The Theoretical Minimum

What You Need To Know To Start Thinking Like a Physicist

This page is designed to support the book, "The Theoretical Minimum" by Leonard Susskind and George Hrabovsky. This book will be released by Basic Books in North America, and Penguin Press in the UK on 29 January 2013.

This site will contain material to support those interested in the book. This will include hints and detailed solutions to the practice problems and additional materials that did not fit, or could not be used in the book.

Here is the cover of the Penguin Press version of The Theoretical Minimum.

A world-class physicist and a citizen scientist combine forces to teach Physics 101—the DIY way.

The Theoretical Minimum is a book for anyone who has ever regretted not taking physics in college—or who simply wants to know how to think like a physicist. In this unconventional introduction, physicist Leonard Susskind and citizen-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Unlike most popular physics books—which give readers a taste of what physicists know but shy away from equations or math—Susskind and Hrabovsky actually teach the skills you need to do physics, beginning with classical mechanics, yourself. Based on Susskind’s enormously popular Stanford University-based (and YouTube-featured) continuing-education course, the authors cover the minimum—the theoretical minimum of the title—that readers need to master to study more advanced topics.

Somewhere in Steinbeck country two tired men sit down at the side of the road. Lenny combs his beard with his fingers and says, “Tell me about the laws of physics, George.” George looks down for a moment, then peers at Lenny over the tops of his glasses. “Okay, Lenny, but just the minimum.”

An alternative to the conventional go-to-college method, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

Note: This book was written and typeset in Mathematica versions 7, 8, and 9.

Leonard Susskind has been the Felix Bloch Professor in Theoretical Physics at Stanford University since 1978. The author of The Black Hole War and The Cosmic Landscape, he lives in Palo Alto, California.

Leonard Susskind, co-author of The Theoretical Minimum

George Hrabovsky is the president of Madison Area Science and Technology (MAST), a nonprofit organization dedicated to scientific and technological research and education. He lives in Madison, Wisconsin.

George Hrabovsky, co-author of The Theoretical Minimum

ADVANCE PRAISE FOR The Theoretical Minimum

What a wonderful and unique resource. For anyone who is determined to learn physics for real, looking beyond conventional popularizations, this is the ideal place to start. It gets directly to the important points, with nuggets of deep insight scattered along the way. I'm going to be recommending this book right and left.”

Sean Carroll, physicist, California Institute of Technology, and author of The Particle at the End of the Universe

"Readers ready to embrace their inner applied mathematician will enjoy this brisk, bare-bones introduction to classical mechanics drawn from Stanford University’s “Continuing Studies” program. Although physicist Susskind (The Black Hole War) and science advocate Hrabovsky touch briefly on electricity and magnetism, the book is primarily about mechanics and the motion of particles. The authors open with a look at closed and open systems and the reversibility of physical laws, a concept central to the field. Next are rigorous chapters on trigonometry and vectors, and a no-nonsense intro to differential and integral calculus, and how these tools are used to calculate the motion of objects through space. Not for the faint of heart, successive chapters introduce Newton’s law of motion, the complex mathematics of “systems” of particles, phase space, conservation of momentum, and the Principle of Least Action, which allows scientists to “package” a system’s velocity, mass, direction, and forces into a single function. The authors intend this book as a toolkit for determined readers who want to teach themselves basic mechanics. Although their discussions are clear enough, even the hardiest reader will want to bring a basic calculus text along for the journey. 62 line drawings."

Publishers Weekly

Click here to visit the MAST web site.


From the Preface

I’ve always enjoyed explaining physics. For me it’s much more than teaching: It’s a way of thinking. Even when I’m at my desk doing research, there’s a dialog going on in my head. Figuring out the best way to explain something is almost always the best way to understand it yourself.

About ten years ago someone asked me if I would teach a course for the public. As it happens, the Stanford area has a lot of people who once wanted to study physics, but life got in the way. They had had all kinds of careers but never forgot their one-time infatuation with the laws of the universe. Now, after a career or two, they wanted to get back into it, at least at a casual level.

Unfortunately there was not much opportunity for such folks to take courses. As a rule, Stanford and other universities don’t allow outsiders into classes, and, for most of these grown-ups, going back to school as a full-time student is not a realistic option. That bothered me. There ought to be a way for people to develop their interest by interacting with active scientists, but there didn’t seem to be one.

