Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning a

This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computabil