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Homework assignments
(MATH 5/4161-001, Spring 2012)

Last update: Monday, April 23, 2012

Disclaimer: The information below comes with no warranty. If, due to typographical error, there is a discrepancy between the exercise numbers announced in class and the numbers below, or this page is not completely up to date, the required homework consists of those exercises which were announced in class. Check for the time of last update above. If, by my mistake, a wrong exercise number shows up below, I will allow you extra time to hand in the exercise whose number was announced in class. If, however, exercise numbers are missing because this page is not up to date, it is your responsibility to contact me before the due date. (No extra time will be allowed in that case.) This page is up to date if the last update happened after the last class before the next due date.

Notation: 1.2/1b means Exercise 1b in Section 1.2. The deadlines do not apply to the Bonus questions, which expire only once we solve them in class.

No. Date due: Problems:

13 We 4/25 No more homework will be assigned this semester.
9.2/4a, 4b (you may use 4a even if you do not succeed proving it), 5; 9.3/4,5a,5b.
Also try 9.2/1,2. The answers for these exercises are in the back of the book, so I will not grade them for credit. However, a question very similar to these is likely to be on the final.

12 We 4/18 8.3/7 8.4/5,11; 9.1/2,4,5a,5b,7.
Also try 8.4/1,2,3. The answers for these exercises are in the back of the book, so I will not grade them for credit. However, a question very similar to these is likely to be on the final.

11 We 4/11 8.2/1a,1b,6a,8a; 8.3/2a,2b,6b.

10 We 4/4 8.1/2a,2c,6a,11a,11b.

9 We 3/28 7.3/1a, 1c, 4,9 7.4/2,5a,5c,8.
Bonus: Prove or disprove that Euler's phi-function φ satisfies φ(n²)=nφ(n) for all positive integer n.
Our second test is on Monday March 26. You may download the Sample Test 2 to prepare for this challenge.

8 We 3/21 6.3/2c,5a,7; 7.2/2,3,6,8.
Bonus: 6.3/6a.

7 We 3/14 6.1/7a,7b,8,9,10a; 6.2/1a,2,4a,4c,7b,8a (use 6.2/3).

6 We 2/29 4.4/10, 17 (show work for both, since answer is in the back!); 5.2/1,4a,4b; 5.3/1a,1b,5a,5b.

5 We 2/22 4.3/5a,5b 4.4/1a,1c,1d,5 (show work since final answers for 4.4/1 and 4.4/5 are in the back of the book!).

E We 4/25 I will give you six test points if you write down an induction proof for all of the following exercises by April 25: 1.1/1d,1e,3,6,7,10,13. There will vbe no partial credit.

4 We 2/15 4.2/2,6a,6c,10; 4.3/2b,2c,9.
Our first test is on Monday February 13. You may download the Sample Test 1 I distributed in class on Wednesday February 8.

3 We 2/8 2.5/1 (also solve those Diophantine equations which can be solved); 3.1/3a, 3b, 6b, 6c; 3.2/4a, 4b, 5; 4.2/5,8b,9
Bonus: Without using Fermat's last theorem, prove that the cube root of two is irrational.

2 We 2/1 2.2/1,2,3b,3c,11; 2.3/1,4b,14a; 2.4/1 (use Euclid's algorithm and show all your work or you will get zero credit as the final answer is in the back of the book).
Bonus: Consider the Euclidean Algorithm presented in section 2.4. Express r₅ as a linear combination of a and b.

1 We 1/18 1.1/1b, 1c, 9; 1.2/2, 3d, 5a; 2.1/1a, 1c.
Bonus: Prove the Second Principle of Induction for any well-ordered set (without reference to arithmetic operations).

No.	Date due:	Problems:
13	We 4/25	No more homework will be assigned this semester. 9.2/4a, 4b (you may use 4a even if you do not succeed proving it), 5; 9.3/4,5a,5b. Also try 9.2/1,2. The answers for these exercises are in the back of the book, so I will not grade them for credit. However, a question very similar to these is likely to be on the final.
12	We 4/18	8.3/7 8.4/5,11; 9.1/2,4,5a,5b,7. Also try 8.4/1,2,3. The answers for these exercises are in the back of the book, so I will not grade them for credit. However, a question very similar to these is likely to be on the final.
11	We 4/11	8.2/1a,1b,6a,8a; 8.3/2a,2b,6b.
10	We 4/4	8.1/2a,2c,6a,11a,11b.
9	We 3/28	7.3/1a, 1c, 4,9 7.4/2,5a,5c,8. Bonus: Prove or disprove that Euler's phi-function φ satisfies φ(n²)=nφ(n) for all positive integer n. Our second test is on Monday March 26. You may download the Sample Test 2 to prepare for this challenge.
8	We 3/21	6.3/2c,5a,7; 7.2/2,3,6,8. Bonus: 6.3/6a.
7	We 3/14	6.1/7a,7b,8,9,10a; 6.2/1a,2,4a,4c,7b,8a (use 6.2/3).
6	We 2/29	4.4/10, 17 (show work for both, since answer is in the back!); 5.2/1,4a,4b; 5.3/1a,1b,5a,5b.
5	We 2/22	4.3/5a,5b 4.4/1a,1c,1d,5 (show work since final answers for 4.4/1 and 4.4/5 are in the back of the book!).
E	We 4/25	I will give you six test points if you write down an induction proof for all of the following exercises by April 25: 1.1/1d,1e,3,6,7,10,13. There will vbe no partial credit.
4	We 2/15	4.2/2,6a,6c,10; 4.3/2b,2c,9. Our first test is on Monday February 13. You may download the Sample Test 1 I distributed in class on Wednesday February 8.
3	We 2/8	2.5/1 (also solve those Diophantine equations which can be solved); 3.1/3a, 3b, 6b, 6c; 3.2/4a, 4b, 5; 4.2/5,8b,9 Bonus: Without using Fermat's last theorem, prove that the cube root of two is irrational.
2	We 2/1	2.2/1,2,3b,3c,11; 2.3/1,4b,14a; 2.4/1 (use Euclid's algorithm and show all your work or you will get zero credit as the final answer is in the back of the book). Bonus: Consider the Euclidean Algorithm presented in section 2.4. Express r₅ as a linear combination of a and b.
1	We 1/18	1.1/1b, 1c, 9; 1.2/2, 3d, 5a; 2.1/1a, 1c. Bonus: Prove the Second Principle of Induction for any well-ordered set (without reference to arithmetic operations).