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Math 3001001: Analysis 1, Fall 2019


Homework




Assignment

Assigned

Due

Problems

HW1 
9/4/18

9/11/18

Read Sections 1.11.3.
1. Do Exercise 1.2.4.
2. Do Exercise 1.2.7(b) and 1.2.7(c).
3. Do Exercise 1.2.8.
Solution sketches.

HW2 
9/11/18

9/18/18

Read Sections 1.41.5.
Read the following problems, but do not turn them in:
1.3.3, 1.3.6(a)(b)(c), 1.4.3, 1.4.8.
1. Do Exercise 1.3.2.
2. Do Exercise 1.3.9.
3. Does the nonArchimedean field
$\mathbb R(t)$ satisfy the Nested Interval Property? Explain.
Solution sketches.

HW3 
9/18/18

9/25/18

Read Sections 1.51.6.
Read the following problems, but do not turn them in:
1.5.4, 1.5.5, 1.5.9, 1.6.10.
1. Do Exercise 1.5.2.
2. Do Exercise 1.5.8.
3. Show that if $S\subseteq [0,1]$ is uncountable, then
there is a real number $r\in[0,1]$ such that
both $[0,r]\cap S$ and $[r,1]\cap S$ are uncountable.
Solution sketches.

HW4 
9/25/18

New Due Date!
10/4/18

Read Sections 2.12.4.
1. Do Exercise 2.2.4.
2. Do Exercise 2.3.7 (a), (b), (c).
3. Do Exercise 2.4.4 (a).
Solution sketches.

HW5 
10/2/18

10/9/18

Read Sections 2.52.6.
1. Do Exercise 2.4.2. (Hint for (b): use MCT to prove
$(y_n)$ converges.)
2. Do Exercise 2.4.3 (a). (Hint: use MCT to prove the sequence converges.
To find the limit, show that it must satisfy $L^22=L$ and $L>0$.)
3. Do Exercise 2.5.1 (a), (b), (c).
Solution sketches.

HW6 
10/16/18

10/23/18

Read Section 2.7.
1. Do Exercise 2.6.2 (a) (c).
2. Do Exercise 2.6.4 (c).
(Where the author says ``Decide whether each
of the following sequences is a Cauchy sequence'', interpret this
to mean ``Decide whether each
of the following sequences MUST BE a Cauchy sequence''.)
3. Do Exercise 2.7.4 (a) (d).
Solution sketches.


