Analysis I

This is the first book of a two-volume textbook on real analysis. Both the volumes-Analysis I and Analysis II-are intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the very beginning-the construction of number systems and set theory (Analysis I, Chaps. 1-5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Analysis I, Chaps. 6-11 on Euclidean spaces, and Analysis II, Chaps. 1-3 on metric spaces), through power series, several variable calculus, and Fourier analysis (Analysis II, Chaps. 4-6), and finally to the Lebesgue integral (Analysis II, Chaps. 7-8). There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) is in two quarters of twenty-five to thirty lectures each.