To the students: you will find some physics crammed in amongst the mathematics. Don't let the physics bother you. As you study the math, you'll learn some physics without extra effort. The physics is a freebie. I have tried to explain the math you need for physics and have left out the rest.

To the professors: the book is for students who also are taking mechanics, electrodynamics, quantum mechanics, and statistical mechanics nearly simultaneously and who soon may use probability or path integrals in their research. Linear algebra and Fourier analysis are the keys to physics, so the book starts with them, but you may prefer to skip the algebra or postpone the Fourier analysis. The book is intended to support a one- or two-semester course for graduate students or advanced undergraduates. The first seven, eight, or nine chapters fit in one semester, the others in a second. A list of errata is maintained at panda.unm.edu/cahill, and solutions to all the exercises are available for instructors at www.cambridge.org/cahill.

Several friends – Susan Atlas, Bernard Becker, Steven Boyd, Robert Burckel, Sean Cahill, Colston Chandler, Vageli Coutsias, David Dunlap, Daniel Finley, Franco Giuliani, Roy Glauber, Pablo Gondolo, Igor Gorelov, Jiaxing Hong, Fang Huang, Dinesh Loomba, Yin Luo, Lei Ma, Michael Malik, Kent Morrison, Sudhakar Prasad, Randy Reeder, Dmitri Sergatskov, and David Waxman – have given me valuable advice.