Readings are assigned from the required textbook.

Ross, Sheldon. A First Course in Probability. 8th ed. Pearson Prentice Hall, 2009. ISBN: 9780136033134.

1 Permutations and combinations Sections 1.1–1.3 (also Pascal's triangle—as studied (not invented) by Pascal, see also correspondence with Fermat: Fermat and Pascal on Probability (PDF))
2 Multinomial coefficients and more counting Sections 1.4–1.5 (see Pascal's pyramid)
3 Sample spaces and set theory Sections 2.1–2.2
4 Axioms of probability Sections 2.3–2.4 (see Paulos' NYT article and a famous hat problem)
5 Probability and equal likelihood Sections 2.5–2.7 (and a bit more history)
6 Conditional probabilities Sections 3.1–3.2 (and Conditional risk)
7 Bayes' formula and independent events Sections 3.3–3.5
8 Discrete random variables Sections 4.1–4.2
9 Expectations of discrete random variables Sections 4.3–4.4 (and, for non-discrete setting, examples of non-measurable sets, as in the Vitali construction)
10 Variance Section 4.5
11 Binomial random variables, repeated trials and the so-called Modern Portfolio Theory Section 4.6 (and the so-called Modern Portfolio Theory)
12 Poisson random variables Section 4.7
13 Poisson processes Section 9.1
14 More discrete random variables Sections 4.8–4.9
15 Continuous random variables Sections 5.1–5.2
16 Review for Midterm Exam 1 No Readings
17 Midterm Exam 1 No Readings
18 Uniform random variables Section 5.3
19 Normal random variables Section 5.4
20 Exponential random variables Section 5.5
21 More continuous random variables Sections 5.6–5.7
22 Joint distribution functions Sections 6.1–6.2
23 Sums of independent random variables Sections 6.3–6.5
24 Expectation of sums Sections 7.1-7.2
25 Covariance Sections 7.3–7.4
26 Conditional expectation Sections 7.5–7.6
27 Moment generating distributions Sections 7.7–7.8
28 Review for Midterm Exam 2 No Readings
29 Midterm Exam 2 No Readings
30 Weak law of large numbers Sections 8.1–8.2
31 Central limit theorem Section 8.3
32 Strong law of large numbers and Jensen's inequality Sections 8.4–8.5 (see also the truncation-based proof on Terry Tao's blog and the characteristic function proof of the weak law) and Jensen's inequality
33 Markov chains Section 9.2
34 Entropy Sections 9.3–9.4
35 Martingales and the Optional Stopping Time Theorem Martingales and the Optional Stopping Time Theorem
36 Risk Neutral Probability and Black-Scholes Black-Scholes (look up options quotes at the Chicago Board Options Exchange)
37 Review for Final Exam No Readings
38 Review for Final Exam (cont.) No Readings
39 Review for Final Exam (cont.) No Readings