The other text book that I know is by Cristian S. Calude, the Prof. of complexity theory that I studied under here in New Zealand. A new version of this book just recently came out. Going by the last version, the book will be somewhat more terse than the Li and Vitanyi book and thus more appropriate for professional mathematicans who are used to that sort of style. The Li and Vitanyi book is also a lot broader in its content.... thus for you I'd recommend the Li and Vitanyi book which is without doubt THE book in the field, as James already pointed out.
There should be a new verson (third edition) of Li and Vitanyi sometime this year which will be interesting. Li and Vitanyi have also written quite a few introductions to the basics of the field many of which you should be able to find on the internet. Cheers Shane
The Li and Vitanyi book is actually intended to be a graduate-level text in
theoretical computer science (or so it says on the cover) and is formatted
like a math textbook. It assumes little and pretty much starts from the
beginning of the field; you should have no problems accessing the content.
It is a well-written book, which is a good thing since it is sort of THE
text for the field with few other choices.
Cheers,
-James Rogers
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