A Capstone Course: Learning Mathematics Through Original Sources

在过去的八年中，我们开发，教授和微调了上师数学课程“伟大的定理：数学的艺术”。与许多通过一系列技术结构呈现一个专业领域的结果的上师课程不同，我们的课程提供了激励问题和开创数学各个分支的原始解决方案（例如整合，数论，分析，抽象代数）。通过阅读原始资料，学生们亲眼目睹了历史上最具革命性的数学思想的起源。 该课程为科学，工程，教育和数学专业的学生提供了生动的顶点体验。它也可以作为一个上师选修谁已经完成了一年的微积分教学的学生提供。 用这种教学法成功地教学不仅需要适当地收集原始资料，还需要数学和历史注释以及注释，将资料置于上下文中。为了满足这一需求，我们将编写一本附有注释的原始资料的书，书名为《思想的发现：数学中的革命性定理》，利用一位高级研究生助理的编辑反馈，他将用我们的手稿进行本课程的学徒教学。

During the past eight years we have developed, taught and fine-tuned the upper division mathematics course "Great Theorems: The Art of Mathematics". Unlike many upper division courses which present the results of one specialized field via a litany of technical constructions, our course offers the motivating problems and original solutions which inaugurated various branches of mathematics (e.g. integration, number theory, analysis, abstract algebra). By reading the original sources, students witness first hand the genesis of history's most revolutionary ideas in mathematics. The course serves as a lively capstone experience for students majoring in science, engineering, education, and mathematics. It can also be offered as an upper division elective to students who have completed one year of Calculus instruction. Teaching successfully with this pedagogy requires not only an appropriate collection of original sources, but also mathematical and historical annotations, as well as commentary, placing the sources in context. We will write a book of annotated original sources entitled "Discovery of Ideas: Revolutionary Theorems in Mathematics," to fulfill this need, using editorial feedback from an advanced graduate assistant who will do apprentice teaching of the course with our manuscript.