Understanding Real Analysis

Pedagogically this is a fine text: the basic ideas of limits, continuity, Cauchy sequences, convergence, et cetera are explained very well. But there is little coverage of convergence tests for infinite series (e.g., even the root test is missing). And there is no coverage of power series. Two other texts that are close to this book in spirit and level of exposition are Howie's "Real Analysis" (Springer) and Dangello and Seyfried's "Introductory Real Analysis" (Houghton Mifflin). Yet both have more coverage of infinite series and both cover power series. Zorn's book might be fine for a weak class or for an "analysis for liberal arts majors" kind of course. But I doubt it will suffice as the text for a first course in analysis for prospective math majors.