### ABB Math Challenge

The program will be held in the format of a 10-day intensive training series. Participants will attend lectures, during which they will become familiar with the theoretical material of each of the topics, and the lectures will be followed by seminars, where participants will consolidate their knowledge by solving problems and case studies. At the end of the shift, participants will be asked to write a final work to consolidate their knowledge, the points that participants earn will go to the overall rating.

Participants will be involved in attending lectures and seminars for 7 academic hours (5 astronomical hours), i.e. 7 lessons. There is a break between each lesson, incl. break for lunch.

The deadline for applications is January 10 Application to the program is currently not active 27 January

10 Days

30 students

Intensive

### Program

###### ABB Math Challenge
8

Number of modules

Definition of an invariant. Exploring properties. Consideration of examples. Principles of application in real problems. Solving typical tasks.

Definition of the average value. Classification of average values. Use cases of averages in probability theory and statistics. Principles of application in real problems. Solving typical tasks.

Definition and classification of graphs. Ways of representing graphs. The extremal principle in graphs. Principles of application in real problems. Solving typical tasks.

Definition of the method of Sequential optimization. Consideration of examples. Principles of application in real problems. Solving typical tasks.

Definition of inversion and symmetry. Consideration of the properties of symmetry and inversion. Variations and generalizations of inversion. Principles of finding symmetry in problems. Simplification of tasks while being in symmetry. Principles of application in real problems. Solving typical tasks.

Theoretical Foundations of Number Theory. Consideration of the theory of integers, algebraic number theory, analytic number theory. Principles of application in real problems. Solving typical tasks.

Definition of functional equations. Recurrent correlations. Methods for solving functional equations and inequalities. Principles of application in real problems. Solving typical tasks.

Final work that covers the topics of existing educational program.