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Магистратура 2020/2021

# Математика

Статус: Курс адаптационный (Политика. Экономика. Философия)
Направление: 41.04.04. Политология
Когда читается: 1-й курс, 1 модуль
Формат изучения: без онлайн-курса
Прогр. обучения: Политика. Экономика. Философия
Язык: английский
Кредиты: 3
Контактные часы: 28

### Course Syllabus

#### Abstract

In the process of studying the discipline, students will become familiar with theoretical foundations and basic methods of solving tasks on the following topics • Derivative and its applications; • combinatorial analysis, definition of probability, random events; • independent events, expected value and variance of random variable; main discrete distributions of random variables; • Normal distribution. Limit theorems; • Sample. Descriptive statistics: sample mean, median, sample variance, quintiles, quartiles

#### Learning Objectives

• The course aims to provide students with understanding of key concepts and methods of calculus and probability theory for understanding other practical courses, related to data analysis and programming and economics.

#### Expected Learning Outcomes

•  know main definitions and results of probability theory and statistics to be essential for understanding further practical courses;  be able to formalize the problem from subject area, choose the adequate methods of solutions, perform calculations and to interpret the results;  have skills of solving problems to be important in professional activity.

#### Course Contents

• Derivative and its properties
([3], Ch 2, 2.7-2.8; Ch 3, 3.1-3.7)
• Combinatorial analysis. Axioms of probability.
Combinations. Permutations. Axioms of probability. Sample space. Event. Main properties of probability ([1], Ch 1, 1.2-1.4, Ch 2, 2.2 – 2.4)
• Classical definition of probability. Conditional probability and independence
Bayes' formula. Independent Events. ([1], Ch 2, 2.5, Ch 3, 3.2 – 3.4)
• Random variables. Main characteristics. Main types of discrete random variables
Distribution function. Discrete random variables ([1], Ch 4, 4.1 – 4.3)
• Expected value and Variance of random variable
Variance and standard deviation of random variable ([1], Ch 4, 4.4 – 4.6)
• Continuous random variables. Normal distribution. Limits theorem
([1], Ch 5, 5.2 – 5.5, Ch 8, 8.2 - 8.3)
• Basic definitions of statistics.
Exploratory data analysis: graphical summaries. Histograms. Kernel density estimates. The empirical distribution function. Scatter plot. The center of a dataset. Empirical quintiles, quartiles, and the IQR. ([2], Ch 15, 16)

#### Assessment Elements

• Control work
• Quizzes and activity
• Exam
• Control work
• Quizzes and activity
• Exam

#### Interim Assessment

• Interim assessment (1 module)
0.25 * Control work + 0.5 * Exam + 0.25 * Quizzes and activity

#### Recommended Core Bibliography

• Calculus early transcendentals, Stewart, J., 2012

#### Recommended Additional Bibliography

• Теория вероятностей и статистика : учеб. пособие для 10 и 11 кл. общеобразоват. учреждений, Тюрин, Ю. Н., 2014