Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions: Interweaving Topics, Problems and Solutions

This book offers several topics from different mathematical disciplines and show how closely they are related. The purpose of the book is to direct the attention of readers who have an interest in and talent for mathematics to engaging and thought-provoking problems that should help them change their ways of thinking, entice further exploration, and could lead to independent research and projects in mathematics. With just a few exceptions, in spite of the many problems' challenging character, solutions require no more than a basic knowledge covered in a high school math curriculum.

To shed new light on a deeper appreciation for mathematical relationships, the problems are selected to demonstrate techniques involving a variety of mathematical ideas. Included are some interesting applications of trigonometry, vector algebra and Cartesian coordinate system techniques, and geometrical constructions and inversion in solving mechanical engineering problems and in studying models explaining non-Euclidean geometries.

The book is primarily directed to secondary school teachers and college professors. It will be useful in teaching mathematical reasoning because it emphasizes how to teach students to think creatively and strategically and how to make connections between math disciplines. The book also can be used as a resource for preparing for mathematics Olympiads. It is also aimed at all readers who want to study mathematics with the help of the book, gain deeper understanding and enhance their problem-solving abilities. Readers will find new ideas and topics offering unexpected insights, new skills to expand their horizons, and to get to enjoying the beauties of mathematics.