That’s when I first found out about Stanford’s Continuing Studies program. This program offers courses for people in the local nonacademic community. So I thought that it might just serve my purposes in finding someone to explain physics to, as well as their purposes, and it might also be fun to teach a course on modern physics. For one academic quarter anyhow.

It was fun. And it was very satisfying in a way that teaching undergraduate and graduate students was sometimes not. These students were there for only one reason: Not to get credit, not to get a degree, and not to be tested, but just to learn and indulge their curiosity. Also, having been “around the block” a few times, they were not at all afraid to ask questions, so the class had a lively vibrancy that academic classes often lack. I decided to do it again. And again.

What became clear after a couple of quarters is that the students were not completely satisfied with the layperson’s courses I was teaching. They wanted more than the Scientific American experience. A lot of them had a bit of background, a bit of physics, a rusty but not dead knowledge of calculus, and some experience at solving technical problems. They were ready to try their hand at learning the real thing—with equations. The result was a sequence of courses intended to bring these students to the forefront of modern physics and cosmology.

Fortunately, someone (not I) had the bright idea to video-record the classes. They are out on the Internet, and it seems that they are tremendously popular: Stanford is not the only place with people hungry to learn physics. From all over the world I get thousands of e-mail messages. One of the main inquiries is whether I will ever convert the lectures into books? The Theoretical Minimum is the answer.

The term theoretical minimum was not my own invention. It originated with the great Russian physicist Lev Landau. The TM in Russia meant everything a student needed to know to work under Landau himself. Landau was a very demanding man: His theoretical minimum meant just about everything he knew, which of course no one else could possibly know.

I use the term differently. For me, the theoretical minimum means just what you need to know in order to proceed to the next level. It means not fat encyclopedic textbooks that explain everything, but thin books that explain everything important. The books closely follow the Internet courses that you will find on the Web.

Welcome, then, to The Theoretical Minimum—Classical Mechanics, and good luck!

Leonard Susskind
Stanford, California, July 2012

I started to teach myself math and physics when I was eleven. That was forty years ago. A lot of things have happened since then—I am one of those individuals who got sidetracked by life. Still, I have learned a lot of math and physics. Despite the fact that people pay me to do research for them, I never pursued a degree.

For me, this book began with an e-mail. After watching the lectures that form the basis for the book, I wrote an e-mail to Leonard Susskind asking if he wanted to turn the lectures into a book. One thing led to another, and here we are.

We could not fit everything we wanted into this book, or it wouldn’t be The Theoretical Minimum—Classical Mechanics, it would be A-Big-Fat-Mechanics-Book. That is what the Internet is for: Taking up large quantities of bandwidth to display stuff that doesn’t fit elsewhere! You can find extra material at the website This material will include answers to the problems, demonstrations, and additional material that we couldn’t put in the book.

I hope you enjoy reading this book as much as we enjoyed writing it.

George Hrabovsky
Madison, Wisconsin, July 2012

Part of Chapter 1.

Calendar of Events

Sunday, 10 March 2013: George Hrabovsky will discuss The Theoretical Minimum in specific and amateur science in general at the Madison Science Pub, 2pm at Brocach Irish Pub on Main Street off the Capitol Square in Madison, WI.

Thursday, 21 March 2013: George Hrabovsky will discuss The Theoretical Minimum at the Madison Science Cafe, 5 PM at the Steep and Brew on State Street in Madison WI.

Thursday, 18 April 2013: George Hrabovsky will give a workshop based on the The Theoretical Minimum at Barnes and Noble Bookstore at East Towne Mall, in Madison, WI, at 5 PM.

Additional Material

These files require either Mathematica 8 or later, or the free Mathematica CDF Viewer, though the viewer cannot run the programs, (you can find that here). There will be pdf options in most cases.

Solutions to Exercises

Errata (pdf)

As of April 2014 there is a new edition containing all of the errata in the previous document. There is a new errata:

Errata (pdf)

Logic and Proof: A short introduction to the principles of logic and how to construct proofs. (pdf)

Additional Titles by The Authors

Leonard Susskind

The Black Hole War

The Cosmic Landscape

An Introduction to Black Holes, Information And The String Theory Revolution

George Hrabovsky

Self-Instruction and Teaching: Science Education for the New Millennium, paperback , hardcover.

For those who are experiencing difficulty with the mathematics, please consult the new course being offered through the MAST website on Elementary Mathematical Methods for Science.