Directions.
- If you want, you may work together with one partner on this and turn in the same pdf for both of you.
- If you do this, please make sure that you truly collaborate on revising the math and typing it up.
- To collaborate with Overleaf, one person should start the project, and then use the share option (on the top menu bar), to share it with their partner.
- Get the template for this assignment (or use your own). Here’s how to do it:
- Go to www.overleaf.com, and make sure you are logged in.
- In a new window, go here: https://www.overleaf.com/read/qwzbbzntvcqd
- Click on the menu icon in the upper-left and select “Copy Project”.
- When ask for a name, choose something like “Math 110B - WA 05” and click “Copy”.
- When this completes you will be back in your own workspace (instead of mine).
- Use $\LaTeX$ to type up your proofs of the Propositions to Prove listed below. Make sure to use complete sentences and appropriate punctuation. Also, make sure to edit for typos.
- Click on the “Download PDF” button (to the right of the “Recompile” button). Save the file somewhere you can easily find it. Submit the pdf in Canvas.
- Let me know if you have any questions!
Remember, if you have trouble finding the command for a math symbol you want to use, try googling it, email me, or try looking in this Short Math Guide for $\LaTeX{}$.
Propositions to Prove.
- Let $F$ be a field. Prove that if $\deg p(x) =2$ or $\deg p(x) =3$, then $p(x)$ is reducible if and only if $p(x)$ has a root in $F$. (See Theorem 5.64)
- The polynomial $p(x) = x^2+x+1$ is irreducible in $\mathbb{Z}_5[x]$. (See Problem 5.46)
Both proofs may be short, but please make sure to carefully cite all results you are using.
