Good mathematical book on algorithms I’m a sucker for mathematical elegance and rigour, and now am looking for such literature on algorithms and algorithm analysis. Now, it doesn’t matter much to me what algorithms are covered, but very much how they are presented and treated.¹ I most value a very clear and precise language which defines all used notions in a stringent and abstract manner.

I found that the classic Introduction to Algorithms, by Cormen, Leiserson, Rivest and Stein is pretty neat, but doesn’t handle the mathematics well and is quite informal with its proofs and definitions. Sipser’s Introduction to the Theory of Computation seems better in that regard, but still offers no seamless transition from mathematics to algorithms.

Can anyone recommend something?



¹: The algorithms should at least invole the management of their needed data using classical non-trivial abstract data structures like graphs, arrays, sets, lists, trees and so on – preferably also operating on such data structures. I wouldn’t be too interested if the issue of usage and management of data structures was ignored altogether. I don’t care much about the problems solved with them, though.
I think the book you describe has a name. It is in seven volumes, only three and half  of which have been published. It is called The Art of Computer Programming,
(TAOCP) and is written by Donald Knuth.

It may be though that he will sometimes describe applications. But you can always skip that, and I doubt it makes much of the content. You should not be too disappointed with the maths.