Boas R. A Primer of Real Functions

4th Edition, Revised and Updated. — Washington: The Mathematical Association of America Inc. (MAA), 1996. — XIV, 306 p.This is a revised, updated, and augmented edition of a classic monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhere-oscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days.It is a great pleasure to see the new, the fourth edition of this gem which is well-known all over the world where mathematicians live. This is an important work especially for teachers and even for (trained) students.This is such a fine, fine book; one of the very best on its topic. Unlike virtually every other author who has written a "Real Analysis" textbook, Boas makes the subject truly interesting and even fascinating. Boas adds humor and curious anecdotes to his presentation of real functions. His book includes Lebesque integration and gives an excellent presentation of the Cantor set.Very good math analysis book! Books like these are rarely written. Read and work through the exercises. Always enjoyed Ralph Boas' mathematical writing style. He is at his best in this small book. He covers topics in introductory and intermediate real analysis of one variable, but with an enthusiasm that pulls you along, like a good novel. This does not mean, however, that Boas skimps on theory and proof. This is an excellent resource for undergraduate/graduate study. The "Notes" section is a cornucopia of references to advanced topics by leaders in the field. And every exercise is answered, or at least addressed.Sets
Functions
IntegrationAnswers to Exercises
Index