Lecture Schedule

Note: The section numbers refer to the course notes for the class.

May 5--9:    Course logistics, and outline. Valid reasoning, the conditional statement, other logical connectives, truth tables. (Sections 1.1, 1.2, 1.3)

May 12--16:    Methods of proof, Mathematical induction, strong induction. (Sections 1.5, 1.6, 1.7)

May 21--23:    Divisibility, properties of the relation, the Division Algorithm, GCD, the Euclid algorithm. (Sections 2.1, 2.3)

May 26--30:    Termination and correctness of the Euclid algorithm, the extended Euclid algorithm, properties of GCD. (Section 2.3)

June 2--6:    Linear Diophantine equations, prime numbers and their properties. (Sections 2.4, 2.5)

June 9--13:    Prime numbers (continued), Rules for divisibility, Congruences and their properties. (Sections 2.5, 3.1, 3.2)

June 16--20:    Further properties of congruences, Review for midterm, Fermat's little theorem. (Sections 3.1, 4.1)

June 23--27:    Linear congruences, Chinese remainder theorem, Private key encryption. (Sections 3.3, 3.4, 5.1)

July 2--4:    Public key encryption, RSA cryptosystem. (Section 5.2)

July 7--11:    Correctness of the RSA cryptosystem, modular exponentiation. Graphs, common classes of graphs. (Sections 5.2, 9.1)

July 14--18:    Walks, paths, cycles; connected graphs, components; bi-partite graphs; the n-cube and its properties; bi-partiteness and odd cycles. (Sections 9.1, 9.3, 10.1, 10.4)

July 21--25:    Isomorphism, subgraphs, cut-edges, trees, spanning trees, breadth-first search. (Sections 9.1, 10.1, 10.2, 10.3, 10.4)

July 28--30:    breadth-first search and applications. (Section 10.4, 10.5)