Books

I have written two textbooks designed for use in university courses.

An Introductory Course in Functional Analysis

By Nigel Kalton (University of Missouri) and Adam Bowers (UCSD)

Table of Contents and Preface (PDF file)

With foreword by Professor Gilles Godefroy

From the back cover:
Based on a graduate course by the celebrated analyst Nigel Kalton, this well-balanced introduction to functional analysis makes clear not only how, but why, the field developed. All major topics belonging to a first course in functional analysis are covered. However, unlike traditional introductions to the subject, Banach spaces are emphasized over Hilbert spaces, and many details are presented in a novel manner, such as the proof of the Hahn-Banach theorem based on an inf-convolution technique, the proof of Schauder's theorem, and the proof of the Milman-Pettis theorem.

Last updated: 06 Oct 2016

Elementary Point-Set Topology: A Transition to Advanced Mathematics

By Andre Yandl (Seattle University) and Adam Bowers (UCSD)

Table of Contents and Preface (PDF file)

From the preface:
As the title indicates, this book is about topology. In particular, this book is an introduction to the basics of what is often called point-set topology (also known as general topology). However, as the subtitle suggests, this book is intended to serve another purpose as well. A primary goal of this text, in addition to introducing students to an interesting subject, is to bridge the gap between the elementary calculus sequence and more advanced mathematics courses. For this reason, the focus of the text is on learning to read and write proofs rather than providing an advanced treatment of the subject itself.

The desire to make this introduction to topology intuitive and accessible to our students has led to several innovations that we feel make our approach to the subject unique [including our approach to product topology and connectedness].

Another aspect of this text which distinguishes it from most introductory topology textbooks is the content ... which demonstrates applications of topological concepts to other areas of mathematics ... include solving differential equations and proving the Fundamental Theorem of Algebra.

Last updated: 06 Oct 2016