This is a very interesting and easy-to-read introduction to combinatorics. It has the flavor of a popular math book, with lots of drawings and not much mathematical jargon, although unlike such books it does has a number of formulas and some infinite series.
The book is based on a course taught at Stanford in the Winter 1978 quarter. George Pólya taught the first two-thirds of the course, which dealt with counting problems. Robert E. Tarjan taught the last third of the course, which dealt with constructive combinatorics and some existential combinatorics. Donald R. Woods was the teaching assistant for the course, and collected and organized the classroom notes into this book. The present volume is an unaltered reprint of the 1983 edition.
Although an introduction, the book goes for depth rather than breadth. It deals with only few problems, but goes into much detail on them and often gives more than one solution. The standout topics are Pólya’s theory of counting, that analyzes the possible isomers of different chemical chemical compounds by treating them as graphs, and the marriage problem, that analyzes many variants of this classic topic.
Despite being 30 years old, the book has aged well, and there’s really nothing to show it is not brand-new. The weak points as a text are lack of an index and the lack of exercises. The book reproduces the mid-term and final examinations, with detailed solutions to the problems, but there are no other exercises except an occasional “exercise for the reader.”
Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.