Math 154 Spring 2026

Probability Theory

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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

  • Next week, we cover more ergodic theory: recurrence and mixing.
  • 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.
The Wednesday presentation: Look at the table of content in the description for the different sections

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

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

Exams

  • In class part Midterm
  • Take home part Midterm
  • Midterm Practice

Syllabus

  • Syllabus [PDF]
An 8 minute video from 2022 with 10 stories.

Math 154, Spring 2026 | | Oliver Knill, knill@math.harvard.edu,SciCenter 432, (617) 495-5549 | Dep. of Math | Harvard|