Expanding Mathematical Toolbox: Interweaving Topics, Problems, and
Solutions offers several topics from different mathematical
disciplines and shows how closely they are related. The purpose of this
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 possibly lead to independent research and projects in
mathematics. In spite of the many challenging problems, most 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.
This book is primarily directed at 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
text also can be used as a resource for preparing for mathematics
Olympiads. In addition, it is aimed at all readers who want to study
mathematics, gain deeper understanding and enhance their problem-solving
abilities. Readers will find fresh ideas and topics offering unexpected
insights, new skills to expand their horizons and an appreciation for
the beauty of mathematics.
