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Theory of Partitions (Encyclopedia of mathematics and its applications ; v. 2 : Section, Number theory): George E. Andrews

This book develops the theory of partitions. Simply put, the partitions of a number are the ways of writing that number as sums of positive integers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. Surprisingly, such a simple matter requires some deep mathematics for its study. This book considers the many theoretical aspects of this subject, which have in turn recently found applications to statistical mechanics, computer science and other branches of mathematics. With minimal prerequisites, this book is suitable for students as well as researchers in combinatorics, analysis, and number theory.

Review:

This is *the* classic and most essential reference on the theory of partitions and related q-series written by the leading authority on the subject. It requires almost no technical prerequisites, starts from scratch, and proceeds in a very clear and orderly manner towards some of the more elaborate aspects of the subject. If you (plan to) work on this subject, buy it.

The book was written in 1976, and as such does not cover the more recent developments, though the bibliography has been updated (to a limited degree) for the current 1998 paperback edition. However, after all these years, it remains *the* introduction to the subject (with the possible exception of chapter 14 on computational methods, which is definitely outdated), and can be supplemented only by Gaspar and Rahman's 'Basic Hypergeometric Series'. I taught a higher undergraduate level course based on chapters 1, 2, 3, 7 and 9, and my students definitely found these chapters to be highly readable.

My one and only complaint is to Cambridge University Press: Dover has shown that paperbacks can be produced in such a way that they can be opened completely flat without being damaged, and quite cheaply too. Why can't you adopt the same technology?

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