Spr05 Math 225

Department of Mathematics
Math 402 - Fall 2007

Non-Euclidean Geometry

Sections M13 and 14

TTh 9:00 - 10:20am in 241 Altgeld Hall

News and Information

Computers available: The computers in IH239 have Geometry Explorer installed. You’re entitled to use them whenever the lab is free. Use your Active Directory username and password to login. The icon for Geometry Explorer is in the Dock at the bottom of the screen. It looks like a little papyrus scroll sitting on top of a flat box. If you run your mouse over the icons you'll also see the text of each application. [posted on August 28, 2007]

Picture Gallery:

Thanks to all of you for your creative Golden Rectangle pictures. Here’s a gallery with them all (without artist signatures, in case you want to preserve your anonymity). I’ll update the gallery whenever new pictures are submitted. [posted on August 29, 2007]
I’ve updated the gallery: all pictures submitted so far are now included. [posted on August 30, 2007]

A possible model for a project?

"The Hyperbolic Geometry Song" A short music video about the basics of Hyperbolic Geometry available at Youtube [posted on September 28, 2007]

NEWS [October 26]

The 2^nd midterm will be on Tuesday November 6
Problem 3 in Homework 8 has been moved to Homework 9, with a due date of Thursday November 1.

Instructor

Professor Steven Bradlow [bradlow@uiuc.edu]
Office: 259 Altgeld Hall
Office Hours: Wednesday12:00-1:00pm, or by appointment

Text

Geometry with Geometry Explorer by Michael Hvidsten (McGraw Hill, 2005)

Syllabus

Part or all of chapters 1,2,3,4,5,7,8,

Grading:

Your grade for the course will be determined by a weighted average of your scores for homework, 2 midterms, a project and a final. The weights of each will be:

Homework	15%
Midterm 1	20%
Midterm 2	20%
Project	15%
Final	30%

Resources

You can’t do better than the web and Google! Here are a few places to start:

Here’s a wonderful online, annotated version of Euclid’s Elements:

http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

If anyone discovers websites they particularly like, send them to me and I’ll post them here for others to see.

Homework

Homework will be posted at this website. A (small) subset will be graded.

Assignment	Due Date
Homework 1:	Thursday August 30
Homework 2:	Thursday September 6
Homework 3:	Thursday September 13
Homework 4:	Thursday September 20
Homework 5:	Thursday October 4
Homework 6:	Thursday October 11
Homework 7:	Thursday October 18
Homework 8:	Thursday October 25
Homework 9:	Thursday November 1

Project

What is it on? The project can be on any topic approved by the course instructor. It’s meant to give you an opportunity to explore some aspect of non-Euclidean geometry which you find interesting but which isn’t covered in class, or to delve more deeply into a topic mentioned in class but dealt with too superficially for your liking. Here’s an incomplete list of possible Project Topics – feel free to come up with your own.

What will the end result be? The end result of the project will be (1) a written paper four or more pages in length and (2) either a poster or an oral presentation of 10 minutes to the class.

What are the relevant due dates?

· Tuesday October 16 – Submit a proposal for the topic you will do. [ Here’s a list of topics that have been submitted ]

· Thursday November 1 - Submit a list of references and an outline of your paper. Also tell me whether you prefer to do a poster or a presentation.

· Tuesday November 27 - papers due

· Thursday November 29 - posters due (poster session in class).

· Tuesday December 2 - class presentations.

How will it be graded? The project will be graded out of 100, with a maximum of 75 for your written report and a maximum of 25 for your poster or presentation.

Exams

There will be two midterms and a final exam. Dates and syllabi will be announced at least one week in advance.

The (tentative) dates for the midterms are Tuesday September 25 and Tuesday October 30.

Midterm 1

When: Tuesday September 25, 9-10am, in 241 Altgeld Hall (i.e. the regular classroom)

On What:

· Section 1.5, 1.6 [Axiom systems]

· Section 2.1, 2.2, 2.5, 2.6 [Euclidean geometry]

· Section 3.1, 3.2 [Cartesian coordinate system and vectors]

Here’s a study guide to help you prepare for the exam.

Midterm 2

When: Tuesday November 6, 9-10am, in 241 Altgeld Hall (i.e. the regular classroom)

On What:

· Section 7.2, 7.3, 7.5, 7.6, 7.7 [Hyperbolic geometry ]

· Section 4.2 [Euclidean constructions]

· Section 5.1, 5.2, 5.7 [Isometries]

Here’s a study guide to help you prepare for the exam.

Final

When: 1:30pm -4:30pm, Monday December 10

On What: Everything we did in class, i.e. everything covered in Midterms 1 and 2, plus:

· Section 7.7 [Tilings]

· Section 3.5, 3.5.1 [Complex numbers]

· Section 8.2 [Mobius transformations]

Here’s a study guide to help you prepare for the exam.

Lecture Log (i.e. what was done in class) [to be added soon]

Last modified December 5, 2007