Module #0: Background, Motivation and Applications

Objectives

1. List application areas of Foundations
   
2. Describe history of Foundations material
   
3. Describe basic questions to be addressed
   
4. Describe importance of abstractions
   
5. Apply and construct inductive and deductive proofs
   
6. Apply and construct proofs by contradiction
   

Topics

1. Models of computation
   
2. Grammars and Languages
   
3. Abstraction
   
4. Effective Computability
   
5. Proofs
   

Background Material

0. Texts:

Hopcroft, Motwani and Ullman: 1.1-1.4
Kozen: Lecture 1
Sudkamp: Chapter 1

1a. Principle of Mathematical Induction animation
1b. Example of Mathematical Induction animation
2. Wikepedia:

1. Computation
   
2. Sets
   
3. Mathematical Induction
   
4. Proof by Contradiction
   
5. Decision Problems
   

3. Dr. J. Paul Gibson's Reasons for Studying Theoretical Computer Science
4. Busch, Shiri & Grahne: Mathematical Preliminaries Audio for these slides