Sedrakyan H., Sedrakyan N. The Stair-Step Approach in Mathematics

Springer International Publishing AG, 2018. — 543 p. — (Problem Books in Mathematics).This book is intended as a teacher’s manual of mathematics and a self-study handbook for high school or college students and mathematical competitors. It only consists of new problems created by authors with author-prepared solutions. It is based on a traditional teaching philosophy and a non-traditional writing approach that authors call stair-step approach. The main idea of this approach is to start from relatively easy problems and step by step increase the level of difficulty of the next problems in order to most effectively maximize students’ learning potential. This aids to develop self-mastery with a slow but continuous rise and to develop creativity for solving mathematical problems. This book covers five main topics of (pure) mathematics and consists of seven chapters; the first five chapters are devoted to the following topics:
Geometry and trigonometry,
Number theory,
Algebra,
Calculus,
Combinatorics.
As it is unusual to include a separate chapter dedicated to Calculus in Chapter 6 are provided some hints for the hardest problems of the chapter Calculus. In Chapter 7 are presented author-prepared solutions. Moreover, in order to promote independent learning and for the reader’s convenience, besides providing the solutions in Chapter 7, we provide a separate table of answers in Chapter 8. Every topic consists of 15 sets of problems. The first 11 sets of problems consist of nine problems of increasing difficulty, and the last four sets of problems consist of twelve problems of increasing difficulty. We provide these additional three problems in the last four sets in order to allow the reader to focus more on advanced level problems instead of intermediate level problems.This book is arranged by topics and difficulty level. It is intended to improve the mathematical knowledge through solving these 15 sets of problems of each topic, that is 147 problems of each topic. Altogether, these 15 sets include 735 problems; all problems are new problems created by the authors (!) and with author-prepared solutions. Some problems in this book are inspired by the previous works of the authors. We hope that this book will help the interested readers to improve their mathematical skills to a truly advanced level.Примечание: это красивая оригинальная коллекция математических проблем, сделаннa известными армянскими авторами, которые являются признанными экспертами в "олимпиадной математике". Эти проблемы могут использоваться в математических кружках, во время приготовлений к математическим конкурсам всех уровней (до IMO). Нет никакой единственной проблемы в книге, в которой требуется доказательство, все проблемы имеют "вычислительную природу". Это другая характерная особенность книги. Эта книга может быть настоятельно рекомендована широкому кругу читателей: талантливым ученикам в средних школах, студентам, также преподавателям, включая всех любителей очень интересных и сложных математических проблем!