| No. | Date | Readings | To do | Remarks | Miscellaneous |
|---|---|---|---|---|---|
| — | Tu 9/1 | Notes for Students; Chapter 1 | |||
| 1. | W 9/2 | Prove propositions 1.7 & 1.10(ii). | |||
| 2. | Tu 9/8 | Chapter 2. | Prove propositions 1.16 & 1.19. | Quiz 1 | |
| 3. | W 9/9 | Carefully read the discussion of "if ... then ..." statements on pages 17-18. |
Prove propositions 1.21 & 1.24(ii, iv). #1A. In the proof of proposition 1.20, the last sentence is wrong. Find the error. |
Take Quiz 1 again and grade yourself (answers will appear). | |
| 4. | F 9/11 | Ch. 2 to p. 26. | Project 2.5. Prove propositions 1.14 & 2.4(ii). List many different ways to say "If apples can write tests, then pencils can grow fat." |
Only propositions 1.14 & 2.4(ii) will be graded. | |
| — | M 9/14 | Continue rewrites. | |||
| 5. | W 9/16 | Ch. 2 to p. 28. | Do Homework Set 5. | ||
| 6. | F 9/18 | Ch. 2 to p. 30. | Do Homework Sheet 6. | No rewrites. Instead, we'll discuss this in class Tuesday. | |
| — | M 9/21 | Continue rewrites. | |||
| 7. | T 9/22 | Ch. 2 complete. Sect. 3.1. |
Prove propositions 2.10, 2.13, 2.16. | Try Quiz 2 again, before looking at the solutions. | Quiz 2 (no solutions). Quiz 2 (solutions). |
| 8. | W 9/23 | Sect. 3.2. | Prove propositions 2.19 & 2.21. Study gcd problems [A,B]. | ||
| 9. | F 9/25 | Sects. 3.1-4. | Do gcd problems (all). | ||
| — | T 9/29 | Keep up the rewrites. | |||
| — | W 9/30 | Sect. 3.3. | Rewrites. | Think about projects 3.1 & 3.3-5 for class discussion. | |
| 10. | F 10/2 | Sects. 3.2-4. | Do projects 3.2 (today) & (today or Tuesday) 3.6. | Keep thinking about projects 3.3-5 for class discussion. | Project 3.2 grading: one grade for formalizing the statement, one for negating it. |
| 11. | M 10/5 | Sect. 4.1. Chs. 3 & 4 announcements. |
Get started on HW 12. | ||
| 12. | T 10/6 | Sects. 4.1-2. | Do project 3.6. Do Homework Set #12. | ||
| 13. | F 10/9 | Sect. 4.2. | Do Homework Set #13. | Also do for class discussion today:
The x+1 Problem. Let xn+1 = xn +1 if xn is odd, xn/2 if xn is even. Does this sequence always reach 1 for any starting point x1 in N? Try some examples. |
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| — | F 10/9 | Discuss projects 3.2 & 3.6. | We will not do rewrites on 3.2 after today. No rewrites on 3.6 for now. | ||
| — | M 10/12 | Discuss project 3.6. | |||
| 14. | W 10/14 | Do Homework Set #14. | |||
| — | M 10/19 | Sect. 4.2. | |||
| 15. | T 10/20 | Sects. 4.2-3. | Prove propositions 4.10(i) & 4.11(ii) (see correction). Do Homework Set #15 [H]. |
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| 16. | W 10/21 | Chapter 5. | Do projects 5.12 & 5.17. | Study especially DeMorgan's Laws, propositions 5.10 & 5.16, project 5.14, & both definitions of a function. | This chapter is mostly familiar to you. |
| 17. | F 10/23 | Sects. 6.0-1. | Prove proposition 6.5 & do project 6.7. | ||
| — | M 10/26 | Review. | |||
| *** | T 10/27 | Midterm Test. | The midterm covers everything we've done in the course up to that time. | ||
| — | W 10/28 | Ch. 8, p. 79. | |||
| 18. | F 10/30 | Sects. 8.1-2. | Prove proposition 8.6. | ||
