Synopses & Reviews
Synopsis
The book contains selected problems aimed for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions. The problems are mostly selected from an extensive collection of problems from Polish Mathematical Olympics and many appear here in English for the first time. Each chapter consists of many sections devoted to a collection of related topics. Each of these sections starts with a problem followed by the necessary background (definitions and theorems used), careful and detailed solution, and discussion of possible generalizations
Synopsis
This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required.
The authors guide the reader to "train their brain" to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems.
The book is designed for self-study. It can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. The reader will develop a deeper understanding in preparation to succeed in more advanced course work.
Features
-The authors employ a six-step process:
1.SOURCE
2.PROBLEM
3.THEORY
4.SOLUTION
5.REMARK
6.EXERCISES
-An Appendix introduces programming in Julia
This book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.