MATH 3T03, Winter 2019
INQUIRY IN TOPOLOGY
Topology is the field of mathematics concerned with studying a formalization of the notion of shape. In topology, we are interested in properties of spaces which remain unchanged under continuous deformation by way of stretching and bending. Hence the joke about a topologist being someone who cannot tell the difference between a coffee cup and a doughnut. In this course, we will define the simple and abstract axioms of topology and basic definitions associated to them (such as continuity of maps, connectedness and compactness). We will also see how topology can provide beautiful insight into practically all other branches of mathematics including analysis, algebra, graph theory, functional analysis. This course will also expose the students to both mathematical rigor and abstraction, giving them an opportunity to further develop their mathematical knowledge. Topics include topological spaces, metric spaces, continuity, homeomorphisms, connectivity, compactness, and separation axioms.
INSTRUCTOR: H. Boden
Size and shape in topology and analysis, compactness, connectedness, limit sets, theory of dimension, fractals and self-similarity.
Three lectures; one term
Prerequisite(s): MATH 2X03 (or ISCI 2A18 A/B)
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS