Logic, Automata, and Computability

Description

During the first half of the course, we will take a tour through some of the rigorous mathematical foundations of modern computer science. Do not let the word ``rigorous'' scare you off---any student who possesses basic number skills, a healthy desire to grapple with abstract concepts, and perserverance may do well in this part. The second half of the course will take a close look at the concept of logical deduction. We will study classical propositional and quantifier logic using an approach called `natural deduction'. Towards the end of the course, we will look at intuitionistic logic, after an introduction to various philosophies of mathematics.

Topics covered:
Lectures for the first half will draw on topics from the following list: formal languages, finite-state automata, push-down automata, computability, Turing machines, Markov algorithms, effective enumerations, the Church-Markov-Turing thesis, the Halting Problem.

The second half of the course will take a close look at the concept of logical deduction. Lectures will cover propositional and first-order natural deduction, soundness and completeness of formal systems, interpretations, Gentzen's sequent calculus, equivalence of logical systems, and links between proof and computation. Time depending, we may venture into aspects of non-classical logics such as intuitionistic logic and substructural logics.