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.

Shanna E. Ratner is the founder and principal of Yellow Wood Associates, a firm specializing in rural economic and community development since 1985. She was selected by the Ford Foundation to conceptualize and support implementation of a new approach to rural economic development that became WealthWorks. Ms. Ratner was trained in systems thinking as a member of the first class of Donella Meadows Fellows and has been a Mel King Fellow at MIT, and a member of the Aspen Institute’s Learning Cluster on Rural Community Capacity Building. She holds a MS degree in Agricultural Economics from Cornell University and a BA in Value Systems from New College in Sarasota, Florida, and lives in rural Vermont.