Relevant textbook chapters: Ch. 0, 1, 2 (up to 2.4), 3.1, 4

Lecture Summary
===============
Week 1 (Jan 8-9): Introduction to induction
   - principle of weak induction
   - example: sequence of numbers is decreasing
Week 2 (Jan 15-19): More induction
   - 12^n - 1 is divisible by 11
   - n^2 <= 2^n
   - postage using 4 and 7 cent stamps
Week 3 (Jan 22-26): strong induction
   - intro to the principle of complete induction
   - max num of nodes in a ternary tree of height h
   - weak induction implies complete induction
   - a non-empty, full binary tree has an odd number of nodes
   - Pascal's triangle
Week 4 (Jan 29-Feb 2): 
   - complete induction implies weak induction
   - finding closed forms
   - recursively defined sets
   - counting binary strings with no adjacent zeroes
Week 5 (Feb 5-9): Program Correctness
   - well ordering principle, on quotients and remainders
   - introduction to program correctness, again on quotients and remainders
Week 6 (Feb 12-16): More Program Correctness
   - correctness of binary search

Tutorial Summary
================
Week 1:
   - review
      - logic operators
      - proof techniques
   - variations on code fragment from lecture
Week 2:
   - sum_{i=1}^{n} (1/root(i)) <= 2 root(n) - 1
Week 3:
   - Fibonacci sequence
   - for all pos. natural numbers n < m, 
        \sum_{k=1}^{m} 1/k - \sum_{k=1}^{n} 1/k >= (m-n)/m
Week 4:
   - solution to A1, question 6
   - defining sets by induction
Week 5:
   - correctness of gcd algorithm