MATH 305
Modern Geometry

Dr. Fenton
Spring 2014

Web page:
http://www.bellarmine.edu/faculty/fenton/

This course meets 3:05 – 4:20 on Tuesdays and Thursdays in Pasteur 104.

I.
INTRODUCTION

Geometry is a large subject with an extensive history. In fact, much of what
we will discuss this semester has been known for decades, centuries, or even
millennia. However, the field has had a renewal of research and
applications, and geometric knowledge continues to grow. Geometry is once
again a major branch of mathematics and a valuable part of a mathematical
education.

This is an unusual undergraduate course, for it does not have a set
of topics that have to be covered to prepare you for a later course. In
fact, the content of an advanced geometry course varies greatly from
university to university. The course includes what I think are significant
and interesting topics: advanced properties of triangles and circles,
analytic geometry, taxicab geometry, transformations, symmetry, and
hyperbolic geometry. Please realize, however, that this is
*not *a review of high school
geometry. The course uses concepts from high school geometry to take a
deeper look at familiar topics, plus additional topics that may be
unfamiliar.

More important than any content, I hope to strengthen your abilities
as mathematicians. This includes practice with exploring mathematical
concepts, raising conjectures, proving and disproving geometric statements,
and communicating your mathematical ideas to others. The course will include
work with *The Geometer's Sketchpad,*
software designed for exploring and experimenting with geometric objects. My
hope is that you will discover many geometric concepts for yourself. There
will be an emphasis on discussing the mathematics and writing your results.

The pedagogy for this course is exploratory learning through small
group work. Each chapter opens with exploration activities, to be done as a
group of two or three people. These activities are introductions to the
concepts. Getting the explorations right or wrong is not the point; what is
important is that you just try them. By working the activities, you will
gain insight into the basic issues and you will have a foundation on which
to build a stronger understanding of the concepts. This will make our class
discussions more valuable for everyone.

II.
CONTACTING ME

My office is Alumni Hall 202, phone 272-8059. My office hours are 2:00-3:00
Tuesdays and Thursdays, or by appointment. Messages or assignments may be
left in my mailbox. I encourage you to contact me electronically either
through the campus email system or at *
wfenton@bellarmine.edu*. Feel free to call me at home 454-7855 (but not
after

Though my schedule is often very erratic, I will be in my office a
good deal and you are welcome whenever my door is open.

IV.
MATERIALS

*
College Geometry Using The Geometer’s Sketchpad*
by Fenton & Reynolds (blue cover)

You will be creating computer files in class and out of class. You
may wish to have a flash drive for saving these files.

The software we will use, The Geometer’s Sketchpad, is available on
campus in Pasteur 104, Pasteur 106, Horrigan 017, and Level B of the
library.

MATH 215 Linear Algebra. While the chapters I have
chosen will not use matrices and vectors, the study of linear algebra
provides mathematical maturity, including experience at developing and
writing proofs.

V.
COURSE DESCRIPTION (from the University catalog)

“A survey of topics in advanced geometry from three historical perspectives:
synthetic, analytic, and transformational. Topics include advanced results
in Euclidean geometry, axiomatics of Euclidean geometry, axioms and results
in non-Euclidean geometry, an introduction to projective geometry, the use
of coordinates, and insights gained from transformations.”

VI.
OBJECTIVES

*
Process Objectives*

At the conclusion of this course, a successful student will:

·
be able to use *Geometer’s Sketchpad*
software as an exploratory tool;

·
demonstrate an ability to generalize and conjecture from geometric examples;

·
demonstrate improved skills at developing logical proofs of geometric
statements;

·
exhibit familiarity with the vocabulary of geometry and use geometric
language more precisely;

·
understand the role of assumptions (axioms) when drawing conclusions.

*
*

*
Content Objectives*

At the conclusion of this course, a successful student will be able to:

·
construct various centers of a triangle and recognize their significance;

·
explain how the various definitions for power of a point are related;

·
relate algebra to geometry through the use of a coordinate system;

·
recognize and compose Euclidean motions visually;

·
use transformations to classify two-dimensional objects by their symmetries;

·
work with the Poincaré disk model of hyperbolic geometry;

·
understand basic results in hyperbolic geometry and the critical role of the
Parallel Postulate;

In addition, MATH 305 addresses the first three goals of the Mathematics
Department. There will be a strong emphasis on problem-solving. There will
be much practice at communicating mathematical ideas, both orally and in
writing. The reading and homework will include understanding and creating
mathematical proofs.

VII.
ATTENDANCE

I will not grade on attendance. However, during class discussions I will
call upon student teams for suggestions and explanations. Further, class
time will include time to work on the exploratory computer assignments, and
time to discuss Exercises with each other and with me. So it is to your
advantage to attend class. (See also the Travel Policy in the section on
University policies.)

VIII. ACADEMIC
HONESTY

(Also see the more complete statement in the section on University
policies.)

“… All members of our community have an obligation to themselves, to their
peers, and to the institution to uphold the integrity of

While this may at first seem inconsistent with the notion of group
work, the principle still applies: you are expected to contribute honestly
to the intellectual work of your group and of the course. Copying the work
of others does not contribute to your learning; you need to put in the time
and effort yourself to really understand the concepts.

IX.
GROUP WORK

Much of the work you do in this course will be in cooperation with other
people, both in and out of class. Here are some things to think about as you
decide who you want to work with.

