Bachelor
2021/2022
Mathematics and Statistics
Type:
Compulsory course
Area of studies:
International Relations
Delivered by:
Faculty of World Economy and International Affairs
When:
1 year, 1 module
Mode of studies:
distance learning
Open to:
students of one campus
Language:
English
ECTS credits:
3
Contact hours:
28
Course Syllabus
Abstract
Mathematics is an important part of the bachelor stage in education of the future political scientists. It has to give students skills for implementation of the mathematical knowledge and expertise. Special attention is paid to interpretation of tables and results and finding the appropriate way to approach statistical problems. The successful completion of the course is absolutely crucial for understanding of the Data Culture course which proceeds after the Calculus and Statistics course.
Learning Objectives
- Acquire knowledge in the field of calculus and linear algebra
- Acquire knowledge in the field of statistics
- Be able to analyze simulated and real situations in the world affairs.
Expected Learning Outcomes
- Be able to compute the probability of an intersection and a union, define statistically independent events and apply Bayes theorem.
- Be able to distinguish between different types of data. Recognize and avoid misleading data representation
- Be able to graphically analyze data using box-and-whiskers plots
- Be able to make graphs of functions and do graph transformations.
- Be able to sketch curves and solve optimization problems
- Be able to solve indefinite integrals, definite integrals and standard integrals and to apply substitution method.
- Define the derivative and explain its meaning. Know the standard derivatives and be able to use derivative rules (product rule, quotient rule, chain rule).
- Know how to calculate variance and standard deviation for population and samples
- Know how to define a function, know the notions of domain and range of a function
- Know the basic definitions of a random experiment and probability and postulates of probability theory. Be able to recognize and avoid common probabilistic mistakes.
- Know the main concepts of set theory and be able to perform operations on sets
- Study the applications of integrals in economics and statistics.
- знать: - базовые понятия и идеи, лежащие в основе теории вероятностей и математической статистики; уметь: - применять основные методы математической статистики к решению различных социально-экономических и политологических исследовательских задач; владеть: - навыками построения теоретико-вероятностных моделей для изучения социально-экономических и политических процессов и явлений;
Course Contents
- Вводная лекция
- Событие.
- Процентные ставки
- Условная вероятность.
- Функции. Основные примеры функций.
- Основы теории вероятностей
- Обратная функция. Композиция функций.
- Дискретные случайные величины.
- Производная функции.
- Системы линейных уравнений.
- Количественный анализ. Элементарная обработка данных.
- Геометрические представления решений.
- Статистические парадоксы.
- Set theory
- Functions
- Graph of a function
- Derivative
- Application of derivative
- Integrals
- Application of integrals
- Main concepts of statistics
- Measures of central tendency
- Measures of central tendency (continued)
- Grouped data and histograms
- Probability
- Probability (continued)
Bibliography
Recommended Core Bibliography
- Essential mathematics for economic analysis, Sydsaeter K., Hammond P., 2012
- Fundamental methods of mathematical economics, Chiang, A. C., 1984
- Fundamental methods of mathematical economics, Chiang, A. C., 2005
- Introduction to mathematical statistics, Hogg, R. V., 2014
- Introductory statistics for business and economics, Wonnacott, T. H., 1990
- Mathematics for economic analysis, Sydsaeter, K., 1995
- Statistics for business and economics, Newbold, P., 2013
- Теория вероятностей : учебник для экономических и гуманитарных специальностей: учеб. пособие для вузов, Тюрин, Ю. Н., 2009
Recommended Additional Bibliography
- Anthony, M., & Biggs, N. (1996). Mathematics for Economics and Finance : Methods and Modelling. Cambridge [England]: Cambridge eText. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=510977
- Анализ социологических данных с помощью пакета SPSS : учеб. пособие для вузов, Крыштановский, А. О., 2006
- Теория вероятностей и математическая статистика : Учеб. пособие для студентов, Шведов, А. С., 1995