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This is an introduction to the history of mathematics from ancient civilizations to present day. Students will study major mathematical discoveries in their cultural, historical, and scientific contexts. This course explores how the study of mathematics evolved through time, and the ways of thinking of mathematicians of different eras - their breakthroughs and failures. Students will have an opportunity to integrate their knowledge of mathematical theories with material covered in General Education courses. Forms of evaluation will include a group presentation, class discussions, and a final paper.
The math major is made up of technical courses on the theory of mathematics from Calculus to more complex concepts. This course is unique in providing a humanities-based approach to understanding math. For example, students are required to use primary sources on a weekly basis. Students study examples of how mathematical advances were made in response to or alongside developments in other branches of science - such as Ptolemy’s work in trigonometry being motivated by applications in astronomy, and Newton as the father of both calculus and modern physics. Students also learn to understand mathematicians as people of their times - for example, how Babylonian mathematicians were motivated by the needs of the empire, or how Evariste Galois was both a brilliant mathematician and a passionate French revolutionary. Additionally, many math majors go on to teach mathematics after graduation, and in this course the history of math is is studied in the context of the history of education.
The homework assignments contain a component where students are required to write short compositions. Many of these assignments will ask students to engage in self-reflection on how their study of the history of mathematics in the current course is influenced by the General Education courses they took. This is not limited to courses carrying the Historical Studies designation, but Economics, Sociology, Science and other modes of human thought all present lenses through which one can study the mathematics and mathematicians that are the focus of the course; the homework assignments will invite students to apply all of those lenses to the topics at hand. Students will also be required to write an interdisciplinary 20-page final essay. Essay topics are developed by the student with assistance from the professor. Students draw not only on their mathematics coursework, but also on the knowledge they have accrued from other GenEd curriculum courses they have experienced in their first two years of college. After seeing how mathematical tools have developed in conversation with history, culture, and science, students can better appreciate the uses and possibilities of advanced mathematics.
A substantial fraction of the course grade is based on a class presentation; this is a major change from standard upper division math/stat requirements. Each group, which typically consists of three students, collaboratively researches and presents an interdisciplinary mathematical topic, chosen by the group from the instructor’s list of suggested topics. This is highly unusual for mathematics classes, where problems are typically presented abstracted from their scientific and cultural roots. These presentations are spaced out throughout the semester, and the students’ work is referenced and discussed in a class discussion later in class.
Additionally, highly unusually for a mathematics course, a large part of the course grade is based on participation in class discussions. Each week, the students are assigned readings. A large amount of weekly class time is devoted to a roundtable discussion of the reading - its implications for modern mathematics, how it was understood at the time, mathematical concepts in the reading, and the close-reading of assigned passages.
See http://people.math.umass.edu/~tevelev/475_2017/ for more information about the course and examples of essays, class presentations, and reading assignments from previous years.