Click on Reload to make sure you get a current copy and not an old cache.
| Section | Practice problems*/Notes | Problems to turn in | Due date |
|---|---|---|---|
| 1 | Fundamentals | ||
| 1.1 | 1, 5 + misc. odds | 2, 16 | F 9/15 |
| 1.2 | 1 + misc. odds | 10, 24
Prove De Morgan's law, #15, p. 9. Please write proof on separate page. | F 9/15 |
| 1.3 | 1, 3, 13, 15, 25, 27 | 17, 18, 22, 26, 28 | F 9/15 |
| 1.4 | 1, 7, 11, 15, 18 | 6, 8, 12, 14 | F 9/15 |
| 1.5 | 6, 8, 24 | F 9/22 | |
| 1.6 | Example 12 | 2, 16, 24, 26 | F 9/22 |
| 2 | Logic | ||
| 2.1 | 1, 7, 15, 21 | 10, 12, 18, 24 &
Is "down-arrow" associative? | F 9/22 |
| 2.2 | 1, 3, 11, 23 | 2, 4, 8, 12, 24 | F 9/22 |
| 2.3 | 1-13 odds | 2, 4, 6, 8 &
Prove: If n is a positive integer and n is not the square of an integer, then the square root of n is irrational. | F 9/29 |
| 2.4 | "The most useful, and simplest, proof
technique in combinatorial mathematics and computer science is mathematical induction."--Alan Tucker | 6 if a is not 1 (What if a=1?), 28, 32 | F 9/29 |
| 3 | Counting | ||
| 3.1 | 1, 21, 25 ... | 4, 22, 28 | F 10/6 |
| 3.2 | 4, 8, 22 | F 10/6 | |
| 3.3 | In-class examples | 6, 16 | F 10/6 |
| 3.4 | In 18b MMDD may be rearranged. | 9, 10, 18, 30, 32 | F 10/13 |
| 3.5 | 1, 3, 5, 13, 17, 19, 26 | 2, 4, 8, 18, 20;
12, 14, 16 | F 10/13 |
| 4 | Relations and Digraphs | ||
| 4.1 | 26 | 10, 14, 18, 28 | F 10/13 |
| 4.2 | 1, 9, 21 | 6, 12, 22, 24, 26 | F 10/13 |
| "It is not an exaggeration to say that
90% of what will be discussed in the remainder of this book will concern some type of object that may be considered a relation." --p. 107 | |||
| 4.3 | 1-8 | 10, 15, 16, 17 | R 10/19 |
| 4.4 | 2, 8, 10, 15, 21 | R 10/19 | |
| 4.5 | 1, 3, 5, 13, 17, 19 | F 10/19 | |
| 4.6 | Optional | ||
| 4.7 | 1, 5, 7, 9, 23 | 2, 8, 12, 16, 18, 22 | F 11/3 |
| 4.8 | 1, 3, 7, 9, 17 | 8, 10, 12, 14
Proof: Prove Theorem 1 of Sect. 4.4. | F 11/3 |
| 5 | Functions | ||
| 5.1 | 1, 11, 15 | 14, 18, 25, 26
In #26 do not assume Dom(f)=A. | F 11/3 |
| 5.2 | 22 | F 11/3 | |
| 5.3 | 1, 7 | 4, 8, 11 | F 11/3 |
| 5.4 | 6, 24
25: Write self-contained PROOFS Turn in proofs separately. | F 11/10 | |
| 6 | Order Relations and Structures | ||
| 6.1 | 1, 3, 5, 9, 13, 27 | 2, 4, 10, 14; 26 | F 11/10 |
| 6.2 | 4, 10, 26, 31 | F 11/10 | |
| 6.3 | Handout | 4, 6, 9,
24 (PROOFS) worksheet | F 11/17 |
| 6.4 | 1, 3, 5, 7, 9 | 2, 4, 6, 8, 10,
14 (PROOF) | F 11/17 |
| 6.5 | "It is almost impossible to overestimate
the importance of these facts [about Boolean polynomials] for the study of computer circuitry." (228) | 2, 6, 16 | F 11/17 |
| 6.5 | Extra credit:
Express all 16 Boolean functions of x, y using NANDs as the only operation. | T 11/21 | |
| 6.6 | 1, 3, 5, 9, 11, 13, 15, 21 | ||
| 7 | Trees | ||
| 7.1 | 2, 3, 9, 10, 11a, 12a, 13, 19, 22-25. | ||
| * | Turn in proof portfolios for review. | W 11/22 | |
| 7.2 | 1, 2, 3, 5, 6, 7, 8, 9, 11, 15 | 4, 10, 12, 16, 20 | F 12/1 |
| 7.3 | 1, 3, 19, 27, 31 | 2, 7, 12, 20, 28, 32 | F 12/1 |
| 7.4 | 6, 14 | F 12/8 | |
| 7.5 | 4, 8 | F 12/8 | |
| 8.1 | 7, 9, 13 | 6, 8, 10, 18, 24;
26 (PROOF) | F 12/8 |
| 8.2 | Example 6 | 4, 6, 10, 12, 14 | F 12/8 |
* These are merely some suggested problems. You should work as many problems as necessary to master the ideas.