Today I am going to review the probability textbook “Introduction to Probability” by David Anderson, Timo Seppäläinen, and Benedek Valkó. I used this book to self study probability several months ago. This ended up being the book I chose because it is (or at least has been) used as the textbook for the probability course at UCSD and my plan was to loosely follow their curriculum. I described my experience self studying the material in another post, but in summary it was successful.
This book is one of those nicely formatted textbooks that is perfect for self study and for classroom use. Each chapter has fully worked example problems scattered throughout, followed by exercises at the end of the chapter. The exercises are divided into several categories. There are section exercises, which are clearly labeled as involving material from a particular section of the chapter. These are followed by a large number of further exercises which are a bit more in depth and contain material from multiple sections. Near the end there are challenging problems which involve a higher level of sophistication. The book contains answers to the even numbered exercises in the back.
The book is in full color and I found the binding to be good quality. It held up well to continuous use. The book is thick enough that it can remain open when lain flat but not so thick as to be cumbersome. The exposition is descriptive and straightforward. Whenever I had any difficulty with an exercise, referring back to the chapter (or a previous one) was often enough to clear up my confusion.
The book expects the reader to have a solid grounding in calculus, particularly integral calculus. I would also recommend some exposure to set theory and proofs. The first chapter presents a a good mathematical foundation by starting from the axioms of probability. This has the potential to get deep into the field of analysis but the authors did a superb job of showing how to construct a probability space without getting too deep in the weeds of sigma algebras or probability measures. Another feature that made this book stand out to me is that every chapter ends with a finer points section. These finer points sections were optional material that discusses the deeper mathematical considerations of the material in the chapter. This keeps the chapter clean and straightforward while also giving a good jumping off point if the reader wants to dig deeper.
The first four of the six appendices provide background and review material in case there is anything you need a refresher on. These include calculus, set notation, counting, and sums, series and products. I personally found the appendices on counting and sums, series and products to be helpful to reference often.
The book has ten chapters which cover what I assume to be the core topics of introductory probability. One comment is that I found several chapters, particularly the first several, to have been packed with content. This meant that those chapters felt slow to get through and could possibly have been split in two for better pacing. Overall I found the topic progression to be logical and easy to follow. Explaining random variables early on helped me to avoid confusion, since in other courses they had been poorly explained to me.
If you are looking for a book to study probability from, this book would be an excellent choice.