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## Math 330 - 03 Homework (Fall 2018)

• LaTeX-ed solutions are encouraged and appreciated.
• If you use LaTeX, hand-in a printed version of your homework.
• You are encouraged to discuss homework problems with classmates, but such discussions should NOT include the exchange of any written material.
• Writing of homework problems should be done on an individual basis.
• References to results from the textbook and/or class notes should be included.
• The following lists should be considered partial and tentative lists until the word complete appears next to it.
• Use 8.5in x 11in paper with smooth borders. Write your name on top of each page. Staple all pages.


Problem Set 05 (partial) Due: 10/01/2018. Board presentation: 10/??/2018

1. Prove Prop. 4.6.iii

Problem Set 04 (complete) Due: 09/17/2018. Board presentation: 09/21/2018

1. Prove Prop. 2.38 (appendix)
2. Prove Prop. 2.41.iii (appendix)

Problem Set 03 (complete) Due: 09/12/2018. Board presentation: 09/17/2018

1. Prove that for all $k\in\N$, $k^2+k$ is divisible by 2.
2. Prove Prop. 2.18.iii
3. Prove Prop. 2.21. Hint: use proof by contradiction.
4. Prove Prop. 2.23. Show, by counterexample, that the statement is not true if the hypothesis $m,n\in\N$ is removed.
5. Fill-in the blank and prove that for all $k\geq\underline{\ \ }$, $k^2 < 2^k$.