HOMEWORK
MTH 435/535 — Spring 2020

Ground Rules

Suggested Reading
It is to your advantage to skim suggested readings as soon as possible. However, do not expect to master this material the first time around. Don't worry; we'll cover it in class, after which the readings should make more sense. But be warned: we will not always cover the material the same way it is presented in the text.
Warmup Problems
Most assignments will include suggested warmup problems, typically with answers in the back of the text. You should attempt as many of these problems as you feel are necessary, but should not turn them in. If you have questions about any of these problems, ask me, although in most cases further discussion should take place during office hours.
Written Work
It is your job to explain your work to me clearly and completely. Here are some guidelines: You may discuss homework problems with anyone you like, and you may use any reference materials you like, although the use of explicit solutions by others to the same problems is strongly discouraged. However, you must write up the solutions in your own words, and you must indicate what help you used. Late homework will be corrected as a courtesy to you, but can earn at most half credit.
Grading
All written assignments will receive two separate scores, one for content and the other for presentation.
Gradescope
Written assignments should be submitted via Gradescope.
Further instructions will be posted on the announcements page.
Videos
For most classes, there will be a short video mini-lecture available beforehand, either to summarize the essential new content of the day, and/or to review prior content. Please watch this video before class.
Video mini-lectures will be available through Canvas.
Classroom sessions will be recorded and should also be available through Canvas.

Assignments
Section numbers refer to O'Neill, 2nd revised edition.
(The 2nd edition is nearly identical; the 1st edition differs only in a few problems.)

Weeks 9–10
Suggested reading: Skim DFGGR §6.1; Read DFGGR §17.1–17.8 and §18.4–18.6.
See the announcement page for ways of accessing my text, DFGGR, online.
Assignment:
none
Week 8
Suggested reading: Skim §7.5; Read §7.6–7.7.
Warmup problems:
§7.6: 1, 2, 3, 5, 9; §7.7: 1, 7
Assignment: HW 8 (due 5/27/20):
§7.6: 6, 7; §7.7: 2, 4.
Extra Credit: (late submissions OK)
§7.7: 6bc
(full credit requires good drawings, preferably by computer)
Week 7
Suggested reading: Read §7.1–7.3; Skim §7.4.
Warmup problems:
§7.1: 3, 5, 7; §7.2: 3, 5; §7.3: 1; §7.4: 1, 3.
Assignment: HW 7 (due 5/18/20):
§7.2: 2; §7.3: 2, 6; §7.4: 8.
Week 6
Suggested reading: Read §6.7–6.8; Skim §6.9.
Warmup problems:
§6.7: 3, 6; §6.8: 1, 3, 4a.
Assignment: HW 6 (due 5/11/20):
§6.7: 2; §6.8: 12.
Week 5
Suggested reading: Read §6.4–6.5; Skim §6.6.
Warmup problems:
§6.4: 1, 7, 8, 9; §6.5: 1; §6.6: 1, 3.
Assignment: HW 5 (due 5/4/20):
§6.4: 13, 14; §6.5: 4; §6.6: 2a.
For §6.4:14, you may use the alternate version of stereographic coordinates introduced in class, where the center of the sphere is located at the origin. You may also use round coordinates (polar; spherical) rather than rectangular coordinates.
Week 4
Suggested reading: Skim/reread §6.1–§6.2; Read §6.3.
Warmup problems:
§6.1: 1; §6.2: 2; §6.3: 1.
Assignment: HW 4 (due 4/27/20):
§6.3: 2, 5.
Week 3
Suggested reading: Skim §4.4–4.5; Read §4.6.
Warmup problems:
§4.4: 4b, 7, 8; §4.5: 11 (reading it is enough); §4.6: 5.
Assignment: HW 3 (due 4/20/20):
§4.5: 2; §4.6: 4, 9.
Week 2
Suggested reading: Read §5.7.
Warmup problems:
§5.7: 3, 5, 6
Assignment: HW 2 (due 4/13/20):
§5.7: 9abd
1. Show that helicoids are twisted surfaces of revolution.
2. §5.7: 9ac
(In the original 2nd edition, these problems are §5.7: 9abd.)
WARNING: The text reverses its usual conventions for $\boldsymbol g$, $\boldsymbol h$ in §5.7:8!
The explicit parameterization in §5.7.8 is $\mathbf{x} = (-\sqrt{1-e^{-2u}}+\tanh^{-1}\sqrt{1-e^{-2u}}, e^{-u}\cos\theta, e^{-u}\sin\theta)$.
Week 1
Suggested reading: Read §5.6. (Also skim as much of §5.1–5.3 as needed to refresh your memory.)
Warmup problems:
§5.6: 3, 7, 15bcd.
Assignment: Use Gradescope (due 4/1/20): Write a few sentences to introduce yourself.
Please include some information about your math background, your major and intended degree(s), your motivation for taking this class, and anything else you think is relevant.
Submit this assignment, and all future assignments, via Gradescope.
Assignment: HW 1 (due 4/6/20):
§5.6: 1, 2ab, 4 (You may use a unit-speed curve in #1, and make a choice of orientation in #4.)
MTH 535 only: §5.6: 5.