MOTV 2023

Lecturers and Seminarists

Lecturer	Vladimir Ulyanov	[]	T924
Seminarist	Samsonov Sergey	[svsamsonov@hse.ru]	T926
TA	Ilya Levin	[...]	T926

About the course

This page contains materials for the Mathematical Foundations of Probability theory course in 2023/2024, mandatory for 1st year Master students of the MML program (HSE and Skoltech).

Grading

The final grade consists of 2 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :

• O_HW for the hometasks
• O_Exam for the final exam

The formula for the final grade is

• O_Final = 0.5*O_HW + 0.5*O_Exam

with the usual (arithmetical) rounding rule.

Table with grades

Lectures

• Lecture №1, 09.09
• Lecture №2, 09.09
• Lecture №3, 16.09
• Lecture №4, 16.09
• Lecture №5, 23.09
• Lecture №6, 30.09
• Lecture №7, 07.10
• Lecture №8, 14.10
• Lecture №9, 21.10

Seminars

• Seminar №1, 23.09
• Seminar №2, 30.09 Hand-written notes
• Seminar №3, 07.10
• Seminar №4, 14.10
• Seminar №5, 21.10

Homeworks

Please send your solutions to svsamsonov@hse.ru

• HW №1, Deadline: 10.10.2023, 23:59
• HW №2, Deadline: 25.10.2023, 23:59 Deadline was updated

Exam

The exam is scheduled for November 1, 2023. There will be two groups for the exam:

• The first group will start at 10:00.
• The second group will start at 12:00.

You may book an exam slot below.

• Exam slots.

Exam questions will contain 1 theoretical question and 1 problem. Using any materials, electronic devices is allowed during preparation, but not during the answer. The proofs that were not given in the lectures can be omitted.

• List of exam questions. The list of questions has been updated to include Fubini's theorem.

Recommended literature (1st term)

• https://59clc.files.wordpress.com/2012/05/paul_r-_halmos_measure_theory_graduate_texts_inbookfi-org.pdf - P. Halmos. Measure theory. Chapters 1-6;
• phys.nsu.ru/korobkov/Fudan_2018_Sobolev_Spaces/Measure-Theory-and-Fine-Properties-of-Functions-Revised-Edition.pdf - L. Evans. Measure theory and fine properties of functions. Chapter 1;
• https://diendantoanhoc.org/index.php?app=core&module=attach&section=attach&attach_id=12514 - V. Bogachev. Measure theory. Chapters 1,2.
• https://www.youtube.com/watch?v=KRtrdtUI9YQ&list=PLhe7c-LCgl4IVzTaYL8kC-exzBJiJms2B - CMC MSU lectures (in russian!)