Chapter 1

Counting Permutations and Combinations. (May 8)

Combinations with repetitions. Pigeonhole Principle. (May 10, corrected after the lecture)

Chapter 2

Introduction to Logic. (May 10, cont'd)

Logical Equivalences. Inference rules. Quantifiers. (May 15)

Chapter 3

Introduction to Set Theory (May 17)

Proofs for sets (May 22)

Power sets. Inclusion-exclusion principle. (May 24)

Counting subsets. Binomial coefficients. (May 29)

Review for Test #1 (May 31)

Chapters 5,7

Relations. Composition. (June 12)

Inverse relation. Closures. (June 14)

Transitive closure. Equivalence relations. Functions.

Composite function. Properties of composite functions. Inverse function. (June 21)

Inverse of the composite function. Proofs with functions. (June 26)

Sets of images and pre-images. Test review. (June 28)

Chapter 4

Mathematical Induction. (July 05)

Induction proofs. (July 10)

Strong Induction. Graphs. (July 12)

Introduction to Number Theory. (July 17).

Prime factorization. Fundamental Theorem of Arithmetic.(July 19)

Chapter 6

Sets of strings. (July 19, cont'd)

Languages and Machines (July 24)