Бакалавриат
2026/2027
За кулисами теории вероятностей
Статус:
Курс по выбору (Экономика и анализ данных)
Кто читает:
Департамент математики
Где читается:
Факультет экономических наук
Когда читается:
2-й курс, 3, 4 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
Probability is not just boring stuff about balls and coins—it's magic, paradoxes, and the hidden gears of the universe. In this course, we'll tear the veils off the divine Gauss and learn how to properly ignore little-o's when calculating probabilities. And yes, there will be reptilians.
Expected Learning Outcomes
- Applies the first-step method to the corresponding problems
- Is able to solve problems that involve the neglect of higher-order infinitesimals in probability elements
- Applies generating functions for sets to solve relevant problems
- Calculates expected values via convergence in probability
- Works with mixed distributions
- Recognizes singular distributions and their properties
- Can apply Bruss's stopping criterion
- Analyzes the trade-off between expected growth and risk of ruin
- Computes Gittins indices for optimal sequential decision-making
Course Contents
- First-step method
- Axiomatic approach to distributions
- Isserlis' theorem. Stein's lemma.
- Probability element in the language of differential forms. Neglect of infinitesimals of higher order in probability elements.
- Generating functions for sets. Pólya's idea with pictograms.
- Decomposition into a sum
- Calculation of the expected value by means of limits in probability
- Mixed distributions
- Singular distributions
- Bruss's stopping criterion
- Kelly criterion
- Gittins index
Assessment Elements
- ExamThe examination consists of open-ended questions and problems requiring detailed solutions and explanations. Based on the results of the written examination, at the instructor's discretion, a selective oral examination of students may be conducted on the topics covered in the exam and on tasks similar to those appearing in the written work. In this case, the final grade for the examination is the average of the grades for the written work and the oral response, weighted equally, provided that the grade for the oral response is not below a passing level; otherwise, the final grade for the examination is equal to the grade for the oral response.
- MidtermThe midterm examination comprises open-ended questions and problems that require complete solutions and justifications, covering all course materials. Following the written midterm, the instructor may conduct a selective oral examination on the topics and problem types covered in the written work. In such cases, the final midterm grade is calculated as the equally weighted average of the written and oral components, provided that the oral grade is at least satisfactory; otherwise, the oral grade determines the final midterm grade.
- QuizzesThe quiz comprises a set of tasks that may be presented in either multiple-choice format or as short open-ended questions. Following the written quiz, the instructor may conduct a selective oral examination on the topics and question types covered in the quiz. In such cases, the final quiz grade is calculated as the equally weighted average of the written and oral components, provided that the oral grade is at least satisfactory; otherwise, the oral grade determines the final quiz grade.
- Home assignments
Interim Assessment
- 2026/2027 4th module0.3 * Midterm + 0.3 * Exam + 0.2 * Quizzes + 0.2 * Home assignments
Bibliography
Recommended Core Bibliography
- Linde, W. (2017). Probability Theory : A First Course in Probability Theory and Statistics. [N.p.]: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1438416
- P A Chemist’s, Guide Density, Functional Theory, Wolfram Koch, Max C. Holthausen, C A Guide, … William Feller. (n.d.). An Introduction to Probability Theory and its. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.DBB27A91
Recommended Additional Bibliography
- Meyn, S. P., & Tweedie, R. L. (2009). Markov Chains and Stochastic Stability (Vol. 2nd ed). Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=313161