# Elements of mathematics in problems. Through olympiads and circles to profession

## TL;DR

This collection of teaching materials showcases mathematical problems designed to teach key ideas and theories, suitable for self-study and instruction, bridging olympiad problems to professional mathematics.

## Contribution

It compiles self-contained, ready-to-use mathematical problems that promote learning important theories, serving as a resource for students and teachers in various educational settings.

## Key findings

- Problems facilitate learning of mathematical ideas
- Materials are suitable for self-study and teaching
- Includes updates from previous arXiv submissions

## Abstract

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important mathematical ideas and theories. The materials can be used by pupils and students for self-study, and by teachers. This is an abridged pre-copyedit version of the published book submitted with the permission of the publisher. Each included individual material is self-contained and ready-for-use. Solutions to problems are not included intentionally. This collection consolidates updates of several arXiv submissions, e.g., arXiv:1305.2598.