This is the second book of a two-volume textbook on real analysis. Both the volumesâAnalysis I and Analysis IIâare intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the very beginningâthe construction of number systems and set theory (Analysis I, Chaps. 1â5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Analysis I, Chaps. 6â11 on Euclidean spaces, and Analysis II, Chaps. 1â3 on metric spaces), through power series, several variable calculus, and Fourier analysis (Analysis II, Chaps. 4â6), and finally to the Lebesgue integral (Analysis II, Chaps. 7â8). There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) is taught in two quarters of twenty-five to thirty lectures each.
