# Math521, 2019 spring

HW#1, due Thursday January 17

- 1.2.1a, 1.2.3acd, 1.2.6c, 1.2.7abc, 1.2.9ab, 1.2.10 [These are updated problems, using the correct, 2nd, edition of the book.]

HW#2, due Thursday January 24

- 1.3.3, 1.3.6, 1.3.7
- 1.4.1, 1.4.2, 1.4.6ab(clearly state dense or not, and give brief argument)

HW#3, due Thursday January 31

- 1.5.5, 1.5.6[hint for (b): you may want to use the fact that every non-empty open interval contains a rational number], 1.5.10
- 1.6.4

HW#4, due Thursday February 7

- 2.2.2ac, 2.2.3
- 2.3.1, 2.3.3, 2.3.4a, 2.3.5, 2.3.9a

HW#5, due Thursday February 14

- 2.4.1, 2.4.3a, 2.4.7ab
- 2.5.1, 2.5.8
- 2.6.2, 2.6.3a

MIDTERM-1: February 19

HW#6, due Thursday February 21

- 2.7.1a, 2.7.4ab, 2.7.7a
- 3.2.3, 3.2.4a, 3.2.7a, 3.2.11a

W#7, due Thursday February 28

- 3.3.1, 3.3.2abde, 3.3.4a(prove or give counterexample), 3.3.5ab(prove or give counterexample), 3.3.6(just claim which are true, don’t need to prove)

HW#8, due Thursday March 7

- 3.3.11
- 3.4.5, 3.4.7
- 4.2.2ab [For this problem you need Definition 4.2.1 which we will discuss on Tuesday; either wait till Tuesday with this problem, or read Definition 4.2.1.]

HW#9, due Thursday March 21

- 4.3.1, 4.3.4a (hint: the notion “lim_{x->c} f(x)” is not affected by the value f(c)), 4.3.6, 4.3.7ab, 4.3.8, 4.3.9, 4.3.11 (Hints: for (a) use the definition of continuity; for (b) use triangle inequality and the convergence of geometric series; for (c) consider the sequence in part b and the f-values of that sequence and recall that f is continuous; for (d) if there were two fixed points, something would go wrong with the displayed formula in the 3rd line of the Exercise.)

HW#10, due Thursday March 28

- 4.4.1bc, 4.4.2a, 4.4.7, 4.4.8ab, 4.4.11

HW#11, due Thursday April 4

- 4.5.2, 4.5.3, 4.5.6 (hint: you may want to consider the function g(x)=f(x+1/2)-f(x) on [0,1/2], and study its properties.)
- 5.3.2 (hint: easy by contradiction), 5.3.3

MIDTERM-2: April 11

HW#12, due Tuesday April 16

- 6.2.1, 6.2.2ab, 6.2.3ab, 6.2.5, 6.2.7(first part only), 6.2.9a

Solution to Midterm-2, problem 4.

HW#13, due Thursday April 25

- 6.3.1, 6.3.4
- 6.4.3, 6.4.5
- 6.5.1(a)first question, 6.5.2(b)second question, 6.5.6, 6.6.2a