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/jnjcpjfydxwg#bf4ef3
- Click on the menu icon in the upper-left and select “Copy Project”.
- Create a name for the assignment 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 $p(x) = x^6-3x^3-1$. Prove that all roots of $p(x)$ lie in the field $\mathbb{Q}\left(\sqrt{13},\sqrt[3]{\frac{3+\sqrt{13}}{2}},\sqrt[3]{\frac{3-\sqrt{13}}{2}},\zeta_3\right)$, and then use this to prove that $p(x)$ is solvable by radicals over $\mathbb{Q}$. (See Problem 4.14)
