Introduction to Analysis

This text is designed for a one semester Introduction to Analysis course. One main difference is the chapter on set, functions and proofs. This book will be attractive when a Transition to Advanced Mathematics course is not offered. The first chapter covers an introduction to proofs. The text progresses into sequences and limits, continuity and differentiation. Riemann Integration, Sequences and Series Functions and the Topology of the Real Numbers round out the presentation. The author does an excellent job of connecting the material by suggesting to students where to find particular theorems, referring back to previous material while introducting new topics.

Introduction to Analysis is an ideal text for a one semester course on analysis. The book covers standard material on the real numbers, sequences, continuity, differentiation, and series, and includes an introduction to proof. The author has endeavored to write this book entirely from the student’s perspective: there is enough rigor to challenge even the best students in the class, but also enough explanation and detail to meet the needs of a struggling student.

From the Author to the student:

"I vividly recall sitting in an Analysis class and asking myself, ‘What is all of this for?’ or ‘I don’t have any idea what’s going on.’ This book is designed to help the student who finds themselves asking the same sorts of questions, but will also challenge the brightest students."