Daily Assignment for Monday, March 3

Due Wednesday, March 5 on Canvas.

• Read §§7.3 and 7.4 of Needham.
• Do exercise 1 on p. 420.
• If \( f(z) \) is a polynomial of degree \( n \), and \( \gamma \) is a very large loop around the origin, compute \( \nu( f\circ \gamma, 0) \).
• In class, I said that the winding number \( \nu(\gamma, a) \) around \( a \) doesn't really make sense if \( \gamma \) passes through \( a \). On the other hand, maybe you could apply the definition \( \nu(\gamma, a) = \int_0^1 d \theta \) to a loop that passes through \( a \). What does this produce for a curve that passes through \( a \) ? Cf. exercise 21 on p. 426.
• 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.