MAT 4141: Capstone in Differential Geometry
Syllabus for 4141
This course is grade on as S/U. To receive an S grade, you must
As per the
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.
- 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
Week 1: Read:
1. LaTeX Software
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
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.
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:
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
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
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
Meet with me. Work on the
You can make a
RAP appointment with the Library for help with your research and
University Writing Center
for help with your writing.
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:
Meet with me.
Continue working on
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.
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
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
The Gauss map
Best Way to Hold a Pizza Slice
Visualization in differential geometry
Physics in differential geometry