Математика и статистика

Бакалавриат 2026/2027

Статус: Курс обязательный (Международная программа «Международные отношения и глобальные исследования»)

Кто читает: Факультет мировой экономики и мировой политики

Где читается: Факультет мировой экономики и мировой политики

Когда читается: 1-й курс, 1, 2 модуль

Охват аудитории: для своего кампуса

Язык: английский

Кредиты: 3

Контактные часы: 40

Full Syllabus Ask Question

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

calculate percentages, percentage changes and percentage-point changes; distinguish between absolute and relative changes; calculate ratios, rates and per-capita indicators; calculate and interpret weighted averages.
solve simple linear equations and rearrange basic formulas; identify and interpret the slope and intercept of a linear function; construct a linear function from numerical information or two data points; distinguish between linear and exponential growth; calculate future values under constant absolute or percentage growth.
describe simple sample spaces and events; calculate probabilities of simple events; calculate probabilities of complementary events; calculate probabilities involving unions and intersections of events; calculate conditional probabilities; use the multiplication rule to calculate joint probabilities; distinguish between conditional and unconditional probabilities; determine whether two events are independent.
calculate the expected value of a discrete random variable; calculate variance and standard deviation; calculate and interpret z-scores; use standardization to compare observations from different distributions; calculate simple probabilities for normally distributed variables; apply the 68–95–99.7 rule to estimate proportions and ranges.
calculate and interpret mean, median and mode; calculate range, quartiles, variance and standard deviation; identify possible outliers in a data set; construct and interpret histograms and box-and-whisker plots; compare distributions using appropriate measures of centre and dispersion; choose suitable summary measures for symmetric and skewed data; calculate sample means and sample proportions; understand that estimates vary from sample to sample; calculate standard errors in simple cases.
сalculate covariance for a small data set; calculate a correlation coefficient; identify the direction of a relationship between two quantitative variables; assess the strength of a linear relationship using correlation; compare correlations between different pairs of variables; distinguish between correlation and causation; use a regression equation to make predictions; calculate and interpret residuals.
calculate a confidence interval for a population mean in simple settings; calculate and interpret the margin of error; interpret the meaning of a confidence level; explain how sample size affects the width of a confidence interval; formulate simple null and alternative hypotheses; calculate a test statistic in basic cases; interpret a significance level; interpret a p-value; decide whether to reject the null hypothesis based on a given significance level.

Course Contents

Percentages, Ratios, Rates and Weighted Averages
Equations, Functions, Graphs and Growth
Basic Probability. Conditional Probability and Independence. Bayes’ Theorem
Random Variables, Expected Value and Variance. Normal Distribution and Z-Scores
Descriptive Statistics and Data Visualization. Samples, Sampling Variability and Standard Error
Covariance and Correlation. Simple Linear Regression
Confidence Intervals. Statistical Hypothesis Testing

Assessment Elements

Individual assignments (quizzes) - 2
Written solution of problems
Individual assignments (quizzes) - 1
Written solution of problems
Midterm
A written test, where you need to solve problems related to probability theory.
Exam
Homeworks
Homework assignments will be in the form of tests in the system
Seminar participation
Problem-solving in seminars

Interim Assessment

2026/2027 2nd module
0.08 * Seminar participation + 0.27 * Midterm + 0.14 * Individual assignments (quizzes) - 2 + 0.15 * Individual assignments (quizzes) - 1 + 0.28 * Exam

Bibliography

Recommended Core Bibliography

Dekking F. M. et al. A Modern Introduction to Probability and Statistics: Understanding why and how. – Springer Science & Business Media, 2005. – 488 pp.
Essential mathematics for economics and business, Bradley, T., 2006
Introductory mathematics for economics and business, Holden, K., 1992
Introductory statistics for business and economics, Wonnacott, T. H., 1990
Introductory statistics for business and economics, Wonnacott, T., 1990
Introductory statistics, Ross, S. M., 2005
Introductory statistics, Ross, S. M., 2010
Jacques, I. (2015). Mathematics for Economics and Business (Vol. 8th ed). Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1419610
Jan Ubøe. (2017). Introductory Statistics for Business and Economics. Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.spr.sptbec.978.3.319.70936.9
Mathematics for economics and business, Jacques, I., 2013
Rohatgi, V. K., & Saleh, A. K. M. E. (2001). An Introduction to Probability and Statistics (Vol. 2nd ed. Vijay K. Rohatgi, A.K. Md. Ehsanes Saleh). New York: Wiley-Interscience. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=396326

Authors

Zakharova Elizaveta Sergeevna
Kuznetsova Elena Viktorovna
Sakharova Nina Evgenevna

Course Syllabus