Mathematics for students

Study groups on advanced topics in mathematical analysis, probability theory, and functional analysis

for 1st-4th year undergraduate students and 1st-2nd year master’s students at the Department of Theory of Stochastic Processes of the Institute of Mathematics of NAS of Ukraine

Study groups on advanced topics in mathematical analysis have been operating at the Department of Theory of Stochastic Processes of the Institute of Mathematics of NAS of Ukraine for over 40 years. During this period, traditions and diverse teaching methods have been established for young people who wish to explore the ideas and methods of modern mathematics that lie beyond university curricula and to try solving engaging problems. The study groups are conducted with the active participation of the attendees — in the form of solving series of problems, discussing fascinating mathematical facts, and giving mini-presentations.  

Recognizing the need to continue working with interested students, the department established a study group on advanced topics in probability theory and functional analysis. Here, students begin to familiarize themselves with the concepts and problems of probability theory and the theory of stochastic processes. The latter discipline is developing rapidly and has numerous applications — both traditional ones in the natural sciences and in modern fields such as data analysis, machine learning, among others. 

By participating in the study groups, students have the opportunity to gain experience in independent research on complex mathematical problems. If they wish, they can write term papers and graduation theses under the supervision of scientists from the Department of Theory of Stochastic Processes. This activity can subsequently lead to postgraduate studies within the department. Many candidates and doctors of sciences in theory of stochastic processes — who now work both in Ukraine and abroad — followed this very path. Nearly all winners of international student mathematics olympiads from Kyiv have attended the study groups at the Department of Stochastic Processes.

In recent years, the study group on advanced topics in probability theory and functional analysis has become international, drawing students not only from Ukraine but also from Germany, China, and Tunisia. Consequently, the sessions are conducted in English. This circumstance naturally reflects the department’s traditionally rich international connections. For instance, the international research seminar “Malliavin Calculus and its Applications”, conducted by Professor A. A. Dorogovtsev, has been active at the department for 30 years, bringing together scientists from Germany, England, France, the USA, and other countries. Participating in these study groups can serve as an impetus for a career in the theory of stochastic processes and its diverse modern applications. Below is the information regarding the study groups for the 2026–2027 academic year. 

Study group on advanced topics in mathematical analysis for 1st-year undergraduate students

Sessions are held every Monday at 17:00 (Kyiv time) via Zoom conference:

Meeting ID: 772 648 6602

Passcode: 898709

List of topics to be covered during the study group sessions in the 2026–2027 academic year:

1. Cardinality of sets
2. Properties of sequences of real numbers
3. Limits of functions and continuity
4. Properties of differentiable functions
5. Riemann integral
6. Convergence of series and their summation
7. Uniform convergence and functional series

Study group instructor:

Oleksii Rudenko, Researcher at the Department of Theory of Stochastic Processes, Candidate of Sciences in Physics and Mathematics

✉ arooden@gmail.com  

Study group on advanced topics in mathematical analysis for 2nd-year undergraduate students

Sessions are held every Thursday at 18:00 (Kyiv time) via Zoom conference:
https://us02web.zoom.us/j/83796473173

List of topics to be covered during the study group sessions in the 2026–2027 academic year:

1. Metric spaces
2. Continuity of functions of several variables
3. Differentiability of functions of several variables
4. Riemann-Stieltjes integral
5. Integrals that depend on a parameter
6. Multiple integrals and differential forms
7. Fourier series and Fourier transform

Study group instructors:

Oleksandr Kukush, Leading Researcher at the Department of Theory of Stochastic Processes, Doctor of Sciences in Physics and Mathematics, Professor

✉ akukush@imath.kiev.ua

Georgii Riabov, Senior Researcher at the Department of Theory of Stochastic Processes, Candidate of Sciences in Physics and Mathematics

✉ ryabov.george@gmail.com

Study group on advanced topics in probability theory and functional analysis

Sessions are held every Wednesday at 18:00 (Kyiv time) via Zoom conference:

https://us06web.zoom.us/j/89240672653?pwd=71abDR47mGcad9bwDFMyx0Eebsdajq.1

Meeting ID: 892 4067 2653

Passcode: 648723

List of topics to be covered during the study group sessions in the 2026–2027 academic year:

1. Geometric probabilities
2. Law of Large Numbers
3. Characteristic functions
4. Uniformly distributed sequences
5. Central Limit Theorem
6. Random walks
7. Brownian motion

Study group instructor:

Andrey A. Dorogovtsev, Head of the Department of Theory of Stochastic Processes, Corresponding Member of NAS of Ukraine, Doctor of Sciences in Physics and Mathematics, Professor

✉ andrey.dorogovtsev@gmail.com

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Lectures for students:

Probability theory. Lectures

Stochastic processes. Lectures

Mathematical statistics. Lectures

Stochastic processes. Advanced course, Fall 2020

Stochastic equations with interaction. Advanced course, Fall 2020