| 18a. | M 11/2 | Reread Sects. 5.1-2. | Prove S = T, where S = { 3x+5 : x in N }, T = {3x-7 : x in N, x ≥ 5 }. Prove example 5.8. |
Notice how odd integers are defined! ("Not even".) | |
| 18b. | T 11/3 | Do Homework Set 18b. | Correction: Every set is supposed to be a subset of Z. | ||
| 19. | W 11/4 | Sect. 8.3. | Prove propositions 8.16 & 8.17. Do project 8.8 (talk to your friends). | ||
| 20. | F 11/6 | Prove proposition 8.25 & corollary 8.20a. | |||
| — | M 11/9 | Submit corollary 8.20a if not already done. | |||
| — | W 11/11 | Sect. 9.1. | |||
| 21. | F 11/13 | Sect. 9.2. | Prove propositions 8.28 & 9.5(i,ii). [(i) is NOT optional – sorry!] Do project 9.3. |
9.5(i) will have ONE rewrite, so make it good! | Reminder: Each HW set must be on a separate paper. |
| 22. | M 11/16 | Do project 9.4. Rewrite of project 3.6. |
Project 3.6: one rewrite only! Due today. Proposition 9.5(i): Original submission due today. | ||
| 23. | T 11/17 | Proposition 9.5(i) rewrite due today. | |||
| W 11/18 | Sect. 10.1. | Begin reading Sect. 10.2. | Re proposition 10.3: Think how to prove it. How is it different from the statement that Z does not have a least element? | ||
| F 11/20 | Sects. 10.2-3. | Start your term project over this weekend. | |||
| M 11/23 | Sect. 10.4. | Start your term project. | |||
| T 11/24 | |||||
| 24. | W 11/25 | Prove proposition 10.16(i). | No rewrites on 10.16(i). Instead, study the proof. | We do have class today! Quiz 3 (no solutions). Quiz 3 solutions. |
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| 25. | M 11/30 | Sect. 10.5. | Prove proposition 10.16(ii) & do homework set 25 (additional). | ||
| T 12/1 | Sects. 11.0-1. | ||||
| 26. | W 12/2 | Sect. 11.2. | Prove proposition 11.6 & corollary 11.8. | This reading tells you a lot about how the integers, rational numbers, and real numbers differ from each other. | |
| Th 12/3 | Homework return time 3:00-4:00 at my office! | ||||
| 27. | F 12/4 | Sect. 11.3 (optional). |
Prove proposition 11.10 & theorem 10.19. Do project 11.14. |
The proof of theorem 10.19 is long. It's important to work on it, but not to get a complete proof. The purpose is that you'll see the ideas used in the proof of theorems 10.18 & 10.19. | 4:30 deadline for HW on Ch. 1-6. |
| *** | F 12/4 4:30 p.m. | Absolute deadline for ... | all HW from Ch. 1-6 (Sets 1 to 17, 18a-b). | ||
| M 12/7 | Sects. 12.0-2. | Study proposition 12.10 carefully. This is a weird one! It's the basis for Theorem 12.11, which is surprisingly important. | Use Sect. 6.3 as a reference for properties of prime numbers and prime factorization that are used in Ch. 11. | ||
| 28. | T 12/8 | Sects. 13.0-1. | Prove propositions 12.3 & 13.1. | ||
| 29. | W 12/9 | Sect. 13.2. | Prove propositions 13.7 & 13.8. | ||
| F 12/11 | Sect. 13.3. | Last rewrites (except HW 28-29). | 4:30 deadline for HW & term project (except HW 28-29 rewrites). | ||
| *** | F 12/11 4:30 p.m. | Absolute deadline for ... | all homework sets & term project. Exception: HW 28-29 rewrites. | ||
| *** | M 12/14 5:00 p.m. | Absolute deadline for ... | HW 28-29 rewrites. | ||
"Where shall I begin?" he asked. "Begin at the beginning," the King said, "and stop when you get to the end."
—Lewis Carroll, Alice in Wonderland