# Spring Teaching - Math 521

## Homework 1 (due to Feb. 3)

Ch. 1, Problems 2, 3, 5, 6, 8.

## Homework 2 (due to Feb. 13)

Ch. 1, Problems 15,17.
Ch. 2, Problems 4,5,8,11.

## Homework 3 (due to Feb. 17)

Ch. 2, Problems 7,9,22,29

## Homework 4 (due to Feb. 24)

Ch. 2, Problems 6, 10, 12, 14, 15, 16.

## Homework 5 (due to March 2)

Ch. 3, Problems 14(a)(b)(d), 20, and the problem: use the definition of the limit to show that, in a metric space, a sequence {p_n} converges to p if and only if every subsequence of {p_n} converges to p. In problem 14 assume the sequence is real.

## Homework 6 (due to March 9)

Ch.3, Problems 21, 22, 23, 5, and the problem: Prove that the upper limit of sequence (s_n) = inf_{N >= 1} (sup_{n >= N} s_n).

## Homework 7 (due to March 23)

Ch.3, Problems 6(a)(b), 7, 8 , 9, 10, 14(c), 16(a).

## Homework 8 (due to March 28)

Ch.4, Problems 1, 2, 3, 4, 8, 10, 11

## Homework 9 (due to April 13)

Ch.4, Problems 12, 14, 15, 18, 20, 21, 23.
Ch.5, Problems 1,2,3.

## Homework 10 (due to April 20)

Ch.5: 5, 8, 9, 11, 14, 26

## Homework 11 (due to April 30)

Ch.6: 1, 2, 4, 8, 11

## Homework 12 (due to May 7)

Ch.6: 5, 10 (a,b,c) [in (c) assume that f,g are real valued functions], 12, 15