The following will be updated throughout the quarter.

Week 1

1. Use the Peano axioms to prove Principle of Mathematical Induction
2. 5.25, page 49.
3. 10.1, page 103.
4. 10.3,10.8, 10.11, page 104.
5. 10.28, page 106.
6. 11.1 and 11.2, page 115.
7. 11.3, page 115.

Week 2

1. Prove that 5 is a prime number.
2. 12.1, 12.2, page 126.
3. 12.3, 12.4, page 127.
4. 12.5, page 127.
5. 12.9, page 127. 6. 12.13, page 128.
7. 12.14, page 128.
8. Prove the following: if y-x>n for a natural number n, then there exist n distinct integers in the interval (x, y).
9. Prove the following: if y-x is at least 1, then there exists an integer n in the interval [x, y].

Week 3

1. 13.1, p.134
2. 13.2, p.135
3. 13.3, 13.4.
4. 13.5
5. 13.7, p.136
6. 13.8
7. 13.9
8. 13.15
9. 13.17
10. 14.1, p.143
11. 14.2, p.144
12. 14.8, p.144

Week 4

1. 16.1, p.163
2. 16.2, p.164
3. 16.3
4. 16.6
5. 16.7
6. 16.8 (Do not use the theorem regarding convergence of subsequences.)
7. 16.9
8. 16.15
9. 17.1, p.172
10. 17.2
11. 17.4.
12. 17.5.
13. 17.6.
14. 17.7.
15. 17.10

Week 5

1. 18.3, page 181
2. 18.4, 18.5
3. 18.7
4. 18.8
5. 18.12
6. 19.1, page 187.
7. 19.2
8. 19.3
9. 19.9
10. 19.11
11. 19.16

Week 6

1. 20.1, p.197.
2. 20.3.
3. 20.6.
4. 20.7.
5. 20.8.
6. 20.15.
7. 20.18 .
8. 21.1. page 206
9. 21.2
10. 21.3
11. 21.8
12. 21.9
13. 22.2, page 214
14. 22.3
15. 22.4
16. 22.7