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## Math 109 Spring 2022 Homework Assignments

### Homework Guidelines

1. Format Guidelines
• Turn in only those exercises enclosed in square brackets, for example [100].
• Use clean, white paper in order to make your solutions clearly legible.
• Start each problem on a new page.
• Write neatly (or type) and use complete sentences in your solutions.
• You may consult any book, periodical, website or person for assistance provided you give credit to your source.
• You must give credit to any book, periodical, website or person from which you obtained assistance.
Examples:
• Mary Jones told you the main idea for proof in problem 1.1. You would write something like: "Mary Smith told me the main idea for this proof."
• You found the solution to problem 2.1 in "Naive Set Theory" by Paul Halmos. You would write something like: "I found this solution in _Naive_Set_Theory_ by Paul Halmos."
• There is no penalty for finding a solution in a book or getting it from a friend; however, failing to give appropriate credit would be considered an academic integrity violation. Please be honest and give credit to your sources. Your integrity will shine by doing this.
• It is, of course, to your benefit to discover and work out as many of the solutions for yourself as possible; however, you should feel free to discuss the problems and make use of available resources (making sure to give appropriate credit).

### Homework 1

#### Turn in only those exercises enclosed in square brackets, e.g. [9].

Due Thursday, April 7
• Exercises:  1.2, 1.5, 2.3, 2.5, 3.2, 3.7, 4.1, 4.7
• Problems I (pg 53-57):  1, 2, [4], 5, [6], [10]
• For number 6, only the first equality in parts (i) and (ii) need be proven.
• For number 10, provide a brief yet clear explanation.
• Extra:  [1.] Let a and b be integers and let d be a positive integer.
1. Prove the following proposition: If d divides a and d divides b, then d divides both a + b and a - b.
2. Is the converse of the proposition in (a) above true? If so, prove it; if not, exhibit a counterexample.

### Homework 2

#### Turn in only those exercises enclosed in square brackets, e.g. [19].

Due Thursday, April 14
• Exercises:  5.1, 5.6, 6.4, 6.6, 6.7
• Problems I (pg 53-57):  11, [14], [19], [21], [25]
• Problems II (pg 115-119):  7, [8]

Midterm Exam 1 (Wednesday, April 20)

### Homework 3

#### Turn in only those exercises enclosed in square brackets, e.g. [45].

Due Thursday, April 28
• Exercises:  7.7, 9.5, 15.5, 15.6, 16.3, 16.4
• Problems II (pg 115-119):  [15], [19]
• Problems IV (pg 225-228):  [1], [4], 6, [7], 8*, 10

### Homework 4

#### Turn in only those exercises enclosed in square brackets, e.g. [12].

Due Thursday, May 5
• Exercises:   17.1, 17.3, 17.6, 19.1, 19.4, 19.5
• Problems V (pg 271-273):   [1], [4], [6], 7, [8]

Midterm Exam 2 (Wednesday, May 11) covers Chapters 1 - 9, 15 - 17, and 19 - 21, with an emphasis on Chapters 15 - 17 and 19 - 21.

### Homework 5

#### Turn in only those exercises enclosed in square brackets, e.g. [12].

Due Thursday, May 19

### Homework 6

#### Turn in only those exercises enclosed in square brackets, e.g. [12].

Due Thursday, May 26
• Exercises:   10.2, 10.3, 11.2, 11.6, 12.3, 12.5
• Problems III (pg 182-183):   1, 2, [6], [7], [11], 12, [14], 17, [18], [20]

### Homework 7

#### Practice for the final examination; not to be turned in.

Due Thursday, June 2
TBD

The Final Examination (8:00am - 11:00am Friday, June 10) is cumulative

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