The following will be updated throughout the quarter.

Week 1

3. 10.1, page 103.
4. 10.3,10.8, 10.11, page 104.
5. 10.28, page 106.

To be graded: 10.3, 10.11, 10.28

Week 2

1. Use the Peano axioms to prove Principle of Mathematical Induction
2. 11.1 and 11.2, page 115.
3. 11.3, page 115.
4. Prove that 5 is a prime number.
5. 12.1, 12.2, page 126.
6. 12.3, 12.4, page 127.
7. 12.5, page 127.
8. 12.6, page 127.
To be graded:
1, 4, 11.3(a)(e)(f)(h), 12.3. (h)(l), 12.5.

Week 3

1. 12.9, page 127.
2. 12.13, page 128.
3. 12.14, page 128.
4. Prove the following: if y-x>n for a natural number n, then there exist n distinct integers in the interval (x, y).
5. Prove the following: if y-x is at least 1, then there exists an integer n in the interval [x, y].
6. 13.1
7. 13.2
8. 13.3
9. 13.5
10. 13.8
To be graded: 1, 2, 3, 5, 6, 8.



Week 4

1. 13.9
2. 13.10
3. 13.12
4. 13.15
5. 13.17
6. 13.20
7. 14.1
8. 14.2
9. 14.3
10. 14.4
11. 14.7
12. 14.8

Week 5

1. 14.12
2. 14. 13
3. 14. 14
4. 16.1
5. 16.2
6. 16.6
7. 16.7
8. 16.8
9. 16.9
10. 18.1
11. 18.2
12. 18.3
(Note: You can find the limit by taking the limit in the equation which defines the sequence recursively.
Then you solve for the limit from the resulting equation.)
13. 18.7