Math and science students are picky about what information we commit to memory. This makes sense, because we’re taught to reject authority and judge information with our own reasoning, and because there’s more information than fits in memory, so we have to identify the essential bits to remember so that we can generate the non-memorized stuff on demand. However, beyond even those considerations, there’s another even more fundamental reason we have to be careful about what we learn: we’re mortal. There are a limited number of hours we get to spend learning stuff, so we want to at least try to spend those hours as efficiently as possible.1 For this reason, we care about the books we choose to read. We all know what it’s like to feel that we’ve wasted a semester course due to a bad book, and we know the joy of learning deeply and quickly from a well written one.
This page lists what I regard to be the most effective books I’ve read during my studies. To get us started, here’s a studious octoups illustrated by Chris Gall.
Mechanics
- An Introduction to Mechanics by Klepner and Kolenkow. Excellent freshman year mechanics book. The section on angular momentum has an illustration that allows the reader to actually undersatnd the right hand rule for torque. I disliked the approach to harmonic oscillation though because I prefer to have the basic mathematics introduced properly before just handing out results as if to be memorized.
Electricity and magnetism
Electricity and Magnetism by Edward M. Purcell. Awesome freshman level book in every way. There is a section on how Maxwell’s equations lead to the usual rules for lumped circuits. There’s also a section explaining how magnetic forces arise from electric forces when special relativity is taken into account.
Introduction to Electrodynamics by Griffiths, More advanced than Purcell, and still very well written. Griffiths goes out of his way to make the notation clear, which I appreciated quite a lot. The book takes necessary detours into the mathematics so that the reader can digest physics more easily. It’s not perfect though, of course. The section on time dependent potentials (a.k.a. Jeffimenko’s equations) is hard to read, but that’s probably at least in part because Jeffimenko’s equations are complicated. It’s too bad this book doesn’t go a little farther in terms of mathematics because it’s a lot more clear than Jackson’s book, which is used in most graduate courses.
Statistical mechanics and Thermodynamics
Prior to taking statistical and thermal physics in my junior year, I was sure I wouldn’t like it. Ever since high school I had a sort of prejudice against statistics as a math subject, and I was particularly annoyed by the idea of studying physics in a case where one couldn’t simply solve for the trajectories of all particles in the system given enough effort. Recognizing that I had these feelings, I thought I wouldn’t do well in statistical physics and was afraid of it. That fear drove me to work really, really hard at it, and fortunately the subject and in particular Reif’s book rewards that effort. Stat mech is, as my professor Doug Stone put it, the bridge between cute intro physics and real life adult physics. Stat mech allows us to understand the observable emergent phenomena of everyday life starting only from some basic physical laws and a set of amazingly physics-independent observations about counting.
Fundamentals of Statistical and Thermal Physics by Frederick Reif. This book changed my life. The first chapter explains the random walk problem in detail, setting the mathematical foundations needed to truly understand entropy and therefore the rest of the book. That chapter turned my fear of statistics into a lifelong love of the subject so strong that I now regard random processes and noise to be one of my strongest areas.2
Thermodynamics and an Introduction to Thermostatistics by Herbert B. Callen. I haven’t read this book, but it’s on this list because it is very highly regarded and has an appendix explicitly explaining how the various thermodynamic potentials are related through Legendre transformations, an important topic often ignored, brushed over quickly, or handled clumsily in other books.
Special Relativity
I “learned” special relativity at least four times: once in high school physics, a second time in freshman physics, and a third and fourth time in my sophomore mechanics and E&M courses. In each of the three college iterations, each professor assumed that the students already mostly understood special relativity from the previous time, which lead to a series of bad “reviews” of special relativity without any real learning. To cope with this, I spent some time rehashing the subject on my own and found the following books useful:
Special Relativity by A. P. French. One of the clearer books on special relativity I’ve seen.
A First Cource in General Relativity by Bernard Schutz.
Spacetime and Geometry by Sean M. Carroll. The first chapter is good for special relativity.
The two GR books are good for GR as well, but they’re here because their special relativity sections are clear.
Quantum mechanics
Principles of Quantum Mechanics by R. Shankar. Very good for both undergraduate and graduate studies.
- Modern Quantum Mechanics by J. J. Sakurai
- The angular momentum chapter is excellent.
- The perturbation theory chapters are also quite good. In particular, note the homework exercise asking how to do degenerate perturbation theory in the case that the perturbation does not lift the degeneracy to first order.
- Quantum Mechanics by Eugene Merzbacher. Good reference for the driven harmonic oscillator, and other clear, mathematical developments of standard topics.
Math
Vector Calculus, Linear Algebra, and Differential Forms by Hubbard and Hubbard. This is one of the best math books ever written. It was the basis of my freshman math course and it left me with almost all the math I would ever need in my student and professional life as a physicist and math enthusiast. This book, plus some education in differential equations and complex analysis, could serve a working physicist for life.
Analysis on Manifolds by Munkres. This is a good book to read after reading Hubbard and Hubbard if you’d like to make your own independent study of multivariable calculus and differential forms. The book is totally free of errors, and I found that working through the proofs gave me deeper understanding of the subject.
Fifty Challenging Problems in Probability with Solutions by F. Mosteller
1: That said, I doubt most of us really approach our maximum possible life study time. Even so, I think huge gains in educational efficiency can be found in choosing the right learning resources.
2: Here’s an excellent first passage problem.