# Homework

Our grader for the class is Prakhar Gupta (pgupta8@umd.edu)

All homework refers to the textbook unless otherwise stated.

Homework 1 (Due 2/7):

1.1: 4, 12.

1.2: 3, 6, 12

Homework 2 (Due 2/16):

1.3: 3, 6

1.4: 1, 2, 5, 7, 10

Extra credit: 1.4: 9

Homework 3 (Due 2/23)

1.5: 1, 2, 4, 8

1.6: 1 (Hint: Use 1.1 #18. I do not require you to prove it [though it's a good exercise to think about the proof])

1.6: 2

Extra credit: 1.5: 11

Homework 4 (Due 3/2)

1.6: 4, 7, 9

Study for midterm

Homework 5 (Due 3/9)

1.8: 3, 4, 5

Homework 6 (Due 3/16)

2.1: 1, 4

2.2: 2, 3, 5, 7 (you can use problem 2.2.6 without proving it)

Homework 7 (Due 4/6)

4.2: 1, 3, 4

4.3: the exercise at the end; the two exercises on p. 163 (one is "check that the important differentials..." and the other is "will force you to check your understanding...")

Homework 8 (also due 4/6 --- see email)

4.4: 2, 3, 4, 5, 8

Homework 9

Study for midterm

Homework 10 (due April 20)

4.4: 9, 11, 12

4.5: 1, 2

Homework 11 (due April 27)

For this, use the definition that a k-form b is closed if db = 0. It is exact if b = dc for another k-1 form c.

4.7: 4, 7, 8

Homework 12 (due May 4)

4.7: 9

4.8: 4

Using the definition of the degree given in terms of integrals, show that the degree of the map z \to z^n from the set of unit size complex numbers to itself has degree n.

Exercises 6 and 8 from Section 2 here: https://arxiv.org/pdf/1604.07862.pdf

Homework 13 (due May 11)

3.3: 2a, 4a, 10, 11 (you can assume Exercise 9 and 1.6.1 for this, without proving it)