Due: Friday, December 2nd
For the final mission, I want your time spent to be very useful. That means the assignment is basically structured studying for the final exam while the semester is still in progress, so it doesn’t creep up on you.
Therefore, the final mission is to work problems on material throughout the course. You should look back through the quiz material lists for quizzes 1-4. (Here are the links: one two three four). You should choose 10 topics that you feel you especially need practice with. You may not choose small topics such as terminology. You must choose meaty topics such as algorithms, proofs, big ideas like finite fields or projective space, or cryptographic protocols. For each topic, you should invent a quiz problem worthy of a full page of a quiz (8+ points) that would test understanding, and work a correct solution. The easiest ones to do this with will be algorithms, but you should not shy away from trying to invent your own problems that test understanding by asking for proofs — please choose whatever you will learn from.
Inventing your own problems is a little more challenge than doing problems from the text, but it (1) gives you freedom to do what is important for your learning and (2) you learn more from the experience (teaches good study habits).
- These must be novel problems of your own creation.
- You may not collaborate.
- You may not use problems/solutions from anywhere else, except as inspiration for creating your own, different, example problems. In particular, you may not do “Prove Fermat’s Little Theorem” (or any theorem in the text) because that’s not novel. You may use problems similar to ones you have seen, however, if the quantities and entities have changed so that the solution is different. For example, you can invent your own example requiring finding the inverse with the Euclidean algorithm, even though finding inverses is a standard problem category. If you want to do a novel proof, you can invent a statement whose proof you have never seen before, and then prove it without consulting resources (this is a challenging but rewarding option).
Grading: Sadly, I will not be able to check the details of your solutions (especially the algebra), but I will grade on whether you have chosen good, meaty problems, and provided understandably written, apparently complete relevant solutions overall (i.e. I’ll look to see your method is correct, but won’t check algebra). You should mark the one problem you are most worried about as “PLEASE CHECK DETAILS”. This I will check in detail and will not penalize errors, as long as a good faith effort has been made. Other requests for checking over details I will happily take in office hour.