Syllabus


==== Math 571 Advanced Probability. Spring 2026.====
Binghamton University 

  * Instructor: Vladislav Kargin
  * Office: WH-136
  * Meeting time and location: TR -- 8:00-9:30AM -- WH 329
  * Office hours: Wednesday -- 12-1:30pm 

** This course is a 4-credit course, which means that in addition to the scheduled lectures/discussions,
students are expected to do at least 9.5 hours of course-related work each week during the
semester. This includes things like: completing assigned readings, participating in lab sessions,
studying for tests and examinations, preparing written assignments, completing internship or
clinical placement requirements, and other tasks that must be completed to earn credit in the 
course. **

=== Prerequisite ===

Probability Theory (MATH 501)

=== Description ===

This course is an introduction to the advanced concepts of probability theory. It covers topics such as: Measure theory, Probability spaces, Random variables, Conditional Expectations, Stochastic processes, Martingales, Limit Theorems, Large deviations
   
The course is intended for students who have a strong foundation in probability theory.



=== Recommended Texts ===


Durrett "Probability: Theory and Examples" 5th edition, pdf available at [[https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf|PTE]].




=== Piazza===

We will use Piazza ("http://piazza.com/") for communication. All announcements will be sent to the class using Piazza.
 


=== Homework Policies === 

Weekly sets. I fully grade two or three problems (announced after submission); the other count for completion. Solutions must be concise (≤1 page/problem) and list the named results used (e.g., “DCT + UI”).
Starting HW2, the solution for these problems must be typed in LaTeX, typeset to pdf and submitted by the due date. 3 late-day tokens total for the term; beyond that late work is not accepted. 

Rubric for a HW problem:
4 = correct & clear; 3 = essentially correct (minor gap); 2 = right idea with major gap; 1 = meaningful progress; 0 = off-track. +0.5 exposition bonus possible (capped at 4).

 I may invite you to brief board checks on your own solutions; these verify understanding and may adjust the HW score slightly.

You may discuss ideas, but write your own solutions.



=== Exam === 
There will be one in-class midterm (open-book/no-web) and a final take-home exam with a brief (~10-12 minutes) oral follow-up. I will choose one of your solutions and ask a few “why does this step hold? / where does the hypothesis bite?” questions. Final is cumulative.




=== Grading ===
  * Homework (45%)
  * Midterm exam (15%)
  * Final write-up (30%)
  * Final follow-up (10%)
 




/*
=== Project ===
You are supposed to prepare a project for this course and make a presentation on the project. 
The project should cover some topic in probability theory. You can choose your own topic. It might be a topic, which is not covered by the lecturer, or it might be a recent paper in a mathematical journal.  
You are supposed to give a 30-minute presentation on the topic, which should be a lecture to your fellow students. You may choose to do a blackboard lecture or a slide presentation, as you prefer.
You presentation will be graded on the following criteria:

    • Clarity: Your presentation should be clear and easy to understand.
    • Engagement: Your presentation should be engaging and interesting.
    • Answering questions: You should be able to answer questions from the audience about your topic.



<h2>Data Analysis Contest</h2>
<p>Students will compete against each other in a Data Analysis Contest. The competition will begin on Tuesday, Feburary 20 and can be completed in teams of 2 &ndash; 4 members. Grades will be based upon a progress report and a final report (one per team) as well as the contest results. Further details about the contest along with specific grading criteria will be given in a separate document and discussed in class.</p>
*/





=== Tentative schedule ===

| Midterm | TBA |
| Final Exam | TBA, as scheduled by the University|