美国夢沃学校(上海)教师文章分享：你也能成为“全球霸主” 

　　我常通过给学生介绍纸板游戏Risk来展示数学在其他领域的应用。游戏任务是成为全球霸主，玩家需要用微积分知识来破解。当然，想要完全明白数学在这个游戏中的作用，需要更深入地去学习博弈论。具体说，是博弈论里面的纳什均衡。

　　Why do I need to take pre-calculus? Why do I have to learn about algebra at MVA Shanghai? These are the type of questions I often get from students at the beginning of each semester.

　　为什么我必须上微积分?为什么在美国梦沃(上海)我得学代数?新学期开始的时候，我常常被学生这样追问。

　　The answer to these questions lies in understanding the infinite possibilities that mathematics can create for explorers of different disciplines. I believe that showing students interesting applications of mathematics demonstrates its usefulness and motivates students to pursue further study—to think beyond the textbook and imagine innovative applications of math in new areas.

　　要想知道这些问题的答案，必须首先明白数学能给不同学科的探索者们带来的无限可能。我相信，如果能给学生展示一些数学在生活中比较有趣的应用、并指出数学的有用之处，就能够激励学生更多更好地去学习数学，超越课本范围的限制，想象数学在新的领域可以怎样被创新性地应用。

　　In terms of application math provides us with a treasure trove of tools to solve problems in the real world. Take a look at the modern technologies we take for granted and you will find mathematics everywhere. Matrix models stemming from algebraic concepts combined with computer engineering support internet search engines such as Google and Baidu. GPS systems use Taylor Expansion (It was NOT invented by Taylor Swift) to approximate complicated equations—and in turn can help you navigate from Shanghai to Kunming. Such a list has no end.

　　谈到数学的应用，就得谈谈数学是怎么为解决世界上的现实问题提供技术保障的。看一看大家身边这些我们觉得理所当然的现代科技，你就能找到数学无处不在的应用。代数里面的矩阵概念可以用来支持谷歌和百度这样的网络搜索引擎。GPS系统则利用泰勒(不是泰勒·斯威夫特发明的!)展开式估算过于复杂的方程式，然后帮助你从上海导航到昆明。这样的例子还很多。

　　Students who have no interest in engineering can find interesting applications elsewhere. I always introduce the board game Risk to demonstrate the usefulness of mathematics. The goal of the game is world domination. Ps want to conquer as many territories as they can and they can choose to either collaborate with each other or defect from alliances. To understand what the optimal strategy is at different point students need to use calculus to model the situation and solve an optimization problem. Of course it requires further study of Game Theory specifically of the Nash Equilibrium to fully appreciate the role of mathematics in playing this game but this fun example opens my students’ eyes to the infinite possibilities that a solid foundation in math creates for their future. Understanding how mathematics can help them solve real world problems inspires them to explore further in the field and beyond.

　　对工程学科不感兴趣的学生也可以在其他领域找到数学的应用。我常通过给学生介绍纸板游戏Risk来展示数学在其他领域的应用。游戏的任务是成为全球霸主，占领最多领土的玩家会获得最终的胜利。游戏过程中，玩家可以选择结盟合作，也可以选择解除盟约。想要知道不同情况下最佳的策略是结盟还是解约，玩家需要用微积分知识来破解。当然，想要完全明白数学在这个游戏里面起到的作用，需要更深入地去学习博弈论。具体说，是博弈论里面的纳什均衡。然而，学生在体验这个有趣的小游戏的同时，切实体会到了良好数学功底给未来创造的无限可能性。明白数学能够怎样帮助学生们解决现实世界的问题，能够激励他们去更多地探索发现数学领域内和领域外的课题。