### MAT 4141: Capstone in Differential Geometry

Syllabus for 4141

This course is grade on as S/U. To receive an S grade, you must
- fill out a survey
- meet with me semi-regularly to discuss your progress
- turn in some course work in LaTeX, using templates, as an introduction
to scholarly research, the software and mathematical writing
- turn in a quality differential geometry project that satisfies the
rubric.

As per the
University-wide
Statement on Student Engagement with Courses
you can expect to spend (on average) **2-3 hours
***outside* of class for each hour in class.
Homework during some weeks may take less than this time---your
other time should be spent on the course project.
### Schedule

Week 1: Read:

1. LaTeX Software

2. Dr.
Bauldry's An Increadibly Brief Introduction to LaTeX

3. Advice from Previous Students

4. **Homework Due**: On the private ASULearn forum,
send me your schedule on ASULearn to set up a meeting time for next week (which might be online).

Week 2: **Meet with me**.

1. Read through the course project ideas at the bottom
of this page and choose a preliminary topic.

2. Prepare to share
your plans for the first year after graduation from Appalachian, and
your longterm career plans. Take a look at
Appalachian's Career Development
Center.

Week 3: **Homework Due**:
Read through Scholarly Peer-Reviewed Sources
and watch the tutorials there. Summarize the main points. Next
search for at least quality
three sources related to your preliminary topic, and identify them
as peer-reviewed or not. Include at least one scholarly peer-reviewed source,
and indicate how you can tell that it is.

Week 4: **Homework Due**:
Historical and MathSciNet or other Library Databases research

Week 5: **Meet with me**.
**Homework Due:**
Read "How to write mathematics"
by Paul Halmos.
Enseign. Math. 16 (1970), 123-152.
Name at least two aspects from the reading that surprised you,
that you found interesting, disagreed with, or had a question on.

Week 6: **Homework Due**:
Preliminary Bibliography.

You can make a RAP appointment with the Library for help with your research.

Week 7: **Homework Due**:
The capstone survey is accessible by this link as long as you are logged in to
Appstate gmail:
http://goo.gl/forms/1Unykkyhe8.

Here is a pdf version in case you would like to look at that first:
PDF version, and I'm happy to help and discuss this with you in
office hours.

Week 8:
**Homework Due**:
Read "Guidelines for Good Mathematical Writing" by Francis Edward Su.
Name at least two aspects from the reading that
surprised you, that you found interesting, disagreed with, or had a question
on. Work on the rough outline.

Week 9: **Homework Due**: Rough Outline

Week 10: **
Meet with me**. Work on the
rough draft.

You can make a
RAP appointment with the Library for help with your research and
with the
University Writing Center
for help with your writing.

Week 11:
Look at
LaTeX
Mathematical Symbols [for anything not on this, I google "LaTeX code" and the
name of the symbol.
Work on the rough draft.

Week 12: **Homework Due**:
Rough Draft

Week 13:
**Meet with me**.
Continue working on
the project.

You can make a RAP appointment with the Library for help with your research and
with the University Writing Center
for help with your writing.

Week 14:
**Homework Due:** For 4040,
you'll be reading
*How to Create Your Own Universe in Three Easy Steps*
by Lawrence Brenton. Math Horizons April 2011, pp. 5-9.
Reflect on the writing. Identify at least three
strengths and/or weaknesses of how Brenton
presented mathematics, especially in reference to
Paul Halmos' and Francis Su's ideas from past readings.
Continue working on the project.

Final Exam Period: **Homework Due**: Final
version of 4141 Project is due.

### Suggestions for Capstone Project Topic

Here are some ideas, just to give you a sense of some possibilities:
See p. 453-454 of our textbook, which lists some final project ideas
5.7 in our textbook: an industrial application of wrapping and unwrapping
Explore a curve, a surface or a metric form
Rudy Rucker's
Software related to How Flies Fly
Designing a Baseball Cover -
the article by Richard B. Thompson - The College Mathematics Journal, Vol.
29, No. 1 (Jan., 1998), pp. 48-61.
Published by: Mathematical Association of America
Explore a theorem or topic from class or the textbook or a related idea.
Explore a related journal article, like
*The Klein Bottle as an Eggbeater* by Richard L.W. Brown.
*Subdivision Surfaces (Geometry and Computing)* by
by Jorg Peters and Ulrich Reif explores the connections between
differential geometry and the popular technique for representing surfaces.
Oddly shaped wheels for nonflat surfaces, like
A Bicycle with Flower-Shaped Wheels
Spirograph parametrizations like
Spirotechnics!
The Gauss map
Minimal surfaces
Schwarzschild solutions
Developable surfaces
Best Way to Hold a Pizza Slice
Visualization in differential geometry
Physics in differential geometry