Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.
However, in this book the reader is led carefully through every step in such a way that he/she will soon be predicting the next step for him/herself.
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.
The text is written to ease the transition from primarily computational to primarily theoretical mathematics.
This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.The ...
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.
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.
As its title indicates, this book is intended to serve as a textbook for an introductory course in mathematical analysis.
This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis.
This book provides an introduction to the basic ideas and tools used in mathematical analysis.