General Information

Topology is the study of invariant spaces under deformation, such as toruses and Klein bottles. In this class, rather than studying from a typical geometrical perspective, in which distances and angles are calculated, you will rather adopt a more qualitative perspective in analyzing shapes. For example, you might define shapes by how many holes they have. The subject finds its applications in string theory in physics and nanostructures in biology.

Prerequisites

The introductory math sequence class (MATH 2210-2220, MATH 2230-2240, or MATH 1920-2940) and familiarity with proofs (a 3000-level math class would be beneficial).

Topics Covered

  • Basic point-set topology: connectedness, compactness, and metric spaces
  • Classification of surfaces (such as the Klein bottle and Möbius band)
  • Elemental knot theory
  • Fundamental group and covering spaces

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Past Offerings

Semester Professor Median Grade Syllabus
Fall 2020 M. Kassabov A