The Theoretical Minimum: What You Need to Know to Start Doing Physics, Leonard Susskind and George Hrabovsky, Basic Books, New York, 2013. $26.99 (238 pp.). ISBN 978-0-465-02811-5

I was pleased to have the opportunity to review *The Theoretical Minimum: What You Need to Know to Start Doing Physics*. The book’s authors hail from different backgrounds: Leonard Susskind is a well-known theoretical physicist at Stanford University; George Hrabovsky is a self-described “‘professional’ amateur scientist” and president of Madison (Wisconsin) Area Science and Technology, a nonprofit organization for amateur scientists. Having read several of Susskind’s other books with great pleasure, I anticipated that this book would be similarly enjoyable and useful.

Enjoyable it was, but its utility is narrower than I might have hoped. In fairness, it seems to be excellent for its stated purpose: as a first textbook for the “ardent amateur” who is perhaps taking a continuing education course or seeking to learn about physics at a level a bit higher than in the usual gee-whiz, calculus-free course. I, however, was eager to analyze the book as a supporting resource for mechanics courses for two different classes of amateurs: life-science students taking physics as a premedical requirement and engineering or physics students with a comparatively weak background. There is a chronic need for a clearly written “theoretical minimum” textbook to help the many students who try to learn physics but cannot remember, or who never properly learned, the necessary elementary math skills—not to mention students whose high school physics course was so poor it actually obstructed their conceptual understanding.

The first half of the book would be useful to life science students taking a calculus-based introductory physics class, such as the one I teach at Duke University. Indeed, I really like chapter 1, The Nature of Classical Physics, which presents a low-level conceptual picture of dynamical processes that transcends mechanics. It reminds me of Julian Schwinger’s *Quantum Kinematics and Dynamics* (paperback reprint, Westview Press, 2000), which equally brilliantly reduces the concept of a system’s state and its measurement to a geometry of the former and an algebra of the latter. Most of the next few chapters—the authors call them “lectures”—are a nice mix that introduces readers to some of the calculus and trigonometry needed to do Newtonian dynamics.

I could definitely see those lectures being beneficial to introductory physics students—if they didn’t rapidly advance to partial derivatives and real mechanics. For example, a short section covers the Lagrangian and Hamiltonians appropriate for electrodynamics at a level completely inaccessible to first-year college students trying to learn either mechanics or electricity and magnetism, and it is written in a style too terse to be particularly useful to a second-year physics major.

While I was working through the book, one of my advisees was struggling in a mechanics course that covered Hamiltonians, Lagrangians, and other subjects discussed by Susskind and Hrabovsky. I loaned her a copy so that I could get a student perspective. She reported back that the book is too elementary and too inconsistent in small ways to be useful to her. It provides a decent overview, but isn’t deep enough to help students much with their problem solving, nor is it organized to offer much help in answering conceptual questions, which require little or no algebra or calculus but do require a clear understanding of units, scaling, and what’s actually going on.

Another complaint is related to the inconsistencies my student found: The book has a handful of errors that perhaps should have been caught and fixed in the editorial process. A position vector is incorrectly called “the displacement” without adding “from the origin.” The natural log is notated as log(*x*) on one page, and as ln(*x*) on another. Those are small errors that I’m sure will be corrected, but they could easily confuse “the professional amateur.”

What I am very happy with is the writing itself. The book is a pleasure to read for a physicist already moderately familiar with the concepts—as I expected it to be, given my earlier experiences with Susskind’s writings. My advisee’s comments notwithstanding, I also think that many physics majors would find the book useful as an adjunct to a second-year mechanics course. It might not help them solve difficult problems, but it will provide them with a beautiful, high-level overview of the entire subject with a sufficiently complete exposition of the supporting mathematics to ensure that a student who is a bit weak in one or more areas can instantly get up to speed. I look forward to keeping *The Theoretical Minimum* on my shelf to help selected students in exactly that way and occasionally taking it out to read myself.