## Books

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

#### An Introductory Course in Functional Analysis

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

**Purchasing Options**

Amazon,
Springer

**Reviews**

zbMATH

**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)

**Purchasing Options**

Amazon,
Dover

**Reviews**

Mathematical Association of America

**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

#### Lectures in Differential Calculus

By Adam Bowers (UC San Diego)

**Purchasing Options**

Amazon

**Table of Contents and Preface (PDF file) **

*Amazon Description:*

This book is a complete course in differential calculus of one variable, based on lectures given by the author at UC San Diego during Spring Quarter 2021. It starts with a review of precalculus concepts, introduces the notions of limits and continuity, and then defines the derivative and gives the standard applications to optimization and graphing. Rather than focusing on proofs, the text attempts to give an intuitive understanding of the concepts. But the proofs are there! In some cases, the proofs are put off until we can give more natural or more enlightening explanations. Additionally, every lecture is accompanied by exercises that are intended to probe understanding and show interesting applications to the sciences.

This book is based on the Math 10A calculus lectures that are posted to my YouTube channel.

Last updated: 02 Oct 2021

#### Lectures in Precalculus

By Adam Bowers (UC San Diego)

**Purchasing Options**

Amazon

*Amazon Description:*

Based on lectures given by the author at UC San Diego during Fall Quarter 2020, this book includes the essential topics needed for an understanding of calculus. The book focuses on functions of various types, including linear functions, polynomial functions, rational functions, exponential functions, logarithmic functions, and trigonometric functions. This concise volume contains a complete precalculus course in 28 lectures. Each lecture includes numerous pictures and examples and is accompanied by a selection of exercises. The goal of this text is to prepare the reader for a study of calculus, and that objective motivates the choice of topics.

This book is based on the Math 3C precalculus lectures that are posted to my YouTube channel.

Last updated: 25 Mar 2023