I'll keep here various external resources from wikipedia which are relevant to each lecture. The book (due to its narrower focus) is no doubt a better resources for reviewing what we cover in each lecture. But the links below will be a good place to gain a broader perspective on what we cover in class. Of course the best resource available for the course is to come by office hours where you can ask specific questions about what we cover.
Lecture 1:

Basic principle of counting.
Lecture 2:

Power sets.
Binomial theorem.
Pascal's triangle.
Lecture 3:

Pigeonhole principle.
Venn diagrams.
Lecture 4:

Sample space.
Probability space.
Inclusion-Exclusion Principle.
Lecture 5:

Countable set.
Cantor's diagonal argument.
Birthday problem.

Lecture 6:

Conditional probability.
The two child problem.
Lecture 7:

Chain rule.
Number of permutations that are derangements.
Lecture 8:

Bayes' Theorem.
Law of total probability.
Independent events.
Mutually exclusive events.