The midterm will take place on Wednesday, Feb. 20. It will cover Sections 10, 11, and 12.

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.


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.

Week 3

1. 12.1, 12.2, page 126.
2. 12.3, 12.4, page 127.
3. 12.5, page 127.
4. 12.6, page 127.

Week 4

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

Please do the part of the homework below which corresponds to the topics covered in the lectures.

Part 1

1. 8.2, page 87
2. 8.3, page 88
3. 8.7, page 88
4. 8.9, page 88
5. 8.11, page 88

Part 2

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

Part 3

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

Part 4

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

Part 5

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