PS01: Background

The problems for this problem set are listed at the bottom of the page. I know there are a ton of them, but many are very small, and many should be using ideas that are familiar to you. This assignment is mostly to help you find which portions of Chapter 2 are unfamiliar to you, so you can study them and ask about them in class on Wednesday.

Here's how you should go about this problem set:

• Skim the whole reading for Wednesday first — § 2.2, 2.3, 2.4–2.4.1 — and read the things that you know look unfamiliar.
• Then work on all the problems below, just trying to knock out the ones that you can do quickly, and spotting the ones that are tough. You should not use a calculator or computer for any of these problems; they're made to be solved by hand. Take note of the tough or unfamiliar problems, and find where in Chapter 2 the relevant ideas are covered.
• Vote in the poll on Moodle for which things you want to talk about on Wednesday. (Voting is a required part of this assignment.)
• Make sure that you've completed your answers for many of the problems, and have at least worked a little on the rest, by class time Wednesday. Don't worry about the LaTeX stuff yet.

In class on Wednesday, we'll review the spots that the most people had trouble with, and take some time to work on some of the problems together. Then:

• On Wednesday afternoon or evening, finish your answers for the remaining questions.
• Give yourself lots of time on Thursday to get set up with LaTeX and to write up your answers. See the homework guidelines for more information, and see the LaTeX resources page for help getting started with LaTeX.
• Use LaTeX to make a beautiful PDF of your work, and submit it on Moodle by the due date.

Most of the problems are from the book (listed at the end of sections 3.2, 3.3, and 3.4). In your writeup, number them consecutively from 1 as shown below; for problems from the book, please also include the number from the book in square brackets at the beginning of your answer. Remember: no calculators or computers when you're solving these problems!

From § 2.2

1. 2.3
2. 2.8
3. 2.11
4. 2.24
5. 2.36
6. 2.40
7. 2.46
8. What is the parity of a number?
9. 2.52
10. 2.53
11. 2.54
12. 2.55
13. 2.56
14. 2.57
15. 2.62
16. 2.70
17. 2.79

From § 2.3

1. 2.86
2. 2.87
3. 2.88
4. 2.91
5. 2.93
6. 2.97
7. 2.99
8. 2.105
9. 2.108
10. 2.114, 2.115, 2.116, 2.117. As your answer, just say which ones are disjoint.
11. 2.118
12. 2.119
13. 2.120

From § 2.4

1. 2.141
2. 2.142
3. 2.146
4. 2.154
5. 2.161, 2.162, and 2.163. When answering questions like these, it's better to leave things in an exact symbolic form (reduced as much as possible), rather than giving a decimal approximation. So, for example, if an answer is the square root of 2, just write “$\sqrt{2}$” rather than “1.4142...”. (You can also give both, if you'd like; the LaTeX code for “$\sqrt{2} \approx 1.4142\ldots$” is $ \sqrt{2} \approx 1.4142\ldots $.)
6. 2.164
7. 2.165
8. 2.166
9. 2.168
10. 2.170