MATH/CS-227 Outline:

Topic	Wks	Sub-Topics
Functions, relations & sets	2	Sets (Venn diagrams, complements, unions, intersections, Cartesian products) DeMorgan’s laws Relations (reflexivity, symmetry, transitivity, equivalence relations) Functions (surjections, injections, inverses, composition)
Logic (Part I)	3	Truth tables Conjunction, disjunction, negation, implication (hypotheses, conclusions, converses, contrapositives) DeMorgan’s laws again Natural Deduction (Modus Ponens, Modus Tollens, etc.) Universal and existential quantification Validity – implication
Matrices	1	Addition Multiplication Inverses
Elementary Number Theory	2	Divisibility Fundamental Theorem of Arithmetic Gcd’s, lcm’s, number of divisors Modular arithmetic Bases (in particular, binary and hex)
Proof Techniques	2	Methods of proof: direct, indirect, contradiction Counterexamples The Principle of Mathematical Induction
Basics of Counting	2	Pigeonhole principle Permutations & combinations Basic probability