Math 70: General Course Outline
Course Description
70. Introduction to Probability. (4) Lecutre, 3 hours; Discussion, 1 hour. Requisites: courses 31A, 31B. Introduction to probability through applications and examples. Topics include laws of large numbers, statistics, chance trees, conditional probability, Bayes? rule, continuous and discrete random variables, jointly distributed random variables, multivariate normal and conditional distributions. In depth discussion of betting schemes in gambling, occurrence of rare events, coincidences and statistical predictions. P/NP or letter grading.
Course Information:
The course introduces a list of standard probabilistic problems and analyzes them in detail within the formalism of probability as a mathematical discipline. At the end of the course, the students will be able to demonstrate their understanding of the foundations and basic facts of probability as a mathematical discipline and apply them to resolve questions with probabilistic content.
Textbook(s)
Tijms, H. Understanding Probability, Chance Rules in Everyday Life, 3rd Edition. Cambridge University Press, 2012
Schedule of Lectures
| Lecture | Section | Topics |
|---|---|---|
|
Week 1 |
Ch. 1-2 |
Laws of large numbers and simulation |
|
Week 2 |
Ch. 3-4 |
Probability in everyday life and rare events |
|
Week 3 |
Ch. 5-6 |
Probability and statistics, chance trees |
|
Week 4 |
Ch. 7 |
Foundations of probability |
|
Week 5 |
Ch. 8 |
Conditional probability and Bayes? Rule |
|
Week 6 |
Ch. 9 |
Discrete random variables |
|
Week 7 |
Ch. 10 |
Continuous random variables |
|
Week 8 |
Ch. 11 |
Jointly distributed random variables |
|
Week 9 |
Ch. 12 |
Multivariate normals |
|
Week 10 |
Ch. 13 |
Conditional distributions |