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

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.

《擴展數學工具箱：交織主題、問題和解決方案》提供了來自不同數學學科的幾個主題，並展示了它們之間的密切關聯。本書的目的是引導對數學有興趣和天賦的讀者關注引人入勝且發人深省的問題，這些問題應該幫助他們改變思維方式，激發進一步的探索，可能還會引導他們進行獨立的數學研究和項目。儘管有許多具有挑戰性的問題，大多數解決方案只需要高中數學課程中涵蓋的基礎知識。

為了對數學關係有更深入的理解，這些問題被選擇來展示涉及各種數學思想的技巧。其中包括一些有趣的三角學應用、向量代數和笛卡爾坐標系統技巧，以及在解決機械工程問題和研究解釋非歐幾何的模型時使用的幾何構造和反演。

本書主要針對中學教師和大學教授。它將在教授數學推理方面很有用，因為它強調如何教導學生創造性和戰略性思考，以及如何建立數學學科之間的聯繫。這本書也可以作為準備數學奧林匹克競賽的資源。此外，它還面向所有希望學習數學、深入理解並提高解決問題能力的讀者。讀者將發現新鮮的思想和主題，提供意想不到的見解，擴展他們的視野，並對數學之美有所體會。

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.

Boris Pritsker在烏克蘭的基輔國立教育大學學習數學，之後在高中擔任數學教師，包括一所專門為具有天賦和才華的學生提供高級代數、幾何、三角學和微積分課程的數學導向學校。在美國，他在紐約市立大學巴魯克學院研究生院獲得了MBA學位。他是紐約州註冊會計師，曾在紐約市會計和咨詢公司CBIZ Marks Paneth LLC工作，並晉升為主管。他在前蘇聯、美國、澳大利亞和新加坡的數學雜誌上發表了許多文章和問題，並且是三本國際公認的數學書籍的作者。