About the Book
Train Your Brain - Challenging Yet Elementary Mathematics (external link, opens in new window) contains carefully selected problems that are challenging yet only require elementary mathematics.
The book is intended to prepare the readers for rigorous mathematics but neither prior preparation nor any mathematical sophistication is required from them before reading this book. The book guides the readers to think and express themselves in a rigorous, mathematical way, to extract facts, analyze the problem, and identify main challenges. Moreover, it shows how to draw appropriate, true conclusions and helps to see a big picture. Despite the fact that this is not the main goal of this book, as a bi-product, the readers are provided with a firm foundation in a diverse range of topics that might be useful in their future work.
We often use computer support to help us get a better intuition into discussed problems. This is a still rather unique approach in mathematics but is getting more and more popular in the current multidisciplinary and data driven world. In the Julia language companion available for free on this page, we provide a thorough introduction to computing using the Julia language (external link, opens in new window) that we use in the book. It also contains detailed explanations of all the codes we present in the book.
(PDF file) Julia language companion (PDF file)
(PDF file) Look inside the book (PDF file)
In the book, we grouped problems into 6 chapters representing various disciplines of mathematics. Each chapter consists of many sections devoted to a collection of related topics. Each of these sections starts with a problem that is followed by the necessary background (definitions and theorems used), careful and detailed solution, and discussion of possible generalizations. The sections finish with a number of additional related exercises that are solved at the end of the book. As a result, this book can be used as a textbook for a systematic and structured introduction to a fascinating world of high school math competitions, or as a book preparing university students for more advanced courses.