Homework

So far in the lectures we have covered topics in the following sections of the textbook: 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 5.1, 5.2, 6.1, 6.2, 6.3, 6.4, 6.5, 7.1, 7.2, 7.3, 8.1, 8.2, 8.5, 8.6, 9.1, 9.3, 9.5, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 11.1, 11.4, 11.5

Homework 1 (Due Friday 1/31):

Section 2.1: 2, 4, 6, 10, 20, 22, 26, 38
Selected Solutions

Suggested Problems 1:

Section 2.1: 1- 11, 17-40
Section 2.2: 1-29

Homework 2 (Due Friday 2/7):

Section 2.2: 4, 16(a,e,d), 24
Section 2.3: 6(a,b), 12(a,b), 14(a,b), 30(b), 40
Note: Remember that to show that two sets A and B are equal, you have to show two things: A is a subset of B, and B is a subset of A.
Selected solutions and comments

Suggested Problems 2:

Section 2.3: 1-23, 28-41
Learn the list of set identities on page 130 and also how to prove each of them.

Homework 3 (Due Monday 2/17): (Note you have a little more time; this is because there will be an exam on 2/21)

Section 2.3: 22(a,c,d), 50
Section 3.1: 4, 8, 24 (write your solutions using pseduocode)
Section 3.2: 2(c,e,f), 10, 18, 20, 28 (a, d, e), 40
Note: For exercise 50 in section 2.3 you should review the definition of the floor and ceiling function on page 149
Selected solutions and comments

Suggested Problems 3:

Section 3.1: 1-25
Section 3.2: 1-50
Review the appendix in the book about pseudocode

Homework 4 (Due Friday 2/28)

Section 3.3: 4, 8, 14
Section 5.1: 4, 6, 10, 20, 32
Section 5.2: 12
Selected solutions and comments

Suggested Problems 4:

Section 3.3: 1- 14 (not including 6 and 12), 25-33 (including corresponding exercises from 3.1)
Section 5.1: 1-24, 38-44

Homework 5 (Due Friday 3/6)

Section 6.1: 8, 12, 22(a,c, f), 40, 48
Section 6.2: 6, 32, 36
Section 6.3: 16, 32(b, c)
Selected solutions and comments

Suggested Problems 5:

Section 6.1: 1-50
Section 6.2: 1- 40
Section 6.3: 1- 32

Homework 6 (Due Friday 3/13) - Note: if you are leaving early for the break it is your responsibility to get the HW to me on time

Section 6.4: 8, 10, 12 (for more on Pascal's triangle see below proof of Pascal identity in book), 28(a)
Section 6.5: 4, 8, 12, 14, 16(a), 20

Suggested Problems 6:

Section 6.4: 1 - 32
Section 6.5: 1 - 24

Selected solutions for HW 6 and HW 7

Homework 7 (Due Friday 3/27)

Section 7.1: 8, 12, 18, 24(c)
Section 7.2: 2, 12, 14

Suggested Problems 7:

Section 7.1: 1-34, read about the Monty Hall problem in the book
Section 7.2: 1-15

Homework 8 (Due Friday 4/10)

Section 7.2: 16, 18, 24, 26, 34
Section 7.3: 4 (read example 1 on pg. 469 for this problem), 18
Section 8.2: 4(c,d,e), 8
Section 8.5: 8, 20, 24
Selected solutions for HW 8

Suggested Problems 8

Section 7.2: 16-36
Section 7.3: 1-4, 13-14, 17-23
Section 8.2: 1-11
Section 8.5: 1-29

Homework 9 (Due Friday 4/17)

Section 8.6: 6 (hint: every number is a product of prime numbers), 16
Section 9.1: 6, 8, 10, 28 (read above for definition)
Section 9.5: 16, 18, 24, 40
Section 10.2: 18, 24, 26 (b) (C_n is the cycle graph with n vertices)
Selected solutions for HW 9

Suggested Problems 9

Section 8.6: 1-16
Section 9.1: 1-30
Section 9.5: 1- 59
Section 10.2: 1-30

Homework 10 (Due Friday 4/24)

Section 10.2: 28, 34, 54 (K_{m,n} is the complete bipartite graph; look up its definition in the section)
Section 10.3: 14, 18, 40, 42
Section 10.4: 6, 8, 12, 14(c), 18
Selected solutions to HW 10

Suggested Problems 10

Section 10.2: 31-70
Section 10.3: 1 - 44
Section 10.4: 1-19

Homework 11 (Due Friday 5/1)

Section 10.4: 60
Section 10.5: 4, 8, 28, 40
Section 10.6: 4, 8(a,b)
Section 10.7: 8, 10, 16, 18

Suggested Problems 11

Section 10.5: 1-45
Section 10.6: 1- 31
Section 10.7: 1-19

Suggested Problems 12

Section 11.1: 14, 16
Section 11.4: 14, 16, 18, 20
Section 11.5: 8, 19 (unique means there is only one minimum spanning tree, meaning every other spanning tree has larger total weight).
Selected Solutions

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