Math 154
Spring 2026
Probability Theory
Home
Blog
Exhibits
About
Course Staff:
Oliver Knill knill@math
Faris Doughan farisdoughan@college
Oscar Melendez omelendez@college
External Links
Math 154 Canvas
Links
Caltech 1994 (book) [PDF]
Caltech 1995 [PDF]
Harvard 2003 [PDF][
Harvard 2011 [PDF]
Arizona 1997 [PDF]
Announcements
1 Minute review slides for final
. See also:
1 Minute review from midterm
.
April 22: Perron Frobenius
.
Here is a list of 40 topic suggestions
. The paper is due Mai 9th.
Oscar has OH Monday and Wednesday 7:30-9:30 at Math D-Hall. Faris is on Thursdays 6-8 PM in Inn (1201 Mass av private dining room). OH Oliver Tuesday 11:30-12:30 AM and Friday 11 AM-12:30 PM
Vitali Set construction (1 minute)
About the Lebesgue integral
.
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Notes
Unit 1: Introduction
Unit 2: Paradoxa
Unit 3: Algebras
Unit 4: Probability measures
Unit 5: Random variables
Unit 6: Distributions
Unit 7: Independence
Unit 8: Characteristic functions
Unit 9: Borel-Cantelli
Unit 10: Exam part 1
,
part II
Unit 11: Inequalities I
Unit 12: Inequalities II
Unit 13: Convergence
Unit 14: Weak law
Unit 15: Strong law
Unit 16: Ergodic theorem
Unit 17: Recurrence
Unit 18: Mixing
Unit 19: Central Limit Theorem
Unit 20: Poisson Limit Theorem
Unit 21: Random walks
Unit 22: Markov
Assignments
1. Homework, Due Fri 2/6/26
2. Homework, Due Fri 2/13/26
3. Homework, Due Fri 2/20/26
4. Homework, Due Fri 2/27/26
5. Homework, Due Fri 3/13/26
6. Homework, Due Fri 3/27/26
7. Homework, Due Fri 4/3/26
8. Homework, Due Fri 4/10/26
9. Homework, Due Fri 4/17/26
10. Homework, Due Fri 4/24/26
Exams
In class part Midterm
Take home part Midterm
Midterm Practice
Syllabus
Syllabus [PDF]
An 8 minute video from 2022 with 10 stories.