An Integrated Approach to Teaching the Languages of Programming and Mathematics in the Computer Science Curriculum

计算机科学教育工作者面临着这样的两难境地：不是一个好的程序员，就不可能做好计算机科学；如果没有扎实的数学背景，就不可能理解计算机科学的基础。这个项目的目标是利用计算机科学专业的前三门课程，让学生流利地讲数学和编程，并让他们接触函数式和命令式语言范例，以便他们能够有效地学习计算机科学。第一学期的《计算机科学I》和《离散数学》将通过综合课程、函数式编程语言和共享实验室，仔细阐述数学和编程之间的紧密联系。在第二学期修读的计算机科学Il将在第一学期的数学观点和通过命令式语言将算法作为指令序列实施之间架起一座桥梁。所有课程还将为高级课程中考虑的计算概念提供坚实的基础。所使用的方法使学生接触到数学和计算机科学中的理论概念，而不是将这些概念作为与应用程序无关的抽象隔离开来，它给学生提供了广泛的编程经验，而不会忽略作为正确性的基础和概括和创造性工作的基础的重要理论概念。

Computer Science educators are faced with the dilemma that one cannot do computer science well without being a good programmer, nor can one understand the underpinnings of computer science without a strong background in mathematics. The goal of this project is to use the first three courses of the computer science major to make students fluent speakers of mathematics and programming, and to expose them to both functional and imperative language paradigms so that they can effectively learn computer science. Computer Science I and Discrete Mathematics, taken in the first semester, will carefully articulate the strong ties between mathematics and programming through an integrated curriculum, a functional programming language and a shared laboratory. Computer Science Il, taken during the second semester, will bridge the gap between the mathematical perspective of the first semester and the implementation of an algorithm as a sequence of instructions through an imperative language. All courses will also provide a strong foundation for the computational concepts that are considered in advanced courses. The approach used exposes students to theoretical concepts in mathematics and computer science without having these concepts walled off as abstractions unrelated to applications, and it gives students extensive programming experience without neglecting important theoretical concepts that are the foundations of correctness and the basis for generalization and creative work.