Daily Assignment for Friday, February 7

Due Monday, February 10 on Canvas.

• Here is the Desmos visualization from class :
• Read §§3.2 and 3.4 of Needham's book if you haven't already.
• Do exercise 5 on pp. 205–206.
• Find the branch points and compute the Riemann surface of the function \( \sqrt{z^5 - 1} \). Can you anticipate how many holes the Riemann surface of \( \sqrt{p(z)} \) will have ? These Riemann surfaces are known as hyperelliptic curves.
• Do exercises 24, 26, 28, 30 on pp. 131–132 if you haven't already.
• If you are feeling good about those, do exercise 33.
• For an extra challenge, try computing the Riemann surface of the multifunction \( f(z) \) whose values at \( z \) are the solutions to the equation \( z^2 - w^3 + 3w = 0 \). This one has a new wrinkle that we probably will not discuss in class.
• 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.