I look for a good text to learn basics of computational complexity.
I've read some parts of the first two chapters of "Computational Complexity: A Modern Approach" by Boaz Barak and Sanjeev Arora, it's readable and gives the big picture but I find it not to be rigorious enough for me. I'm a mathematics student so I want a more rigorous treatment of the subject. So, the text I look for should:-
1- Define Turing machines formally and prove the basic results in a formal way not using handy-waving arguments. For example, Boaz treatment of Turing machines is not rigorous and so I'd love to see more precise treatment of that.
2- Give proofs that are rigorous enough like those I read in mathematics texts and are not just "overviews".
What are your recommendations? What is the texts that satisfies my needs as close as possible?