Бакалавриат
2025/2026
Методы математического моделирования
Статус:
Курс обязательный (Прикладной анализ данных)
Где читается:
Факультет компьютерных наук
Когда читается:
3-й курс, 1, 2 модуль
Охват аудитории:
для своего кампуса
Преподаватели:
Томащук Корней Кириллович
Язык:
английский
Кредиты:
4
Контактные часы:
56
Course Syllabus
Abstract
The main goal of the course is to provide students with a thorough understanding of the entire process of mathematical modeling, which is a systematic approach to studying and predicting the behavior of complex systems in various fields, such as natural sciences, technology, economics, and finance. The course covers the main stages of the modeling process and the types of models used, including deterministic, stochastic, discrete, and continuous models. It also discusses methods for constructing and verifying these models. The emphasis is on a systematic approach to modeling, which involves moving from reality to an abstraction and vice versa. Students learn about decision-making methodologies at each stage of the process, as well as practical skills in applying these techniques through real-world examples and projects in different subject areas.
Learning Objectives
- The primary goal of the course is to equip students with the fundamental principles and practical skills of mathematical modeling. This includes learning how to construct mathematical models for real-world problems, solve them using appropriate analytical and numerical techniques, and critically analyze the results to interpret their meaning, assess their limitations, and inform decision-making.
Expected Learning Outcomes
- Understand the purpose and main stages of the modeling process.
- Be able to classify models and problems by their fundamental types.
- Formulate real-world problems as systems of ODEs.
- Be able to apply numerical methods to solve initial value and boundary problems of ODEs.
- Recognize common real life problems described by PDEs.
- To master the basic numerical algorithms for solving PDEs.
- Formulate real-world problems as variational problems.
- To master the Ritz and Kantorovich methods for solving variational problems.
- Formulate real-world problems as discrete models.
- Apply exact and heuristic solution methods for solving problems of discrete optimisation.
- Formulate, distinguish, and analyze models of complex networks.
- Formulate and solve real-world problems using neural networks.
Course Contents
- Introduction to mathematical modelling
- Models described by ordinary differential equations
- Models described by partial differential equations
- Models described by variational problems
- Discrete Models
- Graph and Network Models
- Mathematical modeling with neural networks
Interim Assessment
- 2025/2026 2nd module0.25 * Exam + 0.25 * Midterm + 0.25 * Project + 0.25 * Quizzes
