Geometry

(15 lectures)

Lecturer 

R Adams

Prerequisites

None. However, this course is a useful preparation for courses in ALGEBRA (particularly, group theory), GEOMETRY (particularly, differential geometry), (geometric aspects of) LIE THEORY, (geometric) MECHANICS, and COMPUTER GRAPHICS.

Description

This course is a (short) elementary introduction to modern geometry (in the spirit of Klein's "Erlanger Programm"). Its aim is to expose students to some useful/important geometric ideas and structures of modern mathematics through geometric transformations.

The fundamental concept is that of transformation. A geometry is viewed as the study of those properties of a "space" that are invariant under a certain group of transformations acting on that space.

TOPICS : the Euclidean plane, transformations (colliniations, dilatations), isometries (translations, halfturns, reflections, glide reflections), classification of isometries.

OPTIONAL READING : symmetry, similarities (stretches, stretch reflections, stretch rotations), classification of similarities.

Textbook

None prescribed. Complete course notes are available online.