This is a very rough tentative calendar and
continuous changes are to be expected.
Announcements made in class always take priority.
This page is under construction
| Week 1 | M Jan 19 | Martin Luther King Holiday | |
| T Jan 20 | Introduction: "Geometry" and "Differential".
Curves in the plane and 3-space. | ||
| Th Jan 22 | class postponed. no meeting today | ||
| Week 2 | T Jan 27 | Frenet Serret formulas intrinsic properties, invariance under ... | |
| Th Jan 29 | Abstract manifolds: motivation and tasks to be addressed | ||
| Week 3 | T Feb 3 | Manifolds and local coordinate charts
Embedded surfaces versus intrinsically defined manifolds | |
| Th Feb 5 | |||
| Week 4 | T Feb 10 | Tangent spaces
"Arrows" versus equivalence classes of curves, differential operators and abstract notion | |
| Th Feb 12 | |||
| Week 5 | T Feb 17 | Tangent bundles and tangent maps
... | |
| Th Feb 19 | |||
| Week 6 | T Feb 24 | Cotangent bundle and pull-backs of differential forms. | |
| Th Feb 26 | Flows of vector fields | ||
| Week 7 | T Mar 3 | Lie derivatives and integrability
Frobenius' theorem Reachable sets and controllability | |
| Th Mar 5 | |||
| T Mar 10 | Spring Break | ||
| Th Mar 12 | |||
| Week 8 | T Mar 17 | Tensor bundles and exterior derivatives
Frobenius' theorem revisited. Observation spaces, state-space realizations of I/O systems. | |
| Th Mar 19 | |||
| Calendar under construction. Below week-2-week topics from 2007 class on geometry | |||
| Week 9 | T Mar 24 | Riemannian metrics
Notion of distance on surfaces and abstract manifolds | |
| Th Mar 26 | |||
| Week 10 | T Mar 27 | Geodesics
Smoothness! Christoffel symbols Apr 1: Class Withdrawal Deadline (online) | |
| Th Mar 29 | |||
|
Apr 3 Course
withdrawal deadline: in person
Apr 5 Course withdrawal deadline: online | |||
| Week 11 | T Apr 7 | Parallel transport Levi-Civita connection Abstracting the ideas behind geodesics | |
| Th Apr 9 | |||
| Week 12 | T Apr 14 | Gaussian curvature
Possible notions of curvature. Invariance. Weingarten map? Possible project: read historical work | |
| Th Apr 16 | |||
| Week 13 | T Apr 21 | Gauss Bonnet theorem
The crowning conclusions: Connecting geometry and topology | |
| Th Apr 23 | |||
| Week 14 | T Apr 28 | Outlook: Many connections
Not necessarily Riemannian settings. Possibly: Control theory or principal bundles (outlook only!) | |
| Th Apr 30 | |||
| Week 15 | T May 5 | Outlook / presentation continued | |
| W May 6 | Reading Day | ||
| Th May 7 |
12:20 - 2:10 Final Exam
Room to be confirmed (or: 2:10 p.m. Final Project due) | ||
| Week 16 | Th May 14 | Commencement | |