Chapter 1. The construction of real and complex numbers
Chapter 2. Metric and Euclidean spaces
Chapter 3. Complete metric spaces
Chapter 4. Normed linear spaces
Chapter 5. Differentiation
Chapter 6. Integration
Chapter 7. Fourier analysis on locally compact abelian groups

There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.The foundational material contained in this book is published separately as Paul Sally's, "Tools of the Trade: Introduction to Advanced Mathematics," also available from the AMS.---Summary provided by publisher