Required textbook
Michael Sipser, Introduction to the Theory of Computation, 2013 (Third Edition, most of the material is also available inside the Second Edition)
Detailed information about the textbook is available at Michael Sipser’s website: http://www-math.mit.edu/~sipser/

CS 525 Reading Schedule, Online Section, Winter 2014
Textbook reading schedule
0.1-0.4 preliminary reading
1.1-1.3 before Wednesday of week 1
1.4, 2.1-2.2 before Wednesday of week 2
2.3-2.4 before Wednesday of week 3
3.1-3.3 before Wednesday of week 4, without Nondeterministic Turing Machines (NTMs)
NTMs and 4.1-4.2 before Wednesday of week 5
5.1-5.3 before Wednesday of week 6
6.1-6.3 before Wednesday of week 7
7.1-7.2 before Wednesday of week 8
7.3-7.4 before Wednesday of week 9, without Cook-Levin (C-L)
C-L and 7.5 before Wednesday of week 10

An extensive reference on the background in logic needed for 6.2 and 7.4 is Mathematical Logic by Stephen Simpson: http://www.personal.psu.edu/t20/notes/logic.pdf

Tips for reading

Concentrate on definitions, examples and the meaning of theorems during your initial reading.

Always try to build your own intuitive understanding out of formal logical proofs.

If you get stuck on a detail do not spend too much time on it, continue reading further. Most often you will be able to figure out the detail later on.

If a proof is totally unclear to you, skip it. Go back to it after you gain a better intuitive understanding achieved by working out some related problems.

If the topic is already familiar to you, only browse through it. Recognize however the differences with the presentation you are familiar with.

Additional reading
The Incompleteness Theorem by Martin Davis (preliminary reading): http://www.ams.org/notices/200604/fea-davis.pdf

Turing's Thesis by Solomon Feferman (preliminary reading): http://www.ams.org/notices/200610/fea-feferman.pdf

The Church-Turing Thesis by B. Jack Copeland (during week 4, parallel to your initial study of Turing machines): http://plato.stanford.edu/entries/church-turing/

 

Undecidability in Number Theory by Bjorn Poonen (during weeks 5,6,7, parallel to the study of computability): http://www.ams.org/notices/200803/tx080300344p.pdf


Turing Reducibility? by Martin Davis (during week 7, parallel to the study of Turing reducibility): http://www.ams.org/notices/200610/whatis-davis.pdf

P, NP and Mathematics by Avi Wigderson (the first three sections, pages 1-24, during weeks 9,10, parallel to the study of computational complexity): http://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/W06/w06.pdf