 Overview
Geometry has a facinating and ancient history, ranging from the first
geometric formulae developed by the Babylonians and Egyptians, to the
beautiful axiomatic system developed by Euclid (c. 500 B.C.E.), to the
more recent development of non-Euclidean geometries in the 18th and
19th centuries, to the very recent developments in fractal geometry and
computer software for exploring various geometries.
This semester we will carefully study the axiomatic systems of
Euclidean, hyperbolic, and elliptic
geometries in selected sections from Chapters 1--4 and 6 from the text.
We will also spend several weeks on the strange world of fractal
geometry where it makes perfect sense to say that an object has
dimension 1.2618. You will learn about other topics in preparation
of your own inclass presentations and from the presentations of other
students. As time allows, we may also cover additional topics.
Evaluation
Your final grade will be determined by
| Homework | 35%
| | Three Major Inclass Presentations | 35%
| | One Takehome Midterm Exam | 10% |
| Comprehensive Takehome Final | 15%
| | Weekly Presentations | 5%
|
Homework
A major emphasis in this course is that you learn how to
write rigorous and precise mathematical proofs. This can be a
challenging endeavor and may require several iterations, but the process will not only aid your
mathematical development but can also great improve your clarity of
thought in other disciplines and areas as well.
With this emphasis, your homework should be precise, comprehensible,
completely justified, and written in complete sentences.
Most of the homework problems will be worth 5 points, and the possible
grades will be 5 , 4 , or No Grade . A few of the problems may be worth 10 points,
and the possible grades will be 10 , 9 , 8 , or No Grade .
After I have returned the homework, I will allow you one opportunity
to rewrite any problem. However, you must turn in your rewrite, along with your original
paper, within one week of when I return the homework to the class.
An important aspect of your mathematical development is that you learn to discuss
mathematics with others and collaborate on problems.
The homework assignments will alternate between Individual
assignments and Group assignments.
On the group homework assignments, you will work in groups of two
and turn in one paper.
It is extremely important that both of you understand every solution
that your group produces. On each assignment, one student will
be designated as the
primary author who writes-up the solutions, and the role of primary
author must alternate between the members of the group.
You may discuss the Individual assignments with other
students, but each person must turn in a separate paper that
represents his/her own work.
Here are a few guidelines for the presentation of your homework. If you do not
follow these, I willreturn your homework to you ungraded!
- Your writing must be clear and legible.
- Be sure to label the primary author on the group assignments.
- Do not turn in your first draft. You should revise, polish
and rewrite your solutions.
- If you write in pen, there should be no scratch-outs.
- Do not turn in paper torn from a spiral notebook with
ragged edges.
The homework is due at the beginning of class on Wednesday.
Be aware that Late homework is not accepted!! No exceptions!!
Presentations
You will each give three major presentations during the
semester.
- The first presentation will be 15 minutes long on a general
topic from geometry of
your choosing.
- The second will be a 20-25 minute long group presentation
including a physical geometric model that you have built.
- The third presentation will be 20-30 minutes long on a
a topic from, or application of, geometry that we have not
discussed in class.
I can recommend some good places to look for topics, and
I will give you more guidance and detailed instructions on my
expectations for these presentations as the time comes closer.
Exams
The midsemester exam and final exam are takehome and will have some problems
that are similar, but not
identical, to homework exercises. However, most of the exam problems
will ask you to combine your knowledge of several different topics
from the course. Although you may not discuss the exams with anyone
else, you can ask me as many questions as you want about the
exams. You will always have at least one week to complete the takehome
exams.
Weekly Presentations
Most weeks, you will a short five minute presentation to the class. This will
usually involve carefully explaining a proof given in the text. This
will be a fairly low-stress activity.
Class Attendance
Although class attendance is not a specified percentage of your grade,
I will keep a class roll to help me determine borderline grades at the
end of the semester. If you do miss class, you are responsible
for the material that was covered.
Getting Help
Please come see me during my office hours! If you have a conflict
and cannot make my office hours, please call or email me and we can set up
an appointment for another time.
If you want to know check on your grade at any time during the
semester, please ask me and I can give you a rough idea of your
current standing.
Important Dates
These are a few important dates for the semester that you'll want to
keep track of.
October 6 - Individual Presentation #1
October 27 - Takehome exam due
November 17 - Group presentations
December 6 & 8 - Individual Presentations #2
December 22 - Takehome final exam due
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