Chapter 1

Counting Permutations and Combinations. (Jan. 10)

Combinations and Permutations with repetitions. (Jan. 17)

Chapter 2

Introduction to logic (Jan. 17, cont'd)

Logic Equivalences. Inference Rules. Quantifiers. (Jan. 22)

Chapter 3

Introduction to Set Theory (Jan. 24)

Set properties. Proofs. (Jan. 29)

Some more proofs about sets. Cartesian product (Jan. 31, corrected after lecture)

Counting problems for sets. (Feb. 5)

Chapters 5, 7

Relations (Feb. 19)

Composition. Inverse relation. (Feb. 21)

Closures of relations. Equivalence relations. (Feb. 26)

Equivalence relations again. Functions and their properties. (Feb. 28)

Functions composition. Inverse function.(March 5)

Chapter 4

Induction Proofs (March 26)

Recursion. Strong induction. (March 28)

Basic results of the Number Theory (April 2)

Euclid Algorithm. Fundamental Theorem of Arithmetic (April 4)

Chapter 6

Sets of strings. Regular languages and regular expressions (April 09)

Algebra of regular expressions. Deterministic Finite Automata. (April 11)

Inductive proofs on strings. (April 16, corrected after lecture)

Chapter 11

Basic facts about graphs (April 23)