Master
2020/2021
Mathematics
Type:
Bridging course (Politics. Economics. Philosophy)
Area of studies:
Political Science
Delivered by:
Department of Higher Mathematics
Where:
Faculty of Social Sciences
When:
1 year, 1 module
Mode of studies:
offline
Instructors:
Vasily Goncharenko
Master’s programme:
Политика. Экономика. Философия
Language:
English
ECTS credits:
3
Contact hours:
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 independenceBayes' formula. Independent Events. ([1], Ch 2, 2.5, Ch 3, 3.2 – 3.4)
- Random variables. Main characteristics. Main types of discrete random variablesDistribution function. Discrete random variables ([1], Ch 4, 4.1 – 4.3)
- Expected value and Variance of random variableVariance 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)
