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In particular, a  lecture   can be moved to on-line mode on a very short notice, so please check your e-mail before every class.

Class number 39720

Math 507a in Fall 2025 semester: Key dates

  • August 25: first day of classes
  • September 1: Labor Day, no class
  • September 12: Last day to drop without a W AND with refund
  • October 9,10: Fall Break
  • October 10: Last day to drop without a W, BUT WITH NO refund
  • October 29: Midterm exam
  • November 14: Last day to drop with a W
  • November 26-30: Thanksgiving Break
  • December 5:  Last day of classes
  • December 12: Final exam (11am-1pm, in KAP 148)

Final project (FP)

Homework Problems (HW)

Instructor: Dr. Sergey Lototsky
Office: KAP 248D.
Phone: 213–740-2389.
E-mail: lototsky (at) USC (dot) edu
URL: https://dornsife.usc.edu/sergey-lototsky/
Lectures:  MWF 12-12:50pm, KAP 148
Office hours: MWF 2:15-3:15pm [in KAP 248D]

Please do not hesitate to talk to me about your problems, questions, or concerns in this class. We can always arrange a special zoom meeting.

Teaching Assistant (Grader): Pengtao Li
E-mail: pengtaol {at} usc [dot] edu
Office hours:  M 2-3pm, F 2-4pm, all  in the Math Center (KAP 263)

  • Textbook: “Probability: Theory and Examples” by Richard Durrett, published by Cambridge University Press. Any edition will do; the most recent is 5th, from 2019. Electronic version (individual chapters) can be downloaded from the USC Libraries.
  • Alternative:   “Probability” by A. N. Shiryaev, published by Springer. The most recent (3rd) edition is in two volumes. Check out the USC libraries.
  • Objective:  To learn the  foundations of measure-theoretic probability by mastering the material in the first three chapters of the book (plus conditional expectation using Section 4.1)) . 
  • Goal:  To be ready for math 507b.
  • The ultimate goal:  To make you comfortable handling probability-related questions at any level and in any conditions.

Save the dates! There will be an in-class one-hour exam (Wednesday, October 29)  during regular lecture time. The two-hour final exam is Friday, December 12, 11am-1pm, in the regular lecture room KAP 148.

Note: You might need a PDF Scanner, to submit your (mostly likely handwritten) work to Gradescope
in PDF format (one PDF per assignment or exam). There are many free phone apps that you can use
to scan your work to make a PDF, for instance Adobe Scan.

Note on Use of AI
You are welcome to use  artificial intelligence (AI) powered programs as a help with homework problems and computer projects, but not with quizzes and exams. While AI tools can help you brainstorm ideas or revise work you have already written, AI text generation tools may present incorrect information, biased responses, and incomplete analyses. To adhere to our university values, you must cite any AI-generated material (such as text or images) included or referenced in your work and provide the prompts used to generate the content.  I will not be using any AI tools in grading your work.

Official grading scheme: 40% Homeworks, 30% Final exam, 20% Midterm, 10% Final project

General plan:  Survey of undergraduate probability and graduate measure theory following Chapter 1,  Section 4.1 and Appendix A of Durrett’s book [Weeks 1-5], convergence in probability and almost sure following Chapter 2 of  Durrett’s book [Weeks 6-10], weak convergence following Chapter 3 of Durrett’s book [Weeks 10-15].

Target dates:  Sep 5 (HW1),  Sep 12 (HW2),  Sep 19 (HW3), Sep 26 (HW4), Oct 3 (HW5), Oct 17 (HW6), Oct 24 (HW7), Nov 7 (HW8), Nov 14 (HW9), Nov 21 (FP), Dec 5 (HW10).

Notes

   Mine: course material

  1. A summary of undergraduate probability (for example USC MATH 407)
  2. Random variables: general definitions and an easy diagram
  3. Basic inequalities
  4. More on probability inequalities
  5. Convergence of random variables and an illustration
  6. A summary of discrete random variables
  7. Gaussian objects: Normal random variables, CLT, and more
  8. The normal tail
  9. Gaussian distribution: a time line
  10. Normal approximation: Binomial(N=30, p=0.5), Binomial(N=30, p=0.1), Poisson(36.6), MatLab codes
  11. Cauchy distribution
  12. Exact relations among probability distributions
  13. Glivenko-Cantelli theorem
  14. A summary of renewal theory
  15. A summary of large deviations
  16. Asymptotic integration
  17. Weak convergence of probability measures
  18. A summary of characteristic functions
  19. A summary of the extreme value theory
  20. Arrivals in the Poisson process and an illustration of clustering
  21. Buffon’s needle and more
  22. The Weierstrass (polynomial) approximation theorem
  23. A summary of random object generation

Mine: extras

Found on line