Dr. Elizabeth Arnold
: Burruss 116
: M-F 2:30-4:30pm
12:30-2:30pm. June 20-July 1.
course will cover topics from Euclidean and non-Euclidean
Geometry. We will use the software Geometry Explorer
as a supplement
to the text. This software can be installed on Windows, Macintosh or
Linux machines. It will be available in the JMU Math computer lab
as well. It is understood
that the students have as a pre-requisite an in-depth understanding of
(high school level) Euclidean geometry. Prior experience with proving
mathematical results is highly recommended. Also desirable is
some experience with matrix algebra and the notion of a group from
abstract algebra. The goal of this class is to expose you to new
concepts in geometry and to deepen your understanding of basic concepts
in Euclidean geometry. This is NOT a methods course, nor is it a
workshop where you will take home worksheets, projects, etc. for your
own students. This is a content
course where you will deepen your knowledge and hopefully your
appreciation of geometry, which should enhance your teaching of your
individual curriculum. Topics for this course will include
axiomatic geometry, more
Euclidean geometry, analytic geometry, transformational geometry,
non-Euclidean geometry and fractal geometry. We will cover most of the
sections in Chapters 1, 2, 5 and 7 of the text, the first 2 sections
only of Chapter 3, and as much of Chapter 9
as we can. A tentative outline is below.
TEXT: Geometry with Geometry
by Michael Hvidsten, Geometry Explorer CD (included
mandatory. Missing one class in this summer session amounts to missing
over 2 weeks of a regular semester class.
The grading will
be assigned on a graduate scale: A, A-, B+, B, B-, C, F.
A=Excellent, B=Good, C=Poor, F=Fail. Grades will be based on
quizzes, computer projects, midterm and attendance/participation.
Quizzes will be short
- 10-15 minutes, and will cover what we have covered through the last
covered the previous day. Quizzes will be given in the afternoon
session and there will be time to ask questions about the previous
day's material in the morning session.
Homework will be
assigned, but not collected. Quizzes will be based on both
lectures/readings and homework. Time will be given in each
morning session to answer questions and go over some (but probably not
all) homework problems. It is recommended that you work on
homework problems together and ask questions during office hours.
will be 5 computer projects assigned during this course. These
projects are designed for you to learn new concepts, solidify concepts
covered in class, and, in general, to get exposure to learning
techniques using geometric software. The software provided with
the textbook is very similar to other commecially available software
packages that you can use in your own classroom. You are
encouraged to work together on the computer projects, but you must
write up your own work to turn in. See "Group Work" below.
There will be a take
home mid-term given out on Friday, June 24 and due on Monday June
27. You may not work together on this, but you may use your
notes, your text book and the software. Please do not use any
other assistance such as other texts, other people or other computer
sites or software.
also called cooperative
learning, is an important and effective learning strategy. You
are encouraged to work together in class and out of class. However
turning in projects or homework, you must write up
the work yourself. If you turn in work that is not your own, you
must have the author's name on it as well. Not crediting the work
correctly is a violation of the honor code.
This is a very
intense class. Plan to work hard, learn a lot and have fun.
It is not recommended that you are taking another class or are working
during this class. There will be homework assigned at every class
and a computer projects assigned at almost every class. I
will be available to help you and answer questions during the lunch
hour and for 2 hours at the end of each day. I am also available
by e-mail in the evening.
520 Summer 2005 tentative outline
June 20 Sections
Homework: Section 1.4: 3-10, Section 1.5: 1, 4-10
Project: Project 1 - The Ratio
Made of Gold 1.3, pp. 8-18. Due Wednesday, June 22
June 21 Sections
Homework: Section 1.6: 2, 3, 5-11
Project: Project 2 - A
Concrete Axiomatic System, pp. 40-49. Due Thursday, June 23
June 22 Sections 2.1-2.3
Homework: Section 2.1: 1-4, Section 2.2: 4-9, 11, 12
Project: Project 1 Due.
June 23 Sections 2.4-2.6
Homework: Section 2.4: 7-10, Section 2.5: 1-4, 7,
2.6: 1-6, 8, 12
Project: Project 4 Circle
Inversion, pp. 98-103,
Project 2 Due.
June 24 Sections 2.7,
Homework: Section 5.1: 3-10; 5.2: 6-11
Take-home Midterm handed out - Chapters
1 and 2
June 27 Sections 5.3-5.5
Homework: 5.3: 4-6, 8; 5.4: 1,2, 4,5, 7,8,9;
Project: Project 7 Quilts
and Transformations pp. 206-211
June 28 Sections 5.6, 7.1
Project 4 Due
Homework: 5.6: 5-11
June 29 Sections7.2, 7.3
Homework: 7.3: 3-6
Project: Project 10 The
Saccheri Quadrilateral, pp 286-290
June 30 Sections
9.1, 9.2, 9.3
Homework: 9.3: 1-5
Project 10 Due