Mark Kac’s Statistical Independence in Probability, Analysis and Number Theory is what I call a “vacation book.” That is, a book that you bring with you when you go on vacation purely for the joy of reading it.
The majority of math books I read to learn something in as quick a manner as possible so that I can apply the new ideas to whatever problems I am currently working on. However, when I go on vacation, it is different. Sure I may bring novels, or other nonfiction works, but I usually bring along some specially selected math too. What are the criteria for a vacation book? It has to be beautifully written. It has to have a gentle approach, as I don’t want to work too hard since the purpose of the vacation is to relax. It has to be about beautiful mathematics, and preferably link to some area of math that will be new to me. And it has to be fun.
This book satisfies all the criteria.
The topics discussed are now all familiar, taught or even relegated to exercises in the standard graduate probability curriculum. These topics are Vieta’s formula, normal numbers, prime numbers and continued fractions, all with a presentation unified by the concept of independence. It is a fun game when reading this book to note where independence is used before the author mentions it. If played carefully, you will be noting it almost every page!
This book is highly recommended to the probabilist (budding or seasoned), looking for a travel companion.
Peter Rabinovitch is a Systems Architect at Research in Motion, and a PhD student in probability. When not working, he likes to eat spicy food. He does not enjoy losing money at casinos, but does enjoy vacationing at Disney World.