Readings

Readings are assigned from the required text.

Amazon logo Ross, Sheldon. A First Course in Probability. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2009. ISBN: 9780136033134.

Additional readings are available in the links listed below.

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