Understanding analysis - Abbott, Stephen, 1964- (Undergraduate texts in mathematics, 2001)
A textbook for an elementary, one-semester course in a mathematically rigorous approach to the study of functions of a real variable. Focuses on the questions that make the subject most interesting to new students, such as whether derivatives are integrable or continuous. Makes topics accessible by answering these questions using mathematics. DLC: Mathematical analysis. *** This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.