Schumacher (Kenyon College) provides a lively and interactive introduction for upper-level undergraduate math majors. Using examples and very useful illustrations she describes the basic building blocks of real analysis, including sets and set notations, functions, and sequences, the real numbers, measuring distances, sets and limits, continuity, real-valued functions, completeness, compactness, connectedness, differentiation of functions of one real variable, iteration and the contraction mapping theorem, the Riemann integral, sequences of functions, differentiation of functions, truth and probability, number properties, exponents, sequences in R, limits of functions from R to R, doubly indexed sequences, sub-sequences and convergence, series of real numbers, probing the definition of the Reimann integral, power series, and Newton's method. The result is a classroom text that is both rigorous and accessible. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)