Last edited 29mat13 by gfrancis-at-uiuc.edu

Class Moodle for netMA403

Regarding online course Summer 2013

## Spring 2011 Course Description:

# netMA403sp11: MODERN EUCLIDEAN GEOMETRY ONLINE

Professor George Francis

contact: gfrancis@illinois.edu, 101 Altgeld Hall, 217-333-4794

Texts: Online Lecture Notes, KSEG geometry software (free)

"Vectors and Transformations" by Ph. Tondeur, Publish or Perish, 1993.
(recommended)

This semester based (16 week) junior/senior level course in classical
Euclidean geometry from a contemporary viewpoint is woven
from five threads (themes)

1. The Physical Origins of Greek Geometry.

2. Renaissance Perspective and 3-dimensional Drawing.

3. The Industrial Origins of Cartesian Geometry.

4. Klein's Erlangen Program to Unify Geometry.

5. The Geometry in Computer Graphics.

The initial 3 week unit on affine geometry, including the theorems
of Ceva, Menelaus, and Desargues,
is a good review of Euclidean plane geometry using vector methods.
There follows a 4-week unit on the practice and theory of
perspective drawing which serves as
an introduction to visualizing 3-dimensions and to classical projective
geometry. A 2 week unit on dilatations applied to constructing
Euler's line and
the Nine-point circle, introduces transformational geometry.
Klein's Erlangen Program, defining geometries in terms of
their isometry groups, and the classification of isometries (congruences)
in the Euclidean plane occupies remaining 6 weeks of the course.

This course satisfies requirements in several math and education
curricula, in particular the Illinois Certification Testing System,
Field 115: Mathematics, November 2003. The course
can also be taken as a technical elective in science
and engineering. Its strong emphasis on visual comprehension and
its historical flavor makes it accessible to students in the fine
and applied arts. The course may be taken for 3 or 4 credit hours.
The 3 credit version does not require the project on
perspective and its documentation.

The student will also learn LaTeX for the preparation of mathematical
documents (software is provided) and KSEG (software can be downloaded
free) for the preparation of mathematical figures.

Prospective students need to consult with the instructor for permission
to take the course. For University of Illinois students, the
prerequisites are met by those portions of Calculus III (MA241)
that introduces and uses vectors, and MA347 for the maturity in
understanding and writing proofs. If you wish to be absolutely certain
that you are well prepared to take the course,
check here.