Rudin W. Principles of Mathematical Analysis

McGraw-Hill, 1976. - 325 Pages. International Series in Pure & Applied MathematicsThe third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I. ) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter
2. There is a new section on the gamma function, and many new and interesting exercises are included.