Homework will be assigned and collected roughly every week. Unless the class decides to revisit the decision, homework will be due on Fridays. Initially, students are permitted to turn in handwritten homework, but this will change with homework #4. I will post LaTeX source files for all homework as a way to ease students into typing the statements being proved.
Below the table of homework, there are some supplementary problems (to do but not turn in), evaluation rubrics and useful resources. I’ll add links from time-to-time, and some documents that were initially links to documents posted elsewhere will be replaced by modified versions I’ve created.
| HW # | Due Date | Statements | Solutions |
|---|---|---|---|
| 1 | 18 Jan 13 | PDF / LaTeX | PDF / LaTeX |
| 2 | 25 Jan 13 | PDF / LaTeX | PDF / LaTeX |
| 3 | 1 Feb 13 | PDF / LaTeX | PDF / LaTeX |
| 4 | 8 Feb 13 | PDF / LaTeX | PDF / LaTeX |
| 5 | 15 Feb 13 | PDF / LaTeX | PDF / LaTeX |
| 6 | 22 Feb 13 | PDF / LaTeX | PDF / LaTeX |
| 7 | 27 Feb 13 | PDF / LaTeX | PDF / LaTeX |
| 8 | 29 Mar 13 | PDF / LaTeX | PDF / LaTeX |
| 9 | 12 April 13 | PDF / LaTeX | PDF / LaTeX |
Supplementary problems
These problems are not to be written up to turn in. However, you are strongly encouraged to do them. I’m happy to discuss them with you in office hours if you have questions about them, too.
| Section | Problems | Comments |
|---|---|---|
| 6C | 9, 10, 11 | Determining if an arbitrary element of \(\mathbb{Z}/m\mathbb{Z}\) is a square is nontrivial. Eventually Gauss provided a method for doing this. |
| 6D | 17, 18, 19, 25, 27, 30 | |
| 6E | 42, 43, 45, 46 | |
| 6F | 56,57, 58 | |
| 7A | 1, 3 | Do 1 using only the ring axioms. (In class, we proved a more general result first.) |
| 7C | 21, 22, 23, 24, 26, 28, 31, 34 | 24 generalizes what we already did for \(\mathbb{Z}/m\mathbb{Z}\) |
| 9A | 1, 3, 4, 7,11 | |
| 9B | 17, 19, 20, 22, 23 | |
| 9C | 40, 41, 42, 43, 46, 52, 55 | |
| 12A | 1–7, 16, 25 | |
| 13A, 13B | 2, 6 | For 6, part (i) is the one I most want to be sure you do. The others are good but take more work. |
| 14A | 1, 4, 5(i), 7, 10 | |
| 14B | 14, 22, 23, 25 | |
| 14C | 34, 36, 37, 39, 41, 42, 43, 46 | |
| 15D | 8, 9, 10, 11, 13, 15, 18 | |
| 7D | 42, 44 | See page 144 near the bottom for the definition of characteristic. |
| 16A | 1,2,3,9,10,12 | |
| 16B | 16, 18, more (PDF) |
Evaluation rubrics
- Three-part rubric (Charles Collins, University of Tennessee-Knoxville)
- One-part problem/proof rubric
Useful resources
- Elements of Style for Proofs (Anders Hendrikson, Concordia College)
- Glossary of Proof Terms (Anders Hendrikson, Concordia College)
- Homework template
- Quick LaTeX guide (Dana C. Ernst, Northern Arizona University)
- Quick Guide to LaTeX (Dave Richeson, Dickinson College) – This is great! It’s a “cheat sheet” you can print on two sheets of paper and contains tons of frequently-used commands.