This is a book about integer partitions. If you have never heard of this concept before, we guess you will nevertheless be quite familiar with what it means. For instance, in how many ways can 3 be partitioned into one or more positive integers? Well, we can leave 3 as one part; or we can take 2 as a part and the remaining 1 as another part; or we can have three parts of size 1. This extremely elementary piece of mathematics shows that the answer to the question is: “There are three integer partitions of 3.”
All existing literature on partition theory is written for professionals in mathematics. Now when you know what integer partitions are you probably agree with us that one should be able to study them without advanced knowledge of mathematics. This book is intended to fill this gap in the literature.
The study of partitions has fascinated a number of great mathematicians: Euler, Legendre, Ramanujan, Hardy, Rademacher, Sylvester, Selberg and Dyson to name a few. They have all contributed to the development of an advanced theory of these simple mathematical objects. In this book we start from scratch and lead the readers step by step from the really easy stuff to unsolved research problems. Our choice of topics was motivated by our desire to get to the meat of the subject directly. We wanted to move quickly to one of the most magnificent and surprising results of the entire subject, the Rogers-Ramanujan identities.