Books in the spirit of Problems and Theorems in Analysis by George Pólya and Gábor Szegő

Solution 1:

Note: Your question is really a challenge, cause the book you're pointing to as reference is a first-class evergreen of highest rank.

So, I was thinking: Which books give me a similar feeling when I am going through them as the classic by Pólya and Szegő and which of them could also play in the same leaque? One other criteria was, that they should provide a reasonable thorough survey through a part of mathematics.

The first two books which came into my mind:

Enumerative Combinatorics by Richard P. Stanley

An outstanding classic to study combinatorics with an enormous wealth of examples and solutions from easy to really hard. E.g. example 6.19 of Volume $2$ provides you with $66$ different combinatorial structures related with the ubiquitous Catalan Numbers.

Applied and Computational Complex Analysis by P. Henrici

is a classic on Complex Analysis from 1977. The keyword in this 3 volume set is applied. You will by guided through lots of enlightning examples, which help you to study complex analysis and become familiar with this part of mathematics. In fact I found this book only a few years ago. I was curious that so many papers had referenced P. Henrici's book. But since I've bought it and read parts of it with great pleasure I know the reason! :-)

Solution 2:

There is a fine book by Laszlo Lovasz "Combinatorial Problems and Exercises". See (Wikipedia) http://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3_Lov%C3%A1sz or (Amazon) http://www.amazon.co.uk/Combinatorial-Problems-Exercises-Chelsea-Publishing/dp/0821842625/ref=sr_1_1?ie=UTF8&qid=1424531944&sr=8-1&keywords=Combinatorial+Problems+and+Exercises . Since you like George Polya check out his two volume "Mathematics and Plausible Reasoning" (ISBN-10: 1614275572).