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Functional Differential Geometry (Mit Press) Illustrated Edition

by Gerald Jay Sussman (Author), Jack Wisdom (Author), Will Farr (Contributor)
4.6 4.6 out of 5 stars 13 ratings
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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.

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  1. ISBN-10
    0262019345
  2. ISBN-13
    978-0262019347
  3. Edition
    Illustrated
  4. Publisher
    The MIT Press
  5. Publication date
    July 5, 2013
  6. Language
    English
  7. Dimensions
    6.25 x 0.56 x 9.25 inches
  8. Print length
    248 pages
  9. See all details
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Editorial Reviews

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.

Product details

  • Publisher ‏ : ‎ The MIT Press; Illustrated edition (July 5, 2013)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 248 pages
  • ISBN-10 ‏ : ‎ 0262019345
  • ISBN-13 ‏ : ‎ 978-0262019347
  • Item Weight ‏ : ‎ 15.8 ounces
  • Dimensions ‏ : ‎ 6.25 x 0.56 x 9.25 inches
  • Customer Reviews:
    4.6 4.6 out of 5 stars 13 ratings

About the author

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Gerald Jay Sussman

Gerald Jay Sussman

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Gerald Jay Sussman (February 8, 1947) is the Panasonic Professor of Electrical Engineering at the Massachusetts Institute of Technology (MIT). He received his S.B. and Ph.D. degrees in mathematics from MIT in 1968 and 1973 respectively. He has been involved in artificial intelligence research at MIT since 1964. His research has centered on understanding the problem-solving strategies used by scientists and engineers, with the goals of automating parts of the process and formalizing it to provide more effective methods of science and engineering education. Sussman has also worked in computer languages, in computer architecture and in VLSI design.

Bio from Wikipedia, the free encyclopedia. Photo by Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science [CC BY-SA 1.0 (http://creativecommons.org/licenses/by-sa/1.0)], via Wikimedia Commons.

Customer reviews

4.6 out of 5 stars
4.6 out of 5
13 global ratings

Top reviews from the United States

W. Ghost
5.0 out of 5 stars Excellent book!
Reviewed in the United States on July 4, 2014
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.
21 people found this helpful
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Alexander Stojanovic
4.0 out of 5 stars Intriguing use of Scheme to study core concepts of Differential Geometry
Reviewed in the United States on February 21, 2015
Verified Purchase
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.
13 people found this helpful
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Top reviews from other countries

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vinu varghese
4.0 out of 5 stars Need an additional package called scmutils to work
Reviewed in India on October 25, 2021
Verified Purchase
Book doesn't mention that we need an additional package called scmutils.
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hape
2.0 out of 5 stars Schöne Idee, nur leider nicht umgesetzt
Reviewed in Germany on August 6, 2016
Verified Purchase
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).
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