History of Mathematics
MATH 621. History of Mathematics
Three Credit Hours (3).
Prerequisite: Undergraduate degree in mathematics or by instructor permission.
This course will help students understand the pursuit of mathematical understanding as a human endeavor. Students will discover how mathematics has developed over the past 5000 years in a variety of cultural and historical settings, including the rise of geometry and number theory, arithmetic and algebra, analysis and foundations, and a variety of other topics.
Detailed Description of Course
A variety of mathematics topics will be examined in their historical context. Topics chosen will include, at a minimum, examples from (1) the development of mathematics as the axiomatic sciences of geometry and number theory in the ancient world, (2) the development of arithmetic and algebra in the early and late middle ages respectively in India and the Islamic empire, and in renaissance Europe, (3) the development of analysis in post-renaissance Europe, (4) the rise of formalism and foundationalism in the modern period, and (5) the advent of computer science.
Detailed Description of Conduct of Course
In addition to lecture, students will work collaboratively on assignments created to help students understand the mathematics introduced throughout history. Calculators and mathematics software (such as Geometer's Sketchpad and Excel) will be used to present and work on the material presented in class, as appropriate. A project will be presented by the students on a topic chosen by the instructor.
Goals and Objectives of the Course
Students will develop an understanding of and appreciation for mathematical rigor and inquiry along with problem-solving in mathematics throughout history. Students will examine the interconnection among the different branches of mathematics and the expansive nature of mathematical development. They will build knowledge of the role of mathematics in understanding the world and of how this understanding can be developed in their own classrooms. They will appreciate mathematics as a culturally shared endeavor.
Students will demonstrate content understanding through written (possibly oral) exams, written homework problems, collaborative work in class, and a project.
Other Course Information
The mathematics and ideas presented during this class will be demonstrated not only at an advanced level but also at a level comparable to that which will be applicable in their classrooms.
Review and Approval
Date Action Reviewed