study, Princeton, New Jersey About the Author Gerald Jay Sussman is Panasonic Professor of Electrical Engineering at MIT.Jack Wisdom is Professor of Planetary Science at MIT.Will Farr is a CIERA Fellow at Northwestern University.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A solid account of Differential Geometry to study core concepts. Having computational assets embedded in the theory is an excellent idea. Suggestion: The use of Scheme might be supplemented by Clojure as a online resource. The appendix of tensors is a good refresher. Clearly aimed as an introductory text, it succeeds admirably.

⭐This is a great book! In the same spirit of Structure and Interpretation of Classical Mechanics — in order to really understand differenitial geometry, you write programs to do the computations. Sussman and Wisdom were very careful and start from the very basics up to applications on relativity and electrodynamics. There is a long appendix on notation and two shorter appendices, one explaining the basics of Scheme (the programming language used in the book), and another with a minimalist introduction to tensors.

⭐Ich habe dank absolviertem Physikstudium durchaus schon etwas Erfahrung von den im Buch besprochenen Themen gehabt. Und die ersten Seiten lesen sich dann auch ganz gut an. Die schwammige, traditionelle Notation soll ersetzt werden, durch eine eindeutigere, und der Computer soll mithelfen eine solche eindeutige Notation zu finden. Nett auch die Idee statt wie die kanonische Physikliteratur die Formalismen zu nutzen um Differentialgleichungen zu lösen und Bewegungsgleichungen zu finden, die Gleichungen einfach eher als Tests für bekannte Gleichungen zu verwenden und residuen zu bestimmen.Leider tauschen die Autoren nur eine schwammige Notation gegen eine andere Schwammige Notation aus. Die Schwammigkeit verlagert sich einfach in polymorphen Scheme-Code (dabei mag ich Scheme).Book doesn’t mention that we need an additional package called scmutils.

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