Geometry

(15 lectures)

Lecturer 

CC Remsing

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.

Tutorials

SIX tutorials.

Tests and Exams

ONE class test and ONE final examination.