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Course Outline
I. Automata and Language Theory (2 weeks): Finite automata, regular expressions, push-down automata, context free grammars, pumping lemmas.
II. Computability Theory (3 weeks): Turing machines, Church-Turing thesis, decidability, halting problem, reducibility, recursion theorem.
III. Complexity Theory (7 weeks): Time and space measures, hierarchy theorems, complexity classes P, NP, L, NL, PSPACE, BPP and IP, complete problems, P versus NP conjecture, quantiers and games, provably hard problems, relativized computation and oracles, probabilistic computation, interactive proof systems. Possible advanced topic as time permits.
Official
18.310 Principles of Applied Mathematics or 18.062J/6.042J Mathematics for Computer Science.
Real
You need some facility with the mathematical concepts of theorem and proof. Most of the assignments in this course require proving some statement and usually some creativity in finding the proof is necessary.
Text
Sipser. Introduction to the Theory of Computation. Thomson/Course Technology, 1996. ISBN: 053494728X.
Recitations are primarily for going over lecture material in more detail, for answering questions and for reviewing homework and exams. Recitation attendance is optional, and you may attend any recitation you wish. BUT, if you are having trouble with the course, I expect you to attend recitations weekly, and doing so may keep you from failing.
No recitations during the first week.
Homework
Consitutes 40% of grade. There will be 6 biweekly problem sets. Cooperation policy: Permitted (though not encouraged). If you do cooperate on some problems, then solutions must be written up individually (not copied). Using course bibles or other outside or online materials is not permitted. Late homework will be accepted the following day, but will be charged a 1 point per problem (out of the 10 point maximum) late penalty. Homework submitted after that will not be graded but will be kept for reference.
Exams
One midterm (20% of grade) during a class session and one final (40% of grade) during finals week. Both open book.