[M1] Introduction to Automata Theory, Languages, and Computation (3rd edition). J.E. Hopcroft, R. Motwani, J.D. Ullman. Addison Wesley, 2007.
[M2] Lecture Notes for Theory of Computing. Diego Calvanese. 2013. Available as scanned pages in pdf.
[M3] Languages and Machines (3rd edition). Thomas A. Sudkamp. Addison Wesley, 2005. Only Chapter 13.
[M4] Complexity Theory. Ingo Wegener. Springer, 2005. Only Chapter 14.
[M5] Exercises on Theory of Computing. Available as scanned pages in pdf.

Lectures 1,2 - 2/10/2013

• Topics [M2: Part 1]
  • course presentation
  • basic definitions about sets
• What you should know after the lecture
  • the basic definitions regarding sets, relations, and their properties

Lectures 3,4 - 7/10/2013

• Topics [M2: Part 1]
  • basic definitions about relations and functions
  • cardinality of a set, countable and uncountable sets, Cantor's theorem
• What you should know after the lecture
  • the definition of cardinality of a set
  • the difference between countable and uncountable sets
  • Cantor's diagonalization argument

Exercise 1,2 - 7/10/2013

• Review of basic proof techniques [M2: Part 0]
  • deductive proofs
  • proving equivalences of sets
  • proof by contradiction
  • proof by induction

Lectures 5,6 - 9/10/2013

• Topics [M2: Part 2]
  • basic definitions about languages
  • the Turing Machine
• What you should know after the lecture
  • the formal meaning of alphabet, string, language
  • how a Turing Machine is formally defined
  • design Turing Machines that recognize some simple languages

Lectures 7,8 - 11/10/2013

• Topics [M2: Part 2]
  • instantaneous description of a Turing Machine
  • recursive and recursive enumerable languages
  • examples of Turing Machines
  • programming techniques for Turing Machines
    • storage in the state
    • multiple tracks
• What you should know after the lecture
  • how one can program a TM easier by imposing structure on states and tape symbols
  • how one can implement a procedure call with a TM

Lectures 9,10 - 14/10/2013

• Topics [M2: Part 2]
  • programming techniques for Turing Machines
    • subroutines and procedure calls
  • multi-tape Turing Machines
  • running time of a Turing Machine
• What you should know after the lecture
  • how a multi-tape TM can be simulated by a single-tape TM
  • the cost of simulating a multi-tape TM by a single-tape TM

Exercise 3,4 - 14/10/2013

• Exercises on deterministic Turing Machines [M5: Exercise 02]

Lectures 11,12 - 16/10/2013

• Topics [M2: Part 3]
  • nondeterministic Turing Machines
  • classes of languages/problems
    • recursive/decidable languages
    • recursively enumerable (R.E.) languages
    • non-R.E. languages
• What you should know after the lecture
  • how a nondeterministic TM can be simulated by a multi-tape TM (and hence also by a single-tape TM)
  • the cost of simulating a nondeterministic TM by a deterministic TM
  • how languages/problems can be classified

Lectures 13,14 - 28/10/2013

• Topics [M2: Part 3]
  • Church-Turing Thesis
  • closure properties of recursive and R.E. languages
• What you should know after the lecture
  • the Church-Turing Thesis and its implications
  • how to prove closure properties of recursive and R.E. languages

Exercise 5,6 - 28/10/2013

• Exercises on non-deterministic Turing Machines and further Turing Machines extensions. Exercises on the correspondence between function computation and language recognition by Turing Machines. [M5: Exercise 03]

Lectures 15,16 - 29/10/2013

• Topics [M2: Part 3]
  • encoding Turing Machines as binary strings/integers
  • enumerating binary strings/Turing Machines
  • showing languages to be non-recursive/non-R.E.
  • a non-R.E. language: the diagonalization languages
  • a non-recursive language: the universal language
  • Universal Turing Machines
• What you should know after the lecture
  • how to encode a Turing Machine as a binary string
  • how to prove that the diagonalization language is non-R.E.
  • how to prove that the universal language is non-recursive

Lectures 17,18 - 30/10/2013

• Topics [M2: Part 3, Part 4]
  • the notion of reduction between problems/languages
  • Rice's theorem
• What you should know after the lecture
  • what a reduction is
  • how to prove Rice's theorem

Exercise 7,8 - 31/10/2013

• Exercises on reductions between problems. [M5: Exercise 04]

Lectures 19,20 - 4/11/2013

• Topics [M2: Part 4]
  • Primitive recursive functions
  • examples of primitive recursive functions
• What you should know after the lecture
  • the definition of primitive recursive functions
  • how to construct some simple primitive recursive functions

Exercise 9,10 - 4/11/2013

• Exercises on Turing Machines computing functions [M5: Exercise 05]

Lectures 21,22 - 6/11/2013

• Topics [M2: Part 4]
  • showing computability of primitive recursive functions
  • bounded operators and bounded minimization
  • Gödel numbering
• What you should know after the lecture
  • how to prove that every primitive recursive function is Turing computable
  • how to define primitive recursive functions using bounded minimizations
  • how to encode and decode a sequence of numbers by means of a single number

Exercise 11,12 - 12/11/2013

• Exercises on the topics of the midterm exam [M5: Exercise 06]

Lectures 23,24 - 13/11/2013

• Topics [M2: Part 4]
  • course-of-values recursion
  • total computable functions that are not primitive recursive
  • mu-recursive functions
  • Turing computability of mu-recursive functions
• What you should know after the lecture
  • how to define functions by means of course-of-values recursion, and how to show that they are primitive recursive
  • how to prove the existence of computable functions that are not primitive recursive
  • the definition of mu-recursive functions
  • how to show that every mu-recursive function is Turing computable

Exercise 13,14 - 15/11/2013

• Exercises on primitive recursive functions [M5: Exercise 07]

Lectures 25,26 - 18/11/2013

• Topics [M2: Part 4]
  • arithmetization of Turing Machines
• What you should know after the lecture
  • how to define a (primitive) recursive function that computes the trace of a Turing Machine computation
  • how to define a mu-recursive function that simulates the computation of a Turing Machine computation

Midterm exam - 18/11/2013

• Topics
  • Turing Machines
  • decidability and undecidability
  • recursive and recursively enumerable languages
  • recursive functions

Lectures 27,28 - 20/11/2013

• Topics [M2: Part 5]
  • tractable and intractable problems
  • the classes P and NP
  • a problem in NP: SAT
  • SAT and CSAT
  • poly-time reductions
• What you should know after the lecture
  • how the classes P and NP are defined
  • how to show a problem to be in NP
  • how to polynomially reduce one problem to another

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