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Electricity and Magnetism for Mathematicians
A Guided Path from Maxwell's Equations to Yang–Mills


  • Date Published: March 2015
  • availability: In stock
  • format: Paperback
  • isbn: 9781107435162

£ 28.99

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About the Authors
  • This text is an introduction to some of the mathematical wonders of Maxwell's equations. These equations led to the prediction of radio waves, the realization that light is a type of electromagnetic wave, and the discovery of the special theory of relativity. In fact, almost all current descriptions of the fundamental laws of the universe can be viewed as deep generalizations of Maxwell's equations. Even more surprising is that these equations and their generalizations have led to some of the most important mathematical discoveries of the past thirty years. It seems that the mathematics behind Maxwell's equations is endless. The goal of this book is to explain to mathematicians the underlying physics behind electricity and magnetism and to show their connections to mathematics. Starting with Maxwell's equations, the reader is led to such topics as the special theory of relativity, differential forms, quantum mechanics, manifolds, tangent bundles, connections, and curvature.

    • The author is well known among mathematics students for his previous book, All the Mathematics You Missed, which has sold over 20,000 copies
    • Does not assume any knowledge of physics, and only basic undergraduate mathematics
    • Maxwell's equations are a fascinating topic
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    Product details

    • Date Published: March 2015
    • format: Paperback
    • isbn: 9781107435162
    • length: 294 pages
    • dimensions: 228 x 151 x 15 mm
    • weight: 0.4kg
    • contains: 81 b/w illus. 2 colour illus. 211 exercises
    • availability: In stock
  • Table of Contents

    1. A brief history
    2. Maxwell's equations
    3. Electromagnetic waves
    4. Special relativity
    5. Mechanics and Maxwell's equations
    6. Mechanics, Lagrangians, and the calculus of variations
    7. Potentials
    8. Lagrangians and electromagnetic forces
    9. Differential forms
    10. The Hodge * operator
    11. The electromagnetic two-form
    12. Some mathematics needed for quantum mechanics
    13. Some quantum mechanical thinking
    14. Quantum mechanics of harmonic oscillators
    15. Quantizing Maxwell's equations
    16. Manifolds
    17. Vector bundles
    18. Connections
    19. Curvature
    20. Maxwell via connections and curvature
    21. The Lagrangian machine, Yang–Mills, and other forces.

  • Author

    Thomas A. Garrity, Williams College, Massachusetts
    Thomas A. Garrity is the William R. Kenan, Jr Professor of Mathematics at Williams College, where he was the director of the Williams College Project for Effective Teaching for many years. He has written a number of research papers and has authored or coauthored two other books, All the Mathematics You Missed (But Need to Know for Graduate School) and Algebraic Geometry: A Problem Solving Approach. Among his awards and honors is the MAA Deborah and Franklin Tepper Haimo Award for outstanding college or university teaching.

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