Daily Assignment for Wednesday, February 5

Due Friday, February 7 on Canvas.

• Try again to compute the Riemann surface of \( \sqrt[3]{z^3-1} \). Suggestions : make branch cuts by connecting the third roots of 1 to \( \infty \). Draw these on the Riemann sphere and unfold them to get a hexagon. Pay attention carefully to how the branches change as you cross each edge of the hexagon and glue 3 hexagons together to get the Riemann surface.
• We will cover the Riemann sphere next. The relevant material is spread out a bit in Needham's book : we need most of §§3.2 and 3.4. You may find it more intuitive to read §3.4 first and refer back to §3.2 as necessary. Our next main goal is the italicized statement at the end of §3.4.2.
• Do exercises 24, 26, 28, 30 on pp. 131–132. Exercises 28 and 30 are shorter, so you might prefer to do those first.
• Assign yourself a grade for this assignment :
  1. At least 60 minutes.
  2. About 45 minutes.
  3. About 30 minutes.
  4. About 15 minutes.
  Submit your grade as a submission comment with your assignment. This comment must be the first comment and it must be exactly 1 character long or the grade won't be registered.