Combinatorics of Finite Sets (Dover Books on Mathematics)

Rating:
Summary: Masterpiece
Review: This book is excellent. I should sincerely congratulate to Prof. Ian Anderson.
The book's subject is about one of the most beautiful and important parts of mathematics, where any result could be one gem.
I think that better than this is not possible, although the book is very cheap, but the reader can obtain the very nice and valuable results of the branch of mathematics once.

Rating:
Summary: An excellent and unique perspective on combinatorics
Review: When one thinks of combinatorics of finite sets, he or she might first think of codes and designs. But this book introduced me to an area of combinatorics which I knew very little about, namely extremal set problems and their solutions which fall under famous Theorems by famous mathematicians: Erdos-Ko-Rado, Sperner, and Kruskal-Katona to name a few. I found these topics fascinating and fun to think about, which is in large part due to the author's coherent style, organization, explanation, and expertise of the subject-matter. Moreover, the author provided solutions to *every* one of the 150+ problems!!! How many math books can boast such a claim? Aside from may be a rough presentation of Lemma 4.3.2 the rest of the book is a masterpiece which I hope will gain more recognition within the next twenty years.

I highly recommend this book to both mathematicians and computer scientists. Although the book has very few "algorithms" in it, the thinking and reasoning about discrete structures (e.g. families of finite sets and multisets) will do wonders in developing the mind of a computer scientist, whether advanced or undergraduate. Yet it is quite sad that many cs departments (and math for that matter) invest little if any curriculum in discrete mathematics. Hopefully this will change at least to the point where the cs major will take two or three semesters of discrete math instead of two or three of calculus. For, as this book demonstrates, calculus is not a prerequisite for engaging one's mind in some quite fascinating mathematical problems related to finite sets.

Finally, it should be noted that Bela Bollobas also has an interesting book titled "Combinatorics: Set Systems, etc...." which significantly intersects with this book, but not to the degree where the reader should think they are interchangeable. I recommend both, and to read Anderson's book first; as I believe this book lays a better foundation than the latter.