The Big Book of Analysis

The content of this book follows the first year courses Introduction to University Mathematics, Analysis 1-3, and second year course Integration at the University of Oxford. The content of this book is presented in a mostly linear delivery since I believe it is the best way to provide motivation as well as justify some constructions or denitions. The discovery and history of mathematics has never been linear, but I leave that to the mathematical historians to discuss. However, minor historical anecdotes, people involved, and quotes are also included in this book for a bit of a human interest and light humour. It is hoped that this could enhance intuition, appreciation, and enjoyment amongst the readers.Despite the generally linear presentation, there are plenty of pauses within the text hinting at what one can expect in the later chapters and urging the readers to try some of the exercise questions. Some of the proofs to the results were also left as exercises for the readers. The text is also punctuated with many concrete examples, counterexamples, and important remarks. These are necessary to solidify, clarify, and motivate the abstract denitions and results. There are more than 600 exercise questions in total in this book and they are presented at the end of each relevant chapters.