The Topic (from the academic calendar)
Introduction to abstraction; use and development of precise
formulations of mathematical ideas; informal introduction to logic;
introduction to set theory; induction; relations and functions;
big-O notation; recursive definitions, recurrence relations and their
solutions; graphs and trees.

1 Proof techniques (without using a formal system)
   - Proof by contradiction
   - Proof by cases
   - Proving implications
   - Proving statements with quantifiers
   - Mathematical induction on natural numbers
2 Naive set theory
   - Proving that one set is a subset of another
   - Proving equality of two sets
   - Basic operations on sets (union, intersection, Cartesian product,
     power sets, ec.)
   - Cardinality of sets (finite and infinite)
   - Strings
3 Functions and relations
   - Review of basic definitions (relation, function, domain,
     range, functions, 1-1 )
   - Equivalence relations
4 Asymptotic notation
   - Big-O, big-Omega, big-Theta
   - Proving f is in O(g), proving f is not in O(g)
   - Classifying functions into a hierarchy of important classes
   - Recursive definitions & solving recurrences
5 Recursive definitions of mathematical objects
   - Solving simple recurrences
   - Bounding divide-and-conquer recurrences of the form using
     structural induction y defined objects
6 Sums
   - Summation notation
   - Computing and bounding simple sums
7 Elementary graph theory
   - Basic definitions of graphs
   - Proving simple facts about graphs
   - Trees