The Department of Mathematical Statistics was established at the Faculty of Computational Mathematics and Cybernetics at Kazan Federal University on April 20, 1988 due to high demand on high-quality specialists in mathematical statistics. Presently there are 22 members of staff, 15 of them have academic degrees of Candidate and Doctor of science.

- The first head of department was Professor Igor Volodin. He leaded the department 20 years from 1988 to 2008.
- From 2008 to 2013 years the head of department was Associate Professor Victor Zheltukhin .
- Since 2013 year the leader of the department is Associate Professor Ekaterina Turilova.

## About the origins of Mathematical Statistics and its scientific essence

Theory of Probability as a science has its roots in the Middle Ages and the first attempts of mathematical analysis of gambling and games of chance (a coin toss, dice throw, roulette). The earliest scientific results in the field of probability theory are dated to the XVII century.

Probability Theory originates the base for modeling physical processes with uncertain outcomes whose properties depend on relative frequency of occurrence of certain events. Based on such probabilistic models, Mathematical Statistics develops rules of inductive behavior in these conditions of uncertaincy. The majority of statistical problems associated reduce to the parameter estimation (usually, scalar or vector valued) and hypotheses testing problems (where an experimenter has to select the most «appropriate» statement about the studied object among the several hypotheses).

Methods of Mathematical Statistics are highly important for various medical and genetic researches, in finances, for quality control and so on. Several actively developed areas, such as Machine Learning, Data Mining, are essentialy based on the concepts of the Statistics. On the other hand, the development of the modern Mathematical Statistics essentially depends on computational systems and Information Technologies.

## Educational Activities

The lecturers of the department conduct classes in «Mathematical Analysis», «Theory of Probability and Mathematical Statistics» for all bachelor’s degree programs of the Institute of Computational Mathematics and Information Technologies and also teach various disciplines in mathematical statistics for the other institutes of Kazan Federal University.

The Department trains bachelors in 01.03.04 «Applied mathematics» as well. The department provides the unique courses for students specializing on the mathematical statistics: General Theory of Statistical Inference, Multidimensional Statistical Analysis, Theory of Stochastic Processes, Actuarial Mathematics, Stochastic Models in Economics and Finances.

Within the Master's degree 01.04.02 «Applied Mathematics and Computer Science (Informatics)» the program "Methods of Applied Mathematical Statistics" is conducted by the department. Postgraduate study in 01.01.05 «Theory of Probability and Mathematical Statistics» is provided.

## Scientific Activities

The department performs high-quality scientific activity in many areas:

- d-Posterior Approach to the Problem of Statistical Inference;
- General Theory of Operator Algebras;
- Theories of Measure and Non-Commutative Integration;
- Quantum Structures of Functional Analysis and Their Application in Quantum Informatics and Quantum Probability;
- Numerical Analysis and its Applications in Problems of Mechanics and Physics.