Math 442: Differential Geometry of Curves and Surfaces

Emily Dumas

University of Illinois at Chicago
Spring 2009

Final exam information

The final exam will be held in SEO 636 on Friday, May 8, 10:30am-12:30pm.

The exam consists of two problem lists (A and B) with four problems each. For full credit, you must complete two problems from each list during the two-hour exam period.

List A is available below. You will receive list B on the day of the exam.

You may not discuss the problems on list A with anyone else until after the exam.

General information

Lectures	MWF 10:00 - 10:50am in SEO 636
Text	Differential Geometry of Curves and Surfaces by Manfredo do Carmo (see also: list of errata) ISBN-13: 978-0-13-212589-5
Instructor	Emily Dumas ()
Office hours	Mondays 2-3pm, Wednesdays 11am-12pm in SEO 503
Homework Policies	Homework will be assigned after most lectures and collected weekly on Monday (or in the first lecture of the week, if Monday is a holiday). The list of challenge problems will also be updated on a regular basis; you must complete two (undergraduates) or four (graduates) of these problems and submit your written solutions before the end of the semester.
	Late homework will not be accepted.
	You can discuss the homework with other students, but you must write (and understand!) your own solutions.
	The homework problems depend on material from both the assigned reading and the lectures. Do not leave the problem sets or reading to the last minute!

Handouts

These documents are available for download in PDF format.

• Course Syllabus
• List of errata in the textbook, compiled by Bjorn Poonen and his students.
• Topic outline for the midterm. At the moment, this only includes the topics we did not have time to cover on Monday, March 2.
• Solution to problem 3.5.11
• Final exam topic outline   -   Last updated
• Final exam problem list A

Important Dates

There will be one midterm exam and a cumulative final exam.

Midterm Exam	Wed, Mar 4	In class
Final Exam	Fri, May 8, 10:30am-12:30pm	SEO 636

Grading

Your course grade will be determined on the following basis:

Homework	30%
Midterm Exam	30%
Final Exam	40%

When computing your homework grade, the lowest weekly homework score will be dropped, and the remaining scores will be averaged with your challenge problem scores. (That is, each challenge problem is worth as much as a weekly homework assignment!)

Assignments

Try out 3d-XplorMath.

Reading

Unless otherwise noted, all reading assignments refer to the textbook, Differential Geometry of Curves and Surfaces by Manfredo do Carmo.

Weekly Problems

Lists

• Problem list (PDF)
• Challenge problems (PDF) - Last updated

Online Resources

These online tools (java applets, etc.) complement the material from the textbook and lectures.

• Integral geometry lecture notes by Andrejs Treibergs
  • See also: Inequalitites that imply the isoperimetric inequality, which includes the proof we discussed in lecture
• 3d-XplorMath: Download the software used in the computer demonstration on January 30.
  • Some of the demonstrations are also available as java applets which you can view in your web browser.
• Frenet frame applet by Martin Raussen at Aalborg University. This applet shows the Frenet frame of an arbitrary parametric curve (by default, the twisted cubic).

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