2015 Theses Doctoral

# Quaternions: A History of Complex Noncommutative Rotation Groups in Theoretical Physics

The purpose of this dissertation is to clarify the emergence of quaternions in order to make the history of quaternions less opaque to teachers and students in mathematics and physics. ‘Quaternion type Rotation Groups’ are important in modern physics. They are usually encountered by students in the form of: Pauli matrices, and SU(2) & SO(4) rotation groups. These objects did not originally appear in the neat form presented to students in modern mathematics or physics courses. What is presented to students by instructors is usually polished and complete due to many years of reworking. Often neither students of physics, mathematics or their instructors have an understanding about how these objects came into existence, or became incorporated into their respected subject in the first place. This study was done to bridge the gaps between the history of quaternions and their associated rotation groups, and the subject matter that students encounter in their course work.

## Files

- Familton_columbia_0054D_12713.pdf application/pdf 2.46 MB Download File

## More About This Work

- Academic Units
- Mathematics Education
- Thesis Advisors
- Vogeli, Bruce R.
- Degree
- Ph.D., Columbia University
- Published Here
- May 12, 2015