Train Your Brain

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.