Course title:

Theory of Probability (Fall 2025)

Sections

MATH-UA.0333-005 and MA-UY 3014-C

Time:

Tuesday Thursday  09:30 AM - 10:45 AM

Room:

Courant Institute / Warren Weaver Hall (251 Mercer St), Room 201

Instructor:

Professor Yuri Bakhtin  (he/him/his)

Communication

Most communication will be done via Brightspace. The best way to contact me is via Brightspace or email yb22@nyu.edu. For efficient email communication and etiquette, I recommend reading materials linked from https://cims.nyu.edu/~bakhtin/email-etiquette.html

Office hours:

(Tentatively) Tuesday 11am-12 Thursday 1:30-2:30pm. My office is 729 at Courant Institute.

Recitation:

Fridays 9:30-10:45 AM at CI / WWH Room 201. 

Recitation Leader: Sheikh Saqlain, ss17808@nyu.edu 

Course description:

An introduction to the mathematical treatment of random phenomena occurring in the natural and social sciences. Axioms of mathematical probability, combinatorial analysis, binomial distribution, Poisson and normal approximation, random variables and probability distributions, generating functions, Markov chains, applications.

Textbook:

The textbook we will be using for the course is Introduction to probability, Second Edition  by Joseph K.Blitzstein and Jessica Hwang (The first edition is OK, too). Paper copies of the textbook can be bought at  at this link. Free online access (no download though) is provided by the authors at Blitzstein Hwang Probability.pdf. Other forms of electronic access are available at this link through NYU.

We will cover or touch the material from almost every chapter in this book but often we will not follow the book literally.

There are many probability textbooks. Last time I taught this class, I used A first course in probability by Sheldon Ross but I like the new one better.

Prerequisites:

This course is intended for math majors and other students with a strong interest in mathematics. It requires fluency in calculus topics such as limits, derivatives, series, (multi-variable) integration. It makes sense to look through the textbook in advance to know what to expect.

Homework

Homework will account for 10% of the final score.  Homework problem sets along with instructions and deadlines will be posted on Brightspace (usually, weekly) and you will submit your work electronically. It can be typed or handwritten but it has to be in the PDF format. Late homework will not be accepted. Two worst homework scores will be dropped for each student.

You may work on problems in groups and use AI/LLM as described below but each student must write down their own solutions. Collaborations and the use of AI must be acknowledged for each problem.

You are allowed to use Large Language Models (LLMs), such as ChatGPT or Claude, as tutoring aids for mathematical problem solving. Your own problem-solving efforts are paramount though. In addition, while LLM models can be valuable resources, they are subject to both obvious and subtle errors. For maximum growth and test preparation you are required to follow the rules below.

1. Do your best to solve the problem without any help from AI/LLM.
   
2. After arriving at your solution, you may consult an LLM to verify the correctness of your answer or proof.
   
3. If the LLM detects mistakes, inquire about the reasons and request guidance to correct your solution.
   
4. Once the correct approach is established, ask the LLM to provide a concise and mathematically rigorous answer.
   
5. Transcribe the answer you consider correct making sure to annotate and explain where your approach diverged from the correct one. This reflection process is key to reinforcing your mathematical understanding.
   

Following these steps you will maximize the educational value of LLM models while maintaining the integrity and independence of your learning.

Quizzes

Throughout the course, 6 (six) quizzes will be given at the beginning of randomly chosen lectures and/or recitations. Each quiz will be closed book and will be entirely based on one of the most recent homework problems, after the assignment is due. It will be assumed that you already know how to solve the problem and all you need to do is to reproduce the solution you just submitted as a part of the homework assignment. For each student, their best 5 quizzes out of 6 will count for 10% of the course grade (i.e., the worst quiz score will be dropped).

Exams:

Two midterm exams and the final exam are in-class and closed book. You are only allowed a pen/pencil, and an eraser. I will provide paper and you will not be allowed to use any other paper.  No electronics (including but not limited to computers, phones, watches, AI glasses), books, notes, or any other aids will be allowed, and this will be strictly enforced.

Your midterm grade will be determined as follows: if your second midterm grade is higher than the first one, then the second midterm grade will be your midterm score; otherwise, the average of the two midterms will be used.

Grading:

Two worse homework scores will be dropped.

The worst quiz score will be dropped.

[Please do not rely on this too much and try to do your best on all the homework and quizzes. These policies take care of all the unexpected situations during the semester (illness, family/personal issues, computer or network issues, tardiness, absent-mindedness, etc)]

The total homework score counts for 10% of the course grade.

The total quiz score counts for 10% of the course grade.

The final grade will be calculated based on the comparison between your final exam grade and your midterm grade as follows:

1. If the final exam grade is higher than the midterm grade:

Final Grade =  10% × Homework + 10% × Quizzes                    

                       + 20% × Midterms + 60% × Final Exam

2. If the final exam grade is lower than the midterm grade:

Final Grade = 10% × Homework + 10% × Quizzes
                     + 40% × Midterms + 40% × Final Exam

The final grades will be assigned based on the following thresholds:

90% guarantees an "A"

80% guarantees a "B"

70% guarantees a "C"

60% guarantees a "D".

Various intermediate grades such as “A-” or “C+” will also be given, at my discretion.

Tentative schedule: