MA 3053 - Homework
 

 

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Homework

Homework 15, not to be collected

Dumas-McCarthy p146: 5.23

A. Show that if limx→∞ f(x) = L and limx→∞ g(x) = M, then limx→∞ f(x) + g(x) = L + M.

B. Show that ℕ × ℕ × ℕ is countable, where ℕ as usual denotes the natural numbers.

Homework 14, due Nov 29 at 9:30am

Dumas-McCarthy p121: 4.3, 4.7, 4.8, 4.10, 4.20
Dumas-McCarthy p146: 5.16 (that is, show that for all a, limxa x  = a.)

A. Explain the trouble with the "all chalk is white" proof that was presented in class. (I want to know the problem in the proof, not that there may exist orange or blue chalk.)

B. Show that there is no value L such that limx→ 0 sin(1/x) = L. (That is, show that limx→ 0 sin(1/x) does not exist.)

Homework 13, due Nov 17 at 9:30am

Read Sections 4.1 and 4.2 carefully, then do:

Dumas-McCarthy p93: 3.15, 3.16, 3.18, 3.24, 3.27
Dumas-McCarthy p121: 4.2

Homework 12, due Nov 10 at 9:30am

Dumas-McCarthy p93: 3.6, 3.8, 3.10, 3.11, 3.13, 3.14

Homework 11, not to be collected

Dumas-McCarthy p93: 3.1, 3.2, 3.3, 3.4, 3.9

Homework 10, due Oct 27 at 9:30am

Read the Introduction to Chapter 3 carefully, then do:

Dumas-McCarthy p65: 2.15, 2.16, 2.17, 2.18, 2.19

Homework 9, due Oct 20 at 9:30am

Dumas-McCarthy p65: 2.5, 2.6, 2.14, 2.23, 2.25, 2.26

Homework 8, not to be collected (Fall Break!)

Dumas-McCarthy p65: 2.21

Recall from class on Oct 6 that well-defined means that the function does not depend on the choice(s) of representatives for the equivalence class(es).

Homework 7, due Oct 6 at 9:30am

Dumas-McCarthy p65: 2.7, 2.13, 2.20, 2.21, 2.22, 2.24

Remark: The notation X/f in Problem 2.20 is a shorthand for X/Rf, where Rf is the equivalence relation that is induced by f from Example 2.18 that we've discussed on several occasions in class.

Homework 6, due Sep 29 at 9:30am

Dumas-McCarthy p65: 2.6 2.4, 2.8, 2.9, 2.10, 2.11, 2.12

Homework 5, not to be collected

Dumas-McCarthy p41: 1.33, 1.35
Dumas-McCarthy p65: 2.1, 2.3

Homework 4, due Sep 15 at 9:30am

Dumas-McCarthy p41: 1.9, 1.10, 1.21, 1.25, 1.29 (except part ii), 1.31 (do not assume that f is continuous or differentiable)

Homework 3, due Sep 8 at 9:30am

Dumas-McCarthy p41: 1.6, 1.8 (except surjections), 1.17, 1.18, 1.20

And the following additional problems:

A. Let X be a set with 3 elements, Y be a set with 4 elements, and Z be a set with 5 elements. How many surjections are there Y X? How many surjections Y Y and Y Z?

Homework 2, due Sep 1 at 9:30am

Dumas-McCarthy p41: 1.4, 1.5, 1.11, 1.12, 1.15, 1.24

Note: We'll talk about bijections and permutations on Tuesday, or you can read about them in 1.4.

Homework 1, due Aug 25 at 9:30am

Dumas-McCarthy p41: 1.1, 1.2, 1.3

And the following additional problems:

A. Let a, b, c, and d be in ℝ (the reals) with a < c < b< d. By showing that each side is a subset of the other, show that [a, b] ∪ [c, d] = [a, d].

B. If a, b, and c are in ℝ (the reals) with a < b < c, then show that [a, b] ∪ [b, c] = [a, c], but that (a, b) ∪ (b, c) is a proper subset of (a, c).

Homework 0, to be completed by Aug 18 at 9:30am

Download (and possibly print) the textbook. Read Chapter 0, and on through Chapter 1.2.2.