In recent years Leonard Susskind has been giving an excellent series of lectures on basic ideas of theoretical physics, under the title The Theoretical Minimum. The general idea seems to be to provide something in between the usual sort of popular book about physics (which avoids equations and tries to give “intutitive” explanations in ordinary language) and conventional undergraduate-level textbooks. Such textbooks generally assume college-level multi-variable calculus, differential equations and linear algebra, and often skip lots of detail and motivation, assuming that the book is a supplement to a standard course of lectures.
For Susskind’s lectures, you mostly just need high-school level mathematics, up to some some basic differential calculus, as well as two by two matrices. Actually though, if you’ve never seen matrices and very simple linear algebra, this is a good place to learn some basics examples of this subject.
A year ago the first book version of some of the lectures appeared as The Theoretical Minimum, with George Hrabovsky writing up Susskind’s lectures on classical mechanics. I wrote a little bit about the book here, and was quite impressed by the way it managed to give the details of the formalism of Hamiltonian mechanics, while sticking to as simple and concrete mathematics and calculational tools as possible.
Today is publication day for the next volume, Quantum Mechanics: The Theoretical Minimum, which is a joint effort this time with Art Friedman. It’s even better than the first volume, taking on a much more difficult subject. About the first two-thirds of the book sticks to the simplest possible quantum system, one with a two-dimensional state space. The linear algebra needed is developed from scratch and Susskind works out at a very leisurely pace all the details of what the quantum picture of reality looks like in this simplest context. There’s a lot about what “entanglement” really is, and this part ends up with an introduction to Bell’s theorem.
The last third of the book is a quicker-paced trip through the usual material about wave-functions and the Schrödinger equation, ending up with the details for the harmonic oscillator potential.
“The Theoretical Minimum” phrase is a reference to Landau, but it’s a good characterization of this book and the lectures in general. Susskind does a good job of boiling these subjects down to their core ideas and examples, and giving a careful exposition of these in as simple terms as possible. If you’ve gotten a taste for physics from popular books, this is a great place to start learning what the subject is really about.
I only noticed one mistake in the book, on its back cover, where one of the blurbs is attributed to a Professor of Mathematics at Columbia, when I know for a fact that his actual title there is “Senior Lecturer”. Susskind does have a bit of history of getting this point wrong, but probably the fault here lies with the publisher.
Update: Nature has a review here.