The nature of computation

Prologue

The basics

Insights and algorithms

Needles in a haystack : the class NP

Who is the hardest one of all? : NP-completeness

The deep question : P vs. NP

The grand unified theory of computation

Memory, paths, and games

Optimization and approximation

Randomized algorithms

Interaction and pseudorandomness

Random walks and rapid mixing

Counting, sampling, and statistical physics

When formulas freeze : phase transitions in computation

Quantum computation

Mathematical tools.