| Assigned |
Due |
Read |
Exercises |
|---|---|---|---|
| 1/22 |
1/31 |
1.1, 2 |
Write a brief (about one or
two paragraphs) description of what you think mathematics is. Don't do
research, I want to see what you think about math. 1.2.2, 3, 5, 9 |
| 1/29 |
2/5 |
1.2, 3 |
1.2.10, 13, 14 |
| 2/5 |
2/12 |
1.3, 4 |
Familiarize yourself with Block World (link above). Using
the default setup, come up with 10 different statements, 5 of which are
true and 5 of which are false. Use all of the five logical operations
(/\, \/, =>, <=>, and ~)in at least two statements each. You
may combine the operations any way you want, as long as each shows up
in at least two different statements. You may find it easiest to submit
your solutions by copying them into an e-mail to me. If you prefer to
print them or write them down by hand, that's fine too. 1.3.1-3 |
| 2/12 |
2/19 |
1.4 |
To complete this Block World project, you first need to
find yourself a partner from the class to work with. Read the note on
saving your work in Block World. This project will be easier to do
if you can save your work. Start by clearing the board. Then place a few (say 5-10) polygons on the board. Make sure you give each a name, so you can refer to them later. Make up 5 true and 5 false statements about your board. Don't use "for all" and "there exists" because we haven't covered these, but do use /\, \/, =>, <=>, and ~. Verify your statements (Eval all). Print or save what you've created, but don't show it to your partner. Clear the board again and swap statements with your partner. (You can just give him/her the file with your saved statements, but not the one with your saved board!) Tell your partner which statements were true and which were false. Now that you have your partner's statements, make up a board with polygons which satisfies those statements, i.e. makes the ones that are supposed to be true true, and the ones that are supposed to be false false. Verify your statements (Eval all). Print or save again. You'll turn in the board and statements you made up as a challenge to your partner, and the board that you made up to satisfy your partner's statements. Make sure you write both your name and your partner's name on each. You may submit your work on paper (as a printout), or by e-mail (attach both the saved board file and the saved statements, that's 4 files total). 1.3.4(1)-(3), 5(1)-(3), 8, 12 |
| 2/19 |
1.4 |
No new homework. |
|
| 2/26 |
3/7 |
1.4, 5 |
1.4.1, 2 |
| 3/7 |
3/14 |
1.5 |
1.4.3, 4 1.5.1 |
| 3/14 |
3/21 |
1.5, 2.1 |
1.
Use the default statements that come with Block World. Translate
statements 3-6 and 8, 9 into reasonably natural English
sentences. This means you should avoid using variables and other
mathematical technicalities in your sentences. (Hint: You can use Block
World to experiment with parts of the statements you need to
translate to make sure you understand what they mean. You can even
change the board to test that you sentences always have the same truth
values as the original statements. Take advantage of the interactivity
the software offers.) 2. Translate the following sentences into statements that Block World understands: (a) Every triangle is smaller than every pentagon. (b) Every pentagon is the same size as some square. (c) There is a triangle that is between a square and a pentagon. (d) There is only one large pentagon. (e) Every medium pentagon is in the same column as a large triangle. (Hint: Again, changing the board lets you test if your constructs work as they should.) 1.5.6 |
| 3/21 |
4/4 |
2.1, 2 |
1.5.8, 10 1.5.11.(1), (3) 1.5.12.(2), (4) |
| 4/4 |
4/11 |
2.3, 4 |
2.2.2, 4, 6, 7 |
| 4/11 |
2.4, 5 |
No new homework this week |
|
| 4/18 |
4/25 |
2.5, 6 |
2.3. 3, 8 2.4. 2, 3, 9 |
| 4/25 |
5/4 (This is a Friday!) |
3.1-3 |
2.5.4.(1),(2) 2.5.9 3.2.4, 15. (1), (4)-(7) (Be sure to explain why!) 3.3.9, 14 |
| 5/3 |
5/7 |
3.3, 4.1 |
Write a brief (about one or two paragraphs) description of what you think mathematics is. Don't do research, I want to see what you think about math. |