• Lecture 1: Samples of possibility and impossibility results in algorithm designing. (Communication complexity, query complexity.)
• Lecture 2: More samples. (Space complexity, branching programs, PIT and arithmetic circuits.)
• Lecture 3: Communication complexity 1. (Rank lower bound, logrank conjecture, Newman's theorem, distributional complexity, discrepancy, Inner Product, Disjointness.)
• Lecture 4: Communication complexity 2. (Multiparty, Number in Hand model, Promised Disjointness, streaming algorithm for frequency moments, Number on Forehead model, discrepancy, Generalized Inner Product.)
• Lecture 5: Formula complexity 1. (Random restriction, tiling number, quadratic lower bound for the parity function.)
• Lecture 6: Formula complexity 2. (Khrapchenko’s bound by general rectangle measures, convex measures and their limit, monotone formula lower bound by Disjointness matrix.)
• Lecture 7: Decision Tree complexity and basic Fourier transform. (Sublinear algorithm, Aanderaa-Karp-Rosenberg conjecture, lower bound by Fourier analysis and inlfuence.)
• Lecture 8: An introduction to expander graphs. (Chapter 1 of the classic survey by Hoory, Linial and Wigderson.)
• Lecture 9: Circuit complexity 1. (Depth-3 circuits, exponential lower bounds for Majority.)
• Lecture 10: Circuit complexity 2. (AC0 circuit, exponential lower bound for Parity, Linial-Mansour-Nisan)
• Lecture 11: Information theoretical argument. (Conditional entropy and mutual information, information complexity, linear lower bound for Disjointness)
• Lecture 12: A glimpse of computational complexity. (Computational classes including P, NP, NPC, PSPACE, L, EXP, NEXP, PH, P/poly, IP, AM, MA, PCP, MIP, etc. and several major results about them.)

Note:

• Open the .docx file with Microsoft Word.
• I'll usually print lecture notes and distribute them in class.