You project will be graded based on the depth of your differential geometry connections, and the clarity and creativity of:

- Maximum 3-Page Typed (Single-spaced)
Review of Material We Covered in Class that is Related to your topic

Include the relevant definitions, mathematical symbols and notation, pictures, theorems, demonstrations, and examples from class, homework and tests that relate to your topic. Part 1 is purely class review. Any new material belongs in part 2. For instance, say your extension incorporates Gauss curvature in some way. Then the new extension is in part 2, while a review of what we already did related to Gauss curvature belongs in part 1 (so part 1 will not cover all class topics--just the ones that relate). Some past students reported that they have found it helpful to think of part 1 as a review of class notes and hw as if they were studying for a final exam [without the exam component - instead the product is finding the connections we covered that relate to your topic]. - An extension of class work, which might be one of the following:
- summary of what you have learned (in your own words) after researching a topic [1 or 2 pages should be sufficient in many cases and it could be in bullet point or paragraph format]
- computer program you write and report back on how that went
- demo you create
- historical timeline you create
- classroom worksheet that you create
- the beginnings of a more extensive research project...
- lots of possibilities here - I encourage you to be creative

- An annotated reference list (to turn in).
**The annotations are brief comments about how you used each reference in your project.**Most topics should utilize journal articles or books from the library and/or my office.

Here is a sample project for a different class (2240) by Russell Chamberlain and Dalton Cook. Here is Russell and Dalton's LaTeX file. If you want to use LaTeX, I can help, and you can copy their file into a site like Overleaf and modify it from there.

**Research Session Presentations on the final exam day**
Bring a printed version of your all of your work.
We will divide up the class into two sessions (half the class will stand next
to their work as the other half examines the projects,
and then we will switch roles).
During your session, you must stand by your work to discuss your topic and
answer questions. If you work with another person, they will be in the
other session so you should be prepared to present the entire project.
The presentation sessions are similar to research day at Appalachian, poster
presentations at research conferences, or science fairs.
In addition, when
you are viewing other projects, you will conduct peer review and a self evaluation.

**For 4141 Students**
In addition, 4141 students turn in a Capstone Project, which has
different requirements. It can be on the same topic as your final project.

**For 5500 Students**
In addition, 5530 students will
research the literature (mathematics and/or physics and/or cs journals) and discuss
some recent work, and if possible an open problem, that relates to your topic.
Summarize what you found in your own words, and be sure to list the
journal articles.

Here are some final project ideas, just to give you a sense of some possibilities: