Geometry and Physics (MAT2245.01)

Andrew McIntyre

This is an introductory course on modern geometry and its relationship to physics. We will be looking at how space might have more than three dimensions, or be combined with time, or be closed in on itself in different ways (such as the surface of a sphere or a donut), or be curved in various ways. Our current theories and observations in physics indicate that space and time are indeed combined, and curved. This is part of the modern theory of gravity, general relativity. In addition, modern theories of electromagnetism and elementary particles are based on similar geometrical ideas, in a more abstract way. Such theories are called “Yang-Mills theories”. For those who know technical terms, this is a course on connections, curvature, and topology, without the usual mathematical machinery involved in those concepts.

Although physics will be used as a motivation, students will not need any background or interest in physics to profitably take the course. The geometry of curved spaces is the main topic of the class. The course may be taken with only a background in high school mathematics. However, the course will be valuable for more advanced students as well. If students have taken linear algebra or multivariable calculus, opportunities will be provided to study the material in more depth.

Prerequisites: None.
Credits: 4
M 10:10am - 12:00pm; Th 10:10am - 12:00pm
Maximum Enrollment: 20
This course is categorized as 2000, All courses, Andrew McIntyre, Four Credit, Mathematics, Monday and/or Thursday Mornings, Physics, and tagged , .