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 |