Train Your Brain: Challenging Yet Elementary Mathematics
暫譯: 訓練你的大腦：具挑戰性但基本的數學

本書包含針對有興趣參加數學競賽的高中生所挑選的問題，或是對於所有年齡和背景的人士，旨在擴展他們的知識並挑戰自己，提供有趣的問題。這些問題大多來自於波蘭數學奧林匹克的廣泛問題集，許多問題在此首次以英文呈現。每一章由多個部分組成，專注於一系列相關主題。每個部分都以一個問題開始，接著提供必要的背景知識（使用的定義和定理）、仔細且詳細的解答，以及對可能的推廣進行討論。

The book contains carefully selected, challenging problems to prepare readers for rigorous mathematics. Neither prior preparation nor any mathematical sophistication is required. The authors guide the readers to think and express themselves in a rigorous, mathematical way, to extract facts, analyze the problem, and identify main challenges. Moreover, they show how to draw appropriate, true conclusions and to see a big picture.

Readers are provided with a firm foundation in a diverse range of topics. Computer support is used to build a better intuition into discussed problems. The book can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses that are offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. It provides a solid foundation of various topics that would be useful for more advanced courses.

The content of 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.

The authors employ a six-step process:

• SOURCE
• PROBLEM
• THEORY
• SOLUTION
• REMARKS
• EXERCISES

All exercises are followed by hints and solutions given at the end of the book.

Additionally, the book is enhanced by a "Julia language companion" available on-line that contains an introduction to the Julia language programming and detailed explanations of the codes used in the book.

這本書包含精心挑選的挑戰性問題，以幫助讀者為嚴謹的數學做準備。讀者不需要任何先前的準備或數學知識。作者引導讀者以嚴謹的數學方式思考和表達自己，提取事實、分析問題並識別主要挑戰。此外，他們展示了如何得出適當且真實的結論，並看到全局。

讀者將在多樣的主題中獲得堅實的基礎。書中使用計算機輔助來建立對所討論問題的更好直覺。這本書可以用來彌補大學中初級微積分/線性代數課程與更高級課程之間的差距。它提高了以嚴謹、成熟的數學方式閱讀、寫作和思考的能力。它提供了各種主題的堅實基礎，對於更高級的課程將會非常有用。

這本書的內容也適合對數學競賽感興趣的高中生，或是任何年齡和背景的人，想要擴展知識並挑戰自己以有趣的問題。

特點
作者採用六步驟過程：
- SOURCE
- PROBLEM
- THEORY
- SOLUTION
- REMARKS
- EXERCISES

所有練習後面都有提示和解答，這些解答在書的末尾提供。

此外，這本書還增強了一個在線的「Julia 語言伴侶」，其中包含對 Julia 語言編程的介紹以及書中使用的代碼的詳細解釋。