Homework |
Problems appearing in boldface should be turned in. I encourage you to also turn in non-boldface problems, even though they won't get graded!
Explain your work: You should always explain your work, even if the book doesn't ask you to. How much should you explain? Pretend you're explaining it to a classmate who doesn't know how to do the problem.
Reminder: The non-boldface problems are as important as the boldface ones. The only reason some are bold and some aren't is that the grader doesn't have time to grade all of them. But you should know how to do all of them. Okay?
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HW # |
Due | Read | Do |
|---|---|---|---|
| W 12/14/05 1:00-4:00 PM Fowler 307 |
Cumulative, with some emphasis on HWs 22-26 and their corresponding sections. | ||
|
26 |
M 12/5 |
Sec 8.4: Definition 3, and Examples 5 and 6. Sec 8.5, up to but not including Hamilton Paths and Circuits. |
Sec 8.4: 3, 4, 5. Sec 8.5: 1, 2, 3, 4, 13, 15. Also do these additional problems (click). |
|
25 |
F 12/2 | Read Sec 7.6: Introduction, and Maximal and Minimal Elements; may skip
Theorem 1. |
Sec 7.6: 1, 9, 27, 35a. |
|
24 |
M 11/28 | Read Sec 7.5: Equivalence Classes and Partitions | Sec 7.5: 29, 32abc, 34, 35ad, 52. |
|
23 |
M 11/21 | Read Sec 7.5 up to and including Theorem 1. | Sec 7.5: 1, 3, 5, 10, 20, 26, 28, 41, 43. |
| W 11/16 | Covers HWs 14-21 (and their corresponding sections). Pigeon-hole principle and binomial coefficients will not be on this midterm. | ||
|
22 |
M 11/14 | Read Sec 7.1 up to but not including Combining Relations. Ignore "antisymmetric" wherever you see it! | Sec 7.1: 1, 2ab, 3cde, 4d, 6c, 7d, 47. |
|
21 |
F 11/11 | Read Sec 5.3 up to but not including Theorem 2. | Sec 5.3: 1, 6, 7, 39-41. |
|
20 |
W 11/9 | Read Examples 1, 2, 4, 6, 7 of Sec 5.2. | Sec 5.2: 1, 2, 7, 8, 9, 10, 23, 24, 27, 28. Turn in the even ones. |
|
19 |
F 11/4 | Sec 4.4: read the first two pages (may skip the rest). Sec 5.1: all. |
Sec 4.4: 7, 8, 10. Sec 5.1: 4, 5, 6, 7-9, 23, 25a, 26a, 27a, 28, 31, 36, 39, 40, 41. |
|
18 |
W 11/2 | Sec 4.2. (The subsection "Some elegant applications of ..."
is optional.) Sec 4.3: read all. Learn the proof of Theorem 2 (it may appear on next exam or final). |
Sec 4.2: 3, 6, 9. Sec 4.3: 4 (let S = {1,2,3,4}), 13, 16, 17, 19, 21, 23, 28, 30, 39, 40. |
|
17 |
M 10/31 | Sec 4.1: read all, some or none! There aren't really any new concepts or definitions or theorems in this section; just a lot of examples. So read as much or as little as you need in order to be able to do the hw problems. | Sec 4.1: 1, 3, 7-9, 15, 16, 19, 20, 25, 26, 27, 31, 32, 33. |
|
16 |
F 10/28 | Sec 3.3: read the Introduction; may skip the subsection titled
"Mathematical Induction"; read Examples 1-4, 9,
10. Also good to read, but optional (good for your own education, but not required for this course): Example 11, and Strong Induction. |
Sec 3.3: 10, 18, 20, 29, 30, 45 (turn in iff you didn't read the answer in the back), 50, 52. |
|
15 |
W 10/26 | Nothing. | Turn in all these problems (HW 15). |
| W 10/19 | Covers HWs 5-13 and Sections 1.5-2.5 (except for skipped material). | ||
|
14 |
M 10/17 | Read the subsection Cardinality in Section 3.2. | Turn in all these problems (HW 14). |
|
13 |
F 10/14 | Read The Euclidean Algorithm in Sec 2.5. We won't cover the rest of Sec 2.5. |
Sec 2.5: 21e, 22bf, 23. Sec 2.4: 46. |
|
12 |
W 10/12 | Nothing new to read. Review previous sections; see which definitions you can remember precisely without looking at the book. | Chapter 1 Supplementary Exercises (page 116): 38, 39, 40, 41, 44, 45a. |
|
11 |
M 10/10 | Read the rest of Sec 2.4 (may skip Applications of Congruences, and Cryptology). | Sec 2.4: 37ab, 21, 22, 25, 26, 40, 41, 42, 43, 44, 45. |
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-- |
F 10/07 | No new material. Use this opportunity to review and catch up -- redo (without looking at any solutions) some of the more difficult HW problems from before. | |
|
10 |
W 10/05 | Read Sec 2.4 up to but not including The Prime Number Theorem. | Sec 2.4: 2-5, 6, 7, 8, 9aefgh, 11ab, 13. Sec 1.8: 37 (for this problem, make sure to re-read the definition of "f ^ -1" before problem 34). Chapter 1 Supplementary Exercises: 42, 48 (page 116). |
|
9 |
M 10/03 | Read the rest of Sec 1.8; don't memorize Table 1; may skip
Examples 22-24. Read Sec 1.6: Cartesian Products. |
Sec 1.8: 9, 15, 14de, 24, 25, 26, 27, 34, 35, 36ab.
