Professor: Jeff Johannes
Section 1
MWF 10:30-11:20a Fraser 116
Office: South
326A
Telephone: 245-5403
Office Hours: Monday 5-6p Fraser 116, Tuesday 8-9p
South 336, Wednesday 2-3p Fraser 104, Thursday 4-5p Fraser 116,
Friday 12-1p Fraser 116, and by appointment or visit.
Email Address: Johannes@Geneseo.edu
Web-page:
http://www.geneseo.edu/~johannes
Textbook
Experiencing Geometry: Euclidean and
Non-Euclidean with History (Third Edition), David W. Henderson
and Daina Taimina or
Experiencing
Geometry: Euclidean and Non-Euclidean with History (Fourth
Edition), David W. Henderson and Daina Taimina
Purposes
To develop a deep and personal understanding of
Euclidean, spherical and hyperbolic geometries and how they relate
to measuring the universe in which we live.
Overview
This course will take a more philosophical
perspective on geometry rather than a computational or result-based
perspective. In this class we will use several different
methods to analyse geometries. We will rarely have traditional
lectures. More frequently will be times for individual work,
group work, and class discussion. Primarily you will be
writing personal discussions of homework problems.
Reading
I have intentionally chosen Henderson's book as
an exploratory and philosophical text. After our
class introductions, please take time to carefully read the chapters
in the book. Notice use of the words “time" and
“carefully". Read the sections slowly. Read actively,
that is while writing and with models at hand. If you do not
understand some statement reread it, think of some potential
meanings and see if they are consistent, and if all else fails, ask
me. If you do not believe a statement, check it with your own
examples. Finally, if you understand and believe the
statements, consider how you would convince someone else that they
are true, in other words, how would you prove them?
Learning Outcomes
Math 335 - Upon successful completion of Math 335
- Foundations of Geometry, a student will be able to:
- Compare and contrast the geometries of the Euclidean and
hyperbolic planes,
- Analyze axioms for the Euclidean and hyperbolic planes and
their consequences,
- Use transformational and axiomatic techniques to prove
theorems,
- Analyze the different consequences and meanings of parallelism
on the Euclidean and hyperbolic planes,
- Demonstrate knowledge of the historical development of
Euclidean and non-Euclidean geometries,
- Use dynamical geometry software for constructions and testing
conjectures, and
- Use concrete models to demonstrate geometric concepts.
Grading
Your grade in this course will be based upon your
performance on homework, a project, and a final experience.
The weight assigned to each is designated below:
Homework Problems 3/5
Project
1/5
Final Experience
1/5
Homework Problems
Throughout the course you will write up
discussions of “Problems" from Henderson's book. Before these
papers are handed in, I strongly suggest somehow submitting drafts
to me for comments (most easily to submit them early via
Canvas). These drafts are not required, but will strengthen
your understanding and your final products. Drafts can either
be submitted in paper or via email. Either way I will return
them with comments and suggestions. The end goal of writing
each problem will be presenting your complete understanding of the
question in a well-written discussion. These discussions will
be graded on a ten point decile scale based on completeness,
accuracy and writing.
These problems will be evaluated similarly to
evaluating papers in an English class.
0 missing or plagiarised
3 question copied, nothing written
6 something written that appears that it was only
written to take up space
7 substantially incomplete. Something
written, but does not really answer the main questions. Major
errors. Very poor writing
8 mostly complete. maybe a few minor errors
9 complete, no errors, some personal insight,
well-written
10 wonderful (includes concise, and to the
the point directly)
Participation Modifier
For each homework problem there will be a
discussion in class introducing it. If you are present in
class and actively and thoughtfully participating in the discussion
on that topic, then you will earn an additional .5 for the
associated homework problem. If you would like to prepare for
the topic, I suggest reading at least the table of contents for the
question. Beyond that, try not reading too much in advance so
as to not spoil the fun. Look here
for an approximate unreliable daily schedule, but more importantly,
pay attention in class to our progress. Two "extra" day
modifiers may be earned by visiting my office during the month of
January.
Solutions and Plagiarism
There are plenty of places that one can find all
kinds of solutions to problems in this class. Reading them and
not referencing them in your work is plagiarism, and will be
reported as an academic integrity violation. Reading them and
referencing them is not quite plagiarism, but does undermine the
intent of the problems. Therefore, if you reference solutions
you will receive 0 points, but you will *not* be reported for an
academic integrity. Simply - please do not read any solutions
for problems in this class.
Projects
Each student is responsible for completing a
project as part of a pair. A project will consist of reading
one of chapters 11, 14-22 from Henderson's book. The materials
for the projects must be chosen by February 23. Each project
will include a write-up of all the problems in the chosen
part. Finally, each of the projects will be presented in the
last two weeks of class.
Final Experience
The final experience will include extensive
writing and focused on summarizing the experience of different
aspects of the course. This product will be due at the
time of the scheduled final exam, May 15, 9-11a, when we will also
meet to discuss the topic and the course as a whole.
Geogebra
We may occasionally using Geogebra as a method of
gaining intuition for geometry. Details for working with this
software will be described in class.
Feedback
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for
how the course is running. Remember, the sooner you tell me
your concerns, the more I can do about them. I have also
created a web-site
which
accepts anonymous comments. If we have not yet discussed
this in class, please encourage me to create a class code.
This site may also be accessed via our
course page on a link entitled anonymous
feedback. Of course, you are always welcome to approach
me outside of class to discuss these issues as well.
Accommodations
SUNY Geneseo is dedicated to providing an
equitable and inclusive educational experience for all students. The
Office of Accessibility will coordinate accommodations, auxiliary
aids, and/or services designed to ensure full participation and
equal access to all academic programs, activities, and services at
SUNY Geneseo. Students with letters of accommodation should submit a
letter and discuss needs at the beginning of the semester. Please
contact the Office of Accessibility Services for questions related
to access and accommodations. Erwin Hall 22 (585) 245-5112 access@geneseo.edu
www.geneseo.edu/accessibility-office.
Religious Holidays
It is my policy to give students who miss class
because of observance of religious holidays the opportunity to make
up missed work. You are responsible for notifying me no later
than February 7 of plans to observe the holiday.
Military Obligations
Federal and New York State law requires
institutions of higher education to provide an excused leave of
absence from classes without penalty to students enrolled in the
National Guard or armed forces reserves who are called to active
duty. If you are called to active military duty and need to miss
classes, please let me know and consult as soon as possible with the
Dean of Students.
Schedule
subject to change. For more similarly unstable daily details,
see here.
January 27 - February 15 Discuss
Chapters 1-5 of Henderson
February 6
As a
homework exercise, show a model of a hyperbolic plane
February 17 - March 20
Discuss Chapters 6, 7, 9 of Henderson
February 20
Drafts of Chapters 1-5 will not be accepted after
February 23
Projects must be chosen by this date.
February 27
Final write up of Chapters 1-5 “Problems" due
March 22 - April 7
Discuss Chapters 8, 10 of
Henderson
March 24
Drafts of Chapters 6, 7, 9 will not be
accepted after
March 31
Final write up of Chapters 6, 7, 9
“Problems" due
April 10 - May 3?
Discuss Chapters 12, 13 of Henderson, and
Constructions
April 10
Drafts of Chapters 8, 10 will not be accepted after
April 17
Final write up of
Chapters 8, 10 “Problems" due
April 29
Drafts of Chapters 12,
13 will not be accepted after
May 5 - May 15
Project presentations
May 8
Written projects due. Final write up of Chapters 12, 13
"Problems" due
Monday May 15, 9-11a Final experience -
leftover presentations.