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.
| Preface |
|
ix | |
| About the Authors |
|
xiii | |
|
|
|
1 | (18) |
|
2 Euclidean Constructions |
|
|
19 | (14) |
|
3 Inversion and Its Applications |
|
|
33 | (16) |
|
4 Using Geometry for Algebra. Classic Mean Averages' Geometrical Interpretations |
|
|
49 | (20) |
|
5 Using Algebra for Geometry |
|
|
69 | (20) |
|
6 Trigonometrical Explorations |
|
|
89 | (24) |
|
|
|
113 | (18) |
|
8 Cartesian Coordinates in Problem Solving |
|
|
131 | (16) |
|
9 Inequalities Wonderland |
|
|
147 | (22) |
|
|
|
169 | (16) |
| Appendix |
|
185 | (18) |
| References |
|
203 | (2) |
| Index |
|
205 | |
Boris Pritsker studied mathematics at Kiev State Pedagogical University, Ukraine, then worked as a math teacher in high schools, including a special math-oriented school for gifted and talented students with advanced programs in algebra, geometry, trigonometry, and calculus. In the US, he earned an MBA degree from the Graduate school of Baruch College, City University of New York. He is a licensed CPA in New York State and has been employed by CBIZ Marks Paneth LLC, New York City accounting and consulting firm, where he became a director. He published numerous articles and problems in mathematical magazines in the former Soviet Union, United States, Australia, and Singapore. He is also the author of three internationally acclaimed mathematics books.
Rohkem infot Taylor & Francis e-raamatute kohta