Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals delves into a comprehensive and thorough analysis of concepts and results related to uniform convergence. This book is authored by Andrei Bourchtein and published by Wiley under the 1st edition in January 2017. It focuses on counterexamples that address false statements often encountered in the study of mathematical analysis and calculus, all connected to the theme of uniform convergence.

The content covers various aspects including the convergence of sequences, series, and families of functions, as well as proper and improper integrals depending on a parameter. The exposition is structured to explore both incorrect and correct versions of fundamental concepts and results in the theory of uniform convergence. Aimed at helping readers understand challenging areas that can be sources of confusion, this book also illustrates the valuable use of counterexamples in mathematical analysis.

The goal is threefold: to provide a brief overview of key results in the theory of uniform convergence, to assist in mastering these concepts and theorems, and to demonstrate the importance of using counterexamples in different contexts. This work is an essential resource for anyone studying or teaching advanced calculus and real analysis.