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

Happy Piday : something to Borel Cantelli, the Monkey story:
  • 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.
  • 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

    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

    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|