Quantitative methods. Track # 2

This course is divided into four modules: Introduction to Mathematics, Mathematical Analysis, Linear Algebra, Fundamentals of 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 help them appreciate the well-defined structure of mathematical knowledge, something which usually remains hidden behind a large number of set formulas, facts and algorithms.

The Mathematical Analysis module is core to this path. It will include material constituting the theoretical basis of the classical methods of mathematical modeling, as they are used in the natural sciences (physics, biology, chemistry, etc.), economy and sociology. For instance, a lot of biological models are described by one differential equation or by a system of differential equations (for example, biological systems models, population growth models, etc.). In economics, also, the modeling of demand and consumption, as well as the application of inventory management models, presupposes a knowledge of the differential and integral calculus functions of one and several variables. Also, many objectives in modeling social phenomena and processes in sociology can be successfully solved with the help of mathematical analysis.

The Linear Algebra module will include study of matrix and vector algebra, as well as the theory of linear algebraic equations. Alongside mathematical analysis, this is the section of mathematics that is mainly used in economics, as well as in the natural sciences and sociology. Examples of the application of linear algebra include balance models in economics, the solutions of transport problems, the matrix models of populations in biology, the methods of multidimensional scaling, as well as the main components in sociology.

Studying the Fundamentals of Mathematical Statistics module will allow students to use basic statistical methods to process and analyze the results of research in various fields of science, as well as to identify and analyze regularities in large data sets. Moreover, a knowledge of the basic concepts and facts of mathematical statistics will make it possible to master special computer programs in the future that will be designed to process statistical information.

Lessons will be structured according to the traditional scheme. Each lesson will involve a brief review and discussion of the main theoretical provisions of the lesson’s topic, as well as a problem solving exercise. In order to successfully master the material, students are required to do fairly intensive individual work, including the completion of a number of home assignments.