- As announced, I will score your term papers using a rubric very similar to the peer review. To help you prepare your paper, here's the form I'll fill out for each paper: term-paper-rubric.pdf. Note that
*my numerical ratings might not agree with those of your peer review*. - Here are some solutions to midterm 2. Please ask me about anything that's unclear.
- In case it's useful to you, here's the concept map we produced during our review for midterm 2. I make no claims about its completeness. You are strongly encouraged to repeat this exercise individually or in a small group after some more studying.
- As you continue drafting your term paper, consider looking at the Chicago REU for (generally) good math writing by undergraduates. These papers don't have the same page limit as yours, but have a similar structure. For
*very*good mathematical writing, check out the "What is..." collection from the AMS Notices. Finally, here's the rubric your classmates will use to review your draft: peer-review.pdf. - If you choose to use grading scheme 2 for your term paper, you will be expected to write an artwork description to go along with your art submission. This description should be 1-2 paragraphs, and address the following questions:
- Is there a brief description of the mathematics that inspired your artwork?
- What techniques did you use to create the artwork?
- What aspect of the artwork is most meaningful to you?

- Per a request, here's a LaTeX template you can use for your term paper: term-paper-template.tex. You aren't required to use LaTeX, though I do request that your paper be a PDF.
- Scheme selection for the term paper has been delayed. You will now choose between the two grading schemes during the week of Oct 31-Nov 4.
- Here are some solutions to midterm 1. Please ask me about anything that's unclear.
- There were a lot of questions about how to get started on exercises 5.3 and 5.5 of activity 5, so I've written up some comments on the 1-dimensional (i.e., curves) version.
- Activity 5 mostly consists of examples of the basic definitions we'll need for discussing surfaces, so it will be "chunked" across the 9/23 and 9/26 classes. Notice that the due date for this activity has been pushed to Oct 3.
- Here's an outline of a solution to problem 6 on homework 2. Surely there are other approaches to this problem, so let me know if you find something more elegant! (And if you use this outline, be sure to explain things in your own words.)
- I failed to record class on Sept 14. The filled-in notes are posted, and you should feel free to ask me any questions. (Of course, questions are always welcome!)
- As you start thinking about topics for your term paper, peruse this list compiled by Prof. Etnyre (scroll to bottom), as well as this Wikipedia list and make sure to ask me any questions you have. (Your topic needs to go beyond this course, so be sure to double-check the schedule below.)
- Per a request, I've added TeX files for homeworks/activities, in case you want to use them. However,
**you are not required to typeset your submissions.**Also, just in case I make typos:**the PDF is the official version of the assignment.** - Visit Georgia Tech's OIT website to download
*Mathematica*. (You'll need to be on campus or using a VPN for this.) Consider taking a look at this tutorial to get started, and ask me any questions that come up. - Be sure to join our class on Discord, and to participate.

The following is a tentative, nonbinding schedule. It will be updated as the term progresses.

Topics covered | Notes | Materials | |
---|---|---|---|

Week 1 (8/22-8/26) |
M: Course goals and first definitions W: Tangent vectors and arc length as geometric invariants F: Activity 1 (linear algebra) |
Aug 22
Aug 24 |
Homework 1 (due 9/9)
homework-1.tex Activity 1 (due 8/31) activity-1.tex |

Week 2 (8/29-9/2) |
M: Arc length parametrizations and Frenet-Serret apparatus W: Frenet-Serret apparatus day 2 F: Activity 2 (Frenet-Serret) |
Aug 29
Aug 31 |
Activity 2 (due 9/7)
activity-2.tex frenet-serret.nb |

Week 3 (9/5-9/9) |
M: Labor Day W: Line integrals and 2D Frenet-Serret F: Activity 3 (evolutes) |
Sept 7 |
Homework 2 (due 9/23)
homework-2.tex Activity 3 (due 9/14) activity-3.tex evolutes.nb |

Week 4 (9/12-9/16) |
M: Rotation index day 1 W: Rotation index day 2 F: Activity 4 (convexity) |
Sept 12
Sept 14 |
Activity 4 (due 9/21)
activity-4.tex |

Week 5 (9/19-9/23) |
M: Isoperimetric inequality W: Isoperimetric wrap-up/multivariable calculus review F: Surfaces definitions/Activity 5 (calculus on surfaces) |
Sept 19
Sept 21 |
Activity 5 (due 10/3)
activity-5.tex surfaces.nb |

Week 6 (9/26-9/30) |
M: More surfaces/activity 5 W: Tangent spaces/midterm 1 review F: Midterm 1 (through isoperimetric inequality) |
Sept 26
Sept 28 |
Practice midterm 1
Practice midterm solutions |

Week 7 (10/3-10/7) |
M: First fundamental form day 1 W: First fundamental form day 2 F: Activity 6 (map projections) |
Oct 3
Oct 5 |
Homework 3 (due 10/14)
homework-3.tex Activity 6 (due 10/12) activity-6.tex map-projections.nb |

Week 8 (10/10-10/14) |
M: First fundamental form day 3 W: Normal and geodesic curvatures day 1 F: Activity 7 (Darboux frame) |
Oct 10
Oct 12 |
Activity 7 (due 10/19)
activity-7.tex |

Week 9 (10/17-10/21) |
M: Fall break W: Normal and geodesic curvatures day 2 F: Activity 8 (Foucault pendulum) |
Oct 19 |
Homework 4 (due 10/31)
homework-4.tex Activity 8 (due 10/26) activity-8.tex foucault.nb |

Week 10 (10/24-10/28) |
M: Geodesic curvature is intrinsic W: Existence and uniqueness of geodesics F: Activity 9 (Clairaut's relation) |
Oct 24
Oct 26 |
Activity 9 (due 11/2)
activity-9.tex |

Week 11 (10/31-11/4) |
M: Length minimizing curves day 1 W: Length minimizing curves day 2 F: Activity 10 (directional derivatives) |
Oct 31
Nov 2 |
Homework 5 (due 11/14)
homework-5.tex Activity 10 (due 11/9) activity-10.tex |

Week 12 (11/7-11/11) |
M: How does a surface curve? W: Properties of the Weingarten map, or writing things down F: Activity 11 (Weingarten map) |
Nov 7
Nov 9 |
Activity 11 (due 11/16)
activity-11.tex weingarten.nb |

Week 13 (11/14-11/18) |
M: The second fundamental form W: Gaussian curvature F: Midterm 2 review (hopefully) |
Nov 14
Nov 16 |
Practice midterm 2
Practice midterm solutions |

Week 14 (11/21-11/25) |
M: Midterm 2 W: Thanksgiving break F: Thanksgiving break |
||

Week 15 (11/28-12/2) |
M: Gaussian curvature as a stretch factor W: Theorema Egregium F: Activity 12 (A rotation index for surfaces) |
Nov 28
Nov 30 |
Homework 6 (due 12/12)
homework-6.tex Activity 12 (due 12/7) activity-12.tex |

Week 16 (12/5-12/9) |
M: The Gauss-Bonnet theorem (final class meeting) F: Term paper due |
Dec 5 |