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Probability Theory 1
MA 538
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Introduction
This course is a rigorous and measure theory oriented viewpoint on probability theory. It also includes some notions of discrete time stochastic processes. It has to be seen as a continuation of MA 532 and MA 544.

We begin by a review of basic probability and measure theory objects. We will then proceed to an in-depth analysis of the various modes of convergence for sequences of random variables. Next we will introduce the delicate notion of conditional expectation. As an important application of this concept, we will then devote a chapter to martingales an their convergence. If our schedule allows it, we will also cover some notions of Gaussian vectors and corresponding central limit theorems.
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Bibliography
  1. Grimmet-Stirzaker, Probability and Random Processes. Fourth edition.
  2. R. Durrett, Probability: theory and examples. Fifth edition.
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Homework
We will follow a problem list. Homework are usually due on Friday at 11:59pm (on GradeScope).
The assignment is given in the attached calendar.

Rules for the homework:
  1. Steps must be shown to explain your answers.
    No credit will be given for just writing down the answers, even if it is correct.
  2. The HW is submitted through GradeScope.
    Please submit each problem separately on a different page to prevent 5% penalty.
  3. Please resolve any error in the grading (HW and tests) WINTHIN ONE WEEK
    after the return of each homework and exam.
  4. No late homework are accepted (in principle).
  5. You are encouraged to discuss the homework problems with your classmates.
    However all your handed-in homework must be your own work.
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Midterm
Our midterm will be on March 6, 4:30-5:30pm, in class. 1 hour long.
Program: Modes of convergence of random variables, Laws of large numbers (sections 1 and 2). Problems 1 to 30.
A cheat sheet is authorized. It should be handwritten, at most 2 pages long, with formulae only.
This link sends you to our Spring 2025 review session
This link sends you to our Spring 2025 Midterm together with some Solutions
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Final exam
Date: During Finals Week. 1 hour long.
Program: Laws of large numbers, Conditional expectation, Martingales. Problems 31 to 67.
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Office hours
Monday 2:30pm-4:00pm, on Zoom.
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Syllabus
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Slides (Feedback on typos appreciated)
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Documents with computations (notes from lectures)
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