·
Is everyone comfortable with the other people in the group?

·
Will we be able to work together productively?

·
Are there definite times when the entire group can meet outside of class?

(This is very important!)

Your group must have two or three members. The decision deadline is Tuesday
January 21^{st}.

X.
COURSE REQUIREMENTS

__
LAB ACTIVITIES__
Ten of these assignments at 10 points each = 100 points

Every chapter begins with a set of lab activities. Each group is to turn in
one assignment together. These will be graded primarily on completeness and
effort. Late homework will not be accepted. If your group has some
difficulty with meeting a deadline, please talk to me
**
before** the assignment is due.
These assignments will be posted on my web page.

Every chapter closes with a set of exercises. Again, each group is to turn
in one assignment together. The Exercises are intended to show what you have
learned about the topic, so they will be graded on correctness and clarity.
Late homework will not be accepted.
Again, if your group has some difficulty with meeting a deadline, please
talk to me **
before** the assignment is due.
These assignments also will be posted on my web page.

__TEST 1__
Tuesday February 18 and the preceding weekend
100 points

Chapters 1, 2,
3, 4

The exam is in
two parts. The first part is a group exam worth 50 points, done out of
class. Your group will work together and turn in one paper. All group
members will get the same grade on the group part. The second part is an
individual exam worth 50 points, done in class on February 18.

__TEST 2__
Tuesday April 1 and the preceding weekend
100 points

Chapters 5, 6,
8

The exam is in
two parts. The first part is a group exam worth 25 points, done out of
class. The second part is an individual exam worth 75 points, done in class
on April 1.

__
FINAL EXAM__
Tuesday April 29, 3:00-6:00
150 points

This is solely an individual exam. It will be comprehensive, covering the
entire semester but with extra emphasis on Chapters 10 and 11.

XI.
GRADING

Grades will be assigned as follows:

A+
Impress me!
A
92% or higher
A-
88 – 91%
B+
84 – 87%
B
79 – 83%
B-
75 – 78%
C+
70 – 74%
C
63 – 69%
C-
60 – 62%
D+
58 – 59%
D
52 – 57%
D-
50 – 51%
F
0 – 49% |
Lab Activities
100 points
Exercises
135 points
Test 1
100 points
Test 2
100 points
Final Exam
150 points |

Your course grade will be your point total as a percentage of the 585 possible
points.

XII. __UNIVERSITY POLICIES__

__
__

__
Attendance Policy__

The University requires students who will be absent from class while
representing the University to inform their instructors in two steps.
During the first week of the course, students must meet with each instructor to
discuss the attendance policy and arrangements for absences related to
University-sponsored events. Second, students must provide the instructor
with a signed __Student Absentee Notification Form, available via the student
portal on the University intranet__, at the earliest possible opportunity, but
not later than the week prior to the anticipated absence. The Student
Absentee Notification Form does not serve as an excused absence from class.
Your instructor has the final say about excused and unexcused absences
and it is the student’s responsibility to know and abide by the instructor’s
policy.

__
__

__
Academic Honesty__

I strongly endorse and will follow the academic honesty policy as published in
the Bellarmine University
Course Catalog, available on the
university website. Students and faculty must be fully aware of
what constitutes academic dishonesty; claims of ignorance cannot be used to
justify or rationalize dishonest acts. Academic dishonesty can take a
number of forms, including but not limited to cheating, plagiarism, fabrication,
aiding and abetting, multiple submissions, obtaining unfair advantage, and
unauthorized access to academic or administrative systems. Definitions of
each of these forms of academic dishonesty are provided in the academic honesty
section of the Course Catalog.
All confirmed incidents of academic dishonesty will be reported to the Assistant
Vice President for Academic Affairs, and sanctions will be imposed as dictated
by the policy. The instructor’s choice
of penalty ranges from a minimum penalty of failing the assignment or test to
failing the course itself.
If the student has a record of one prior offense, he or she will be suspended
for the semester subsequent to the one in which the second offense took place.
This sanction is in addition to the penalty imposed by the faculty
member. If the student has a record
of two prior offenses, he or she will be immediately dismissed from the
university upon the third offense.

*
*

__
Disability Services__

Students with disabilities who require accommodations (academic adjustments
and/or auxiliary aids or services) for this course must contact the Disability
Services Coordinator. Please do not
request accommodations directly from the professor.
The Disability Services Coordinator is located in the Counseling Center,
phone 272-8480.

**
**

*
Suggestions for Working in Groups*

•
Let everyone know that their ideas are of value, that no question is too
trivial to ask, and that everyone makes mistakes. Criticism should be directed
at ideas, not at individuals.

•
Cooperate with other group members. This means listening to the ideas of
others, trying methods that may be different from yours, and then coming to an
agreement on a group solution.

•
Be flexible, especially about finding time for the group to meet.
Cooperation includes compromise. Remember that you are expected to work 6 - 8
hours a week outside of class. Work together as much as possible.

•
Make sure that everyone participates. If someone is not offering her/his
ideas, stop and ask for their perspective on the problem.

•
Make sure everyone understands the solutions that are submitted for
grading and be sure that everyone has written up some of these solutions.

**
•
The most important thing is that the work must be done cooperatively!
Dividing up the set of problems without ever coming together to discuss them is
not an effective way to learn. Everyone needs to understand the questions asked
in all of the problems and the ideas involved in solving them.**