This book grew out of class notes [ 3 ] for a course on Reference Frames, which in turn forms part of a major upper-division curriculum reform effort, entitled Paradigms in Physics, which was begun in the Department of Physics at Oregon State University in 1997. The class notes were subsequently published online in wiki format [ 4 ], and are now used as the primary text in that course; an abbreviated version was also published as a journal article [ 5 ].

I am grateful to all of the faculty involved in this effort, but especially to the leader of the project, my wife, Corinne Manogue, for support and encouragement at every stage. The Paradigms in Physics project has been supported in part by NSF grants DUE–965320, 0231194, 0618877, and 1023120, supplemented with funds from Oregon State University; my own participation was made possible thanks to the (sometimes reluctant!) support of my department chair at the time, John Lee. I was fortunate in having excellent teaching assistants, Jason Janesky and Emily Townsend, the first times I taught the course.

A course based on an early draft of this book was taught at Mount Holyoke College in 2002, giving me an opportunity to make further revisions; my stay at Mount Holyoke was partially supported by their Hutchcroft Fund. I am grateful to Greg Quenell for having carefully read the manuscript at that time, and for suggesting improvements, and to Alex Brummer, who did the same more recently.

I thank David Griffiths, an old friend (and Corinne's former teacher), for permission to “borrow” homework problems from his standard textbook [ 6 ], and to include solutions using hyperbola geometry.

Last but not least, I thank the many students who struggled to learn physics from a mathematician, enriching all of us.