Understanding Topology

Build intuition as well as a rigorous understanding of hard-to-visualize topics in mathematics, from hyperbolic geometry to the 4th dimension and space-time.

There are things in math and science that are often difficult or impossible to visualize: the 4th, 5th, and 6th dimensions, space-time, non-Euclidean geometry… the list goes on. When a mathematician pictures these things in their head, they have an intimate understanding of the workings of these strange and often counterintuitive ideas. How have they come to this understanding? We will be delving into the depths of this awesome and peculiar mathematical universe. We will talk of cases in which a straight line is not the shortest distance between two points, explore spaces in which you can travel in any direction and always end up back where you started, and the many good reasons why every mathematician who studies these things seems to be obsessed with donuts.

Geometry and topology are the fields of mathematics that are concerned with the study of many of these bizarre and profoundly interesting topics. We will study how these fields came to be, what influenced their development and the many beautiful and mind-blowing consequences that result. This will be a crash course on some of the most important ideas that are used in modern mathematical inquiry, and by the end of the course we will have built enough tools to tackle the mathematics used in Einsteinian relativity and space-time.

For the application...

Prerequisites

Single variable calculus, trigonometry, planar (Euclidean) geometry.

A student will not be rejected for a lack of any particular one of these prerequisites but this will be a challenging course requiring a strong background in mathematics.

Relevant experience

List any past work with linear algebra or vectors, non-Euclidean geometry, any exposure to abstract algebra e.g. groups, rings, fields; any and all advanced mathematics classes you have taken, books you have read or any other relevant activities. (Don’t worry if it’s not much! This info just helps put your application in context.)

Application Question (Core-specific free response)

Please click here to download the application questions for this course.