A Capstone Course: Learning Mathematics Through Original Sources

点击翻译按钮获取中文摘要

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.