Homework assignments
Homework 1, due September 17.
Exercises in Ch. 2 of Lang's book: 1(a), 3, 5, 25 (for definitions see 22), 2,
Exercises in Ch. 4 of Lang's book: 1, 15,
Prove the `uniform boundedness principle' stated in class:
Let F be a family of real valued continuous functions defined
on a complete metric space X. Suppose, for any x in X,
there is a number M_x such that f(x) < M_x for any f in F.
Show that there is a nonempty open set U and a number M such that
f(x) < M for any x in U and f in F.
Homework 2, due September 24.
Exercises in Ch. 2 of Lang's book: 6, 7, 8,
Exercises in Ch. 3 of Lang's book: 10, 6.
Homework 3, due October 1.
Exercises in Ch. 4 of Lang's book: 3, 4, 6, 12,
18.
Homework 4, due October 15.
Exercises in Ch. 5 of Lang's book: 2, 6, 7, 8,
Exercises in Ch. 6 of Lang's book: 3, 4.
Homework 5, due October 22.
Exercises in Ch. 6 of Lang's book: 2, 7a), 5, 12, 21.
Homework 6, due October 29.
Exercises in Ch. 6 of Lang's book: 14, 13, 24, 25, 26.
Homework 7, due Nov. 5.
Exercises in Ch. 6 of Lang's book: 11, 15, 17, 18, 19.
Homework 8, due Nov. 26.
Exercises in Ch. 7 of Lang's book: 3, 4, 5, 6,
Exercises in Ch. 7 of Lang's book: 14, 21.
Exercises in Ch. 7 of Lang's book: 12, 13.
Homework 9, due Dec. 3
Exercises in Ch. 8 of Lang's book: 1, 2, 3, 4, 7.
Homework 10, due Dec. 10
Exercises in Ch. 8 of Lang's book: 8, 9, 10, 11, 12.