MAT 4141: Capstone in Differential Geometry


Syllabus for 4141

This course is grade on as S/U. To receive an S grade, you must
  1. fill out a survey
  2. meet with me semi-regularly to discuss your progress
  3. turn in some course work in LaTeX, using templates, as an introduction to scholarly research, the software and mathematical writing
  4. 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