Older lectures (These are from previous years, and I will mostly stick to them)
Lecture 1 Read Sections 1, 2, and 3 from Ch. 1 Introduction
Lecture 2. Read beginning of Section 4 in Ch. 1 Introduction and Section 6 in Chapter 0.
Lecture 3. Finish reading Ch. 1. Read last section of chapter 0 on sets. (I will go over the handshake Lemma next time, but read Section 5 of Ch. 1)
Lecture 4 Finish reading Ch. 1, read Section 4 of Ch. 2. Do the exercises suggested in the last slide.
Lecture 5 (Last two pages are useful for homework 2) Read Ch. 2 Sections 1 and 3, and the first two pages of Section 6 (until the table with one entry missing).
Counting Supplement Read this summary of the previous lecture
Practice counting and here
Lecture 6 Read last section of chapter 0 and the first two pages of Section 2 in Ch. 2.
Lecture 7 Read Ch. 2 Section 6.
Lecture 8 Read Ch. 2 Section 5.

Lecture 9 Read Ch. 3 Section 6 and first page of Section 7.
Lecture 10 Finish Section 7 in Ch. 3.
Lecture 11 Read Ch. 3 Sections 2 and 3.
Summary of proof techniques so far
Lecture 12 Read Ch. 3 Section 8.
Lecture 13 Inclusion-Exclusion. Read Ch. 4 Sections 1, 2, 3, 4, and 6.
Lecture 14 The pigeonhole principle. Read Ch. 4 Sections 8 (some examples were not covered in lecture, and vice-versa).
Lecture 15 Proofs by induction.
Lecture 16 Continue with proofs by induction, strong induction.
Lecture 17 Recurrences and Induction. Read Ch. 6 Sections 1, 2, 3, and 4.
Lecture 18 Finish first 6 pages of Ch. 6. The remaining parts of Ch. 6 are not going to be covered.
Lecture 19 (combined with above) More examples of solving recurrences.

Lecture 20 Number theory. Divisibility and the Euclidean algorithm, Ch. 7 Sections 1-4.
Lecture 21 Primes, co-primes, equivalence relations, and congruence. Ch. 2, pages 4-5, Ch. 7 Sections 5, 6, 7, 9 (exluding modular arithmetic)
Lecture 22 Partial order relation (Ch. 2 pages 5-7, we did not cover chains and antichains however), modular arithmetics, finding inverses using Euclidean algorithm, Ch. 7 pages 8-10 (we did not cover Chinese remainder theorem).
Lecture 23 Fermat's little theorem and primality testing. Read Ch. 7 Section 11.
Lecture 24 Cryptography. Read Ch. 7 Section 12.
Lecture 25 Graphs. Read Ch. 8 Sections 1, 2, 4, 5, 6.

Actual class notes from Fall 2022 (also based on the older lectures above)
Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 What to focus on for final