Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.
In this book the author steers a path through the central ideas of real analysis.
The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem.
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible.
As its title indicates, this book is intended to serve as a textbook for an introductory course in mathematical analysis.
The text is written to ease the transition from primarily computational to primarily theoretical mathematics.
This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds ...
From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis.
This book presents a concise and sharpley focused introduction to the basic concepts of analysis - from the development of real numbers through uniform convergences of a sequence of functions - and includes coverage both of the analysis of ...
From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students.