150 beautiful tasks for future mathematicians. With detailed solutions. Evnin A.Yu.

This book contains the tasks of mathematical competitions regularly held at the South Ural State University (SUSU) since 2009. The competition of the competition is the group “Mathematical Competition in SUSU” in the Social Network “In contact”. Thanks to the Internet, not only students and graduate students of the SUSU included the Internet, but also students of other universities and adult fans of mathematics from different cities of Russia and neighboring countries.

In each competition - six tasks varied in the subject (from elementary geometry and algebra to selected chapters of mathematical analysis and discrete mathematics) and complexity (from entertaining tasks such as puzzles to tasks containing new scientific results).

A number of tasks are designed to show the application and power of the mathematical apparatus when solving “practical problems” (for example, about the field of grazing, about the scan of the cut of the buffet of sausage, about the old ready). Some tasks of the competition have the goal of expanding the mathematical horizons of participants, drawing their attention to interesting mathematical plots. Examples of such plots: the number of van der Varden, which produces the function of Fibonacci numbers, chain fractions, Helly theorem, the extreme Turan theorem, the geometric theorems of Zhergon, Stuart and the Stretch Demolian.

As the reviewers note, the tasks "are fresh, non -trivial and interesting."

This collection of tasks can be used in the work of student and school mathematical circles, to prepare for the Olympics and for self -education.