(Do 15 before 14, b/c answers for 15 are in the back of the book.) Sec 1.6: 19, 22, 25, 26. |
|
8 |
F 9/30 | Read Sec 1.8 up to but not including Inverse Functions. (May skip "bit strings.") | Sec 1.8: 1, 4ab, 5d, 10, 11, 12abc, 13abc, 16, 32, 33. |
|
7 |
W 9/28 | Read Sec 1.7. Learn all of Table1. Optional: membership tables. Skip "computers". | Sec 1.7: 1, 3, 5, 8, 10, 11a, 12d, 13a, 14e, 15, 17c, 21, 22a, 23, 37. |
|
6 |
M 9/26 | Read Sec 1.6, skip "Cartesian Products" (we'll cover it with Sec 1.8), but do read "Using Set Notation with Quantifiers." | Sec 1.6: 3, 5, 6, 7, 9, 11, 12, 13, 16, 17, 27. |
| W 9/21 | Covers HWs 1-4, Sections 1.1-1.4. Start reviewing now! My suggestion for how to study for the midterm: For each section, first quickly review the definitions and main ideas, then do each HW problem in that section that you're not sure about. If you have to look at the book or your notes in order to do a problem, make sure to try that problem again a few hours or days later, with no book or notes. |
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|
5 |
M 9/19 | Read Sec 1.5 pages 63-72. | Sec 1.5: 23, 24, 25, 27, 28, 29, 34, 46, 51, 52. |
|
4 |
F 9/16 | Read Sec 1.4; may skip "loops"; but do read Example 16. | Sec 1.4: 2b, 3, 5f, 6e, 9, 10dfgj, 19ab, 20c, 21, 23c, 27ab, 28ef, 31, 32c. |
|
3 |
W 9/14 | Read Sec 1.2; ignore "contingency"; Examples 5 & 6
may be skipped; read but don't memorize Tables 5-7 or the
terminology in them.
Read Sec 1.3 (may skip everything about algorithms and computer programs). |
Sec 1.2: 5, 6, 12, 15, 16, 21, 22, 29.
Sec 1.3: 5, 7, 9, 10, 11, 14, 21a, 48, 49, 55, 56. |
|
2 |
F 9/9 | Sec 1.1 pages 8-10, plus "Boolean Searches" on page 12 (skip page 11). Ignore "inverse" on top of page 8; "converse" and "contrapositive" are the important ones. Preview Section 1.2. | Sec 1.1: 21, 22bc (ignore "inverse"), 24abf, 29a, 50, 51, |
|
1 |
W 9/7 | Sec 1.1 pages 1-7, plus "Logic Puzzles" on pages 12-13. | Sec 1.1: 1, 5dg, 7, 9defg, 17dg, 18abdfg, 23bef, 40, 52. |
EC: Extra Credit problems are optional, and do not carry any points. If you do them, do not turn them in with your regular homework; you can show them to me during office hours. These are problems that are interesting and sometimes more challenging. Work on them only if and when you have mastered all the other problems.