Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell's Equations to Yang–Mills 1st Edition

A brilliant survey of the mathematical framework of electrodynamics, field theories, and more. This book is not (and is not intended to be) a comprehensive introduction to "electricity and magnetism" or any other topic in physics, nor is it a text on mathematical physics. Although one need not actually be a mathematician to appreciate the material, a certain amount of mathematical sophistication and background is required. The author himself requires students to have taken multivariable calculus and linear algebra when using the text to teach. The book's value is found in the presentation of a variety of topics, from classical and quantum physics to vector bundles and differential forms, together with references for further study all in a remarkably concise form. In under 300 pages, the manages to introduce the readers to 200+ years of developments in physics and mathematics with an emphasis on the mathematical formalisms and frameworks of or relating to electromagnetism. The order of presentation mostly follows that of historical discovery, moving from Maxwell and early work in atomic physics (e.g., Coulomb's law) to special relativity, the (mostly) 20th century developments in mathematical physics (e.g., Noether's theorem, exterior calculus, forms, connections, etc.), quantum physics, and even the basic use of such mathematics in the standard model. Apart from a survey of such topics for those with a fair degree of mathematical sophistication, this text can serve well as a complementary text in courses in (or self-study of) physical mathematics, differential geometry, advanced multivariable calculus, analytical dynamics, advanced courses in electrodynamics and classical field theories, or surveys of physics for students majoring in mathematics, engineering, etc.

PLUS: I benefited from Prof. Garrity exposition of the nuts and bolts of differential forms as applied to Maxwell's Eqns.MINUS: The level of rigor is quite uneven. For example his section on Hilbert Spaces is quite mathematical and would take a big effort by the average reader to understand (I had never heard about Schwartz spaces before)MINUS: The book has a limited level/coverage of Maxwell's Eqn.(Prof Zee's Gravitation in a nutshell book covers with much more insight the "differential form" description of Maxwell's Eqns.)PLUS: The latter chapters of the book are quite valuable because they provide at an elementary level the connection between current abstract math concepts and the physics of Non-Abelian (Yang Mills) Gauge Theories.PLUS: Though the subject is covered in little detail, he makes it possible for a "physicist" with limited abstract math knowledge to have a glimpse at the connection between abstract math and the physics of the Yang Mills fields.

I really enjoyed this book! It gives a truly well-explained tour through physics and explaining everything needed in understanding the framework of modern physics. Concluding in force=curvature and gauge=connection, an integral part of physics and then Yang-Mills theory.

Really a set of lecture notes. Not really for the mathematician in that it isn't very rigorous. Rather, it tries to develop the reader's physical understanding which is a fine goal but done more successfully in standard intermediate and advanced physics text books. The author "follows" i.e., borrows extensively from other authors' books. The book reviews topics in linear algebta, Hilbert space, differential forms, differential geometry and Lagrangian mechanics in order to discuss topics in Maxwell's theory and quantum theory. This is useful for physicists but I would expect a mathematician to know this material.

I was trained as a differential geometer and over the years have periodically made an effort to learn E&M. I am, of course, fully aware of all the "fancy" approaches that can be taken, but that's not what I needed. Some people think that if a mathematician wants to learn physics, then they want to read books like Sachs and Wu's Relativity for Mathematicians, or other mathematically sophisticated sources. That is not always the case. Sometimes they want to have another mathematician explain elementary physics to them in precise and clear language. (Spivak's mechanics book is in this vein.) I've learned a lot from Garrity's book - it is a first rate piece of exposition. I wish that there were more books like this.

This is not in any sense "electricity and magnetism for mathematicians". Rather, it's an introductory and fairly rushed text on electromagnetism and calculus on manifolds for undergraduates. Readers looking for the connection with Yang-Mills theories should look elsewhere - only a single page is devoted to this topic.

This is a very enjoyable book. A stimulating mixture of historical anecdote, basic undergraduate physics, relevant mathematical tools and methods. In places appropriate mathematical rigour enhances the exposition but does not obfuscate the main purpose of the book or detract from its flow and therefore enjoyment of the content. The subtitle 'A guided path from Maxwell's Equations to Yang-Mills' is spot on as the necessary mathematics is presented to take the reader to the point where he/she could begin to study or appreciate Yang-Mills theory. It does not pretend to be a text on Yang-Mills. The path leads from Munchkinland to the gates of The Emerald City. There are many exercises in the book for the reader to test his/her understanding of the material covered. Very pleasingly , personal communication with the author elicited a swift response allowing me to check my own solutions to the problems. This is especially helpful for those studying on their own, so step into Dorothy's ruby slippers and set off on The Path.