Intro to Geometry

MATH 5700 (UVA)

Course information

  • Lectures: Mondays, Wednesdays, & Fridays, 1:00pm-1:50pm
  • First Lecture: 1. February, 2021
  • Office: 311
  • Wednesday 4:00-6:00pm on Zoom (link on Collab). Additional office hours by appointment.
  • Syllabus


Our aim here is to provide an overview of various geometries. The most familiar geometry for most of you, Euclidean Geometry, can be seen as a prototypical example — Geometry concerns itself with the study of shapes: points, lines, polygons, conics, etc. This semester we will take a tour of various geometries: Euclidean Geometry, Affine Geometry, Projective Geometry, and (time permitting) Hyperbolic Geometry.

In this course, we will adopt the perspective — associated with Felix Klein in modern mathematics — that to understand a geometry, all one need do is understand its symmetries. To this end, we will also be discussing some basic group theory, so as to give us a language to describe symmetry transformations.