This course is divided into five modules: Introduction to Mathematics, Sets, Discrete Mathematics, Probability Theory, and Mathematical Statistics.
Studying the Introduction to Mathematics module will allow students to look at mathematics as a “living” developing science, one with an interesting history as well as wide possibilities of practical application. It will also allow them to appreciate the well-defined structure of mathematical knowledge, something which usually remains hidden behind a large number of set formulas, facts and algorithms.
The Sets and Discrete Mathematics modules will include sections on sets and their operations, correspondences and relations, mathematical logic, and graph theory. The material from these sections is necessary for mastering a number of important special courses in the field of computer sciences, including the field of programming and database design. For example, the most common relational data models and relational databases are based on set theory. The concepts and methods of set theory and discrete mathematics are also actively used in the field of humanities research, typically for complex mathematical modeling. For example, graph theory is used in the study of social networks (human social connections analysis, media content analysis, etc.); set theory and mathematical logic can be successfully used in comparative historical studies; and graph theory can be used in the cause-effect and structural-functional analysis of historical processes.
Studying the Probability Theory and Mathematical Statistics modules will allow students to use probabilistic and statistical methods in a wide range of areas of knowledge, including processing and analyzing the results of scientific research, and identifying and analyzing regularities in large data sets. Ultimately, this path requires the mastery of all the preceding sections of mathematics featured in this course.
Lessons are structured according to the traditional scheme. Each lesson will involve a brief review and discussion of the main theoretical provisions of the topic of the lesson, as well as a problem solving exercise. In order to successfully master the material, a fairly intensive amount of individual work is required, including the completion of a number of home assignments.
Within the Quantitative Methods course (path # 1), students will be divided into groups according to their initial level of knowledge of mathematics, as determined by the results of the test.