# Assignments

### Assignment 9

NOT TO BE HANDED IN
You are responsible for this material though, and if you don't practise it by doing problems, your performance on the exam will suffer. I will post solutions on the web on Wednesday March 29.
• Section 6.1, numbers 1ce, 3, 4, 22, 24, 27
• Section 6.5, numbers 3, 11-14 (you should look over section 6.3 for this) 15, 19, 25, 31, 35
• Section 4.1, numbers 29, 39
• Section 4.3, numbers 4, 5bc, 6bc, 20, 23, 25, 26, 39
Solutions

### Assignment 8

Due Friday March 24, 4:30 PM.
• Section 3.1, numbers 21, 24, 30, 49
• Section 3.2, numbers 6, 8, 14, 20, 26
Note that in number 6 above, you gave a direct proof of something like this on an earlier assignement. The point of this question in to give an inductive proof.

Note also that in problem 26, you are allowed to use the result of problem 25, without having to actually do problem 25.

### Assignment 7

Due Monday March 13, 4:30 PM.
• Section 2.4, numbers 2e, 6ab, 8ab, 11bc, 12ab
• Section 2.5, numbers 1ch, 2dh, 7, 8, 12
Solutions

### Assignment 6

Due Friday March 3, 4:30 PM.
• Section 2.3, numbers 6, 7, 14, 24, 31, 35, 36, 37, 42
Note that the book uses the notation

for the remainder of a upon division by m. It also uses the notation

for the statement that after dividing by m, the remainders of a and b are equal. Since the first notation is so easily confused with the second, I only used the second notation, and I did not adopt the book's shorthand for remainders. However, to do problem 42 above, you will have to understand the book's notation for remainders, and you will have to read the book's example on pseudorandom numbers (p. 123-124).

### Assignment 5

Due Friday February 25, 4:30 PM.
• Section 1.7, numbers 6ade, 10ab, 13, 15c, 16, 18a, 20
• Find formulae for the sum of the first n
• even numbers [hint: try dividing the sum by 2]
• odd numbers [hint: try adding in the first n even numbers]
Solutions

### Assignment 4

Due Wednesday February 23, 4:30 PM
The due date was so far off, to let you concentrate on the midterm, and to allow you time to ask about questions that may arise during reading week. But don't leave it till the last minute, as Assignment 5 is also be due the same week.
• Section 1.6, numbers 2, 4ac, 8, 9, 14, 16bc, 19b, 26b, 27, 29, 30a, 44, 52
Solutions

### Assignment 3

Due Friday January 28, by 4:30 PM
POSTPONED, to be due Monday January 31, by 4:30 PM
• Section 1.4 numbers 3, 4, 6, 7, 8, 9, 11, 17b, 22ab
• Section 1.5 numbers 4, 8, 14, 17ac, 20, 21
Solutions

### Assignment 2

Due Friday January 21, by 4:30 PM
• Section 1.2 numbers 8a, 9a
• Section 1.3 numbers 2, 6bc, 8acd, 12abcde, 22ace, 24abc, 36, 40
Solutions

### Assignment 1

Due Friday January 14, by 4:30 PM
(either handed in during class, or put in the course mailbox, on the 5th floor, North wing of the Ross building, by the elevators)
• Section 1.1 numbers 8, 9(a-c), 10, 16, 19, 21c
• Section 1.2 numbers 5, 8b, 24
Solutions