Functional Differential Geometry by Sussman, Wisdom & Farr
Functional Differential Geometry - Table of Contents
1. Introduction
2. Manifolds
3. Vector Fields and One-Form Fields
4. Basis Fields
5. Integration
6. Over a Map
7. Directional Derivatives
8. Curvature
9. Metrics
10. Hodge Star and Electrodynamics
11. Special Relativity
What You Will Learn in Functional Differential Geometry
"Functional Differential Geometry" by Gerald Jay Sussman, Jack Wisdom, and Will Farr is an unconventional and conceptually rich introduction to differential geometry, written with a strong emphasis on meaning rather than formal symbolism. The book rethinks how geometry should be learned, especially by students of physics and computation, by focusing on "functions", "structure", and "interpretation" instead of heavy tensor index manipulation.
A defining feature of the book is its integration of "computation" into mathematical understanding. The authors encourage readers to express geometric ideas as executable procedures, using programming as a way to test intuition and verify correctness. This functional perspective makes abstract ideas—such as vector fields, differential forms, curvature, and metrics—feel more concrete and operational. The approach aligns closely with modern thinking in "differential geometry", where coordinate-free reasoning and transformations take center stage.
The text is particularly well suited for readers interested in "physics", especially areas like electromagnetism and relativity, where geometry is not just formal but deeply physical. It also stands out as a thoughtful bridge between mathematics, physics, and computation, offering a fresh way to understand geometric ideas at their core.
Book Details & Specifications
Title:
Functional Differential Geometry by Sussman, Wisdom & Farr
Publisher:
The MIT Press
Year:
2013
Pages:
249
Type:
PDF
Language:
English
ISBN-10 #:
0262019345
ISBN-13 #:
978-0262019347
License:
CC BY-NC-SA 4.0
Amazon:
Amazon
About the Author: Gerald Jay Sussman, Jack Wisdom, Will Farr
The author
Gerald Jay Sussman, Jack Wisdom, Will Farr
, a longtime MIT professor, is known for promoting "computational thinking" as a way to understand complex mathematical ideas, emphasizing meaning over symbolic manipulation. Jack Wisdom brings deep insight from "dynamical systems" and planetary physics, grounding geometry in real physical behavior. Will Farr, an expert in "astrophysics" and statistical methods, adds modern computational rigor. Together, they blend "geometry" and computation into a concept-driven approach that reflects how mathematics is actually used in scientific research.
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