Last edited 15jan13. Click here for Class Webpages

## Spring 2013 Course Description:

# MATH 402: POST-EUCLIDEAN GEOMETRY

Professor: George Francis

Email: gfrancis@uiuc.edu

Office: 101 Altgeld Hall

Text: Michael Hvidsten, *Geometry with Geometry Explorer*

Software: Michael Hvidsten, *Geometry Explorer 2.0*

Prerequisites: MA241 and MA347, or consent of instructor.

Geometry is one of the richest areas for mathematical exploration.
The visual aspects of the subject make exploration and experimentation
natural and intuitive. At the same time, the abstractions developed to
explain geometric patterns and connections make the subject extremely
powerful and applicable to a wide variety of physical situations. In this
book [and course] we give equal weight to intuitive and
imaginative exploration of
geometry, and to abstract reasoning and proof.
From the Introduction of Hvidsten't text

This course is a practical introduction Non-Euclidean geometry from an
experimental viewpoint. It is also a thorough review of axiomatic
and analytical Euclidean geometry, as well as a gentle introduction to
complex numbers. It also serves as an introduction to rigorous proofs
and good mathematical exposition. While experience with plane vectors
(MA 241) and symbolic logic (MA 347) are recommended, motivated students
may complete supplementary lessons to learn these techniques early in
the term. The course may be taken for 3 or 4 credit hours.
To pursue these twin goals quoted above, we use a balanced mixture of contemporary online
and classical learning techniques. All lessons are held in a
computer equipped classroom. Hvidsten's temporarily out of print textbook
is online together with extensive notes, explanations, examples, tutorials
and exercises. We use a custom edition of his geometric drawing software,
*Geometry Explorer* (GEX), which downloads to all platforms.
Students have the opportunity to learn and use *LaTeX*, the universal
scientific and technical typesetting tool, with our custom webtool
*texWins*. Students also keep a hand-written journal of what they
have learned, which may be used during tests. We use the * ATLAS Moodle *
for online consultation, discussion, and submission of homework. Daily
work (30%), tests(40%) and the final (30%) are announced in the online
syllabus.