Video Proof #2

You should work on this problem individually (no partners) and submit your answers as a .mp4 file to Gradescope.
Read the instructions below carefully before creating your video.


Introduction

Proof-writing is one of the skills you're practicing this semester, by applying known proof techniques to problems in Theory of Computation and by learning new proof techniques. You can think of proof-writing as a means of argumentation, with its own language, norms, and expectations, but also with room to explore and be creative. Plus, as we progress through the semester, you'll see how, as the Computer Science community proved various results, it made significant breakthroughs that changed the landscape completely. So, writing and reading proofs is a way to connect with the history of the field, which is important in order to create a better future for it. Since proofs are arguments, they can be delivered through multiple means. You've seen some proofs by now that include a visual/auditory component, either in the videos you've watched for class or in class itself. So, the proof is not just the words and symbols we end up writing, but a reading (or presentation) of it as well, perhaps with additional diagrams, if necessary, and with careful explanations for those. This exercise will have you practice with this style of delivering proofs.

Instructions

  1. Look at the proofs you have written for problems 3 or 4 of Assignment 4. Pick one that you would like to record a video for.
  2. Record a video of yourself in which you "deliver" the proof, by writing out each step and describing each step and notation carefully.
  3. You are welcome to use Zoom for this, as well as any other software you are comfortable with.
  4. The video should be self-contained: it should start with the writing of and the description of the problem you're solving, and continue with the writing and presentation of the proof.
  5. You are welcome to record yourself writing the proof on the board (as you've seen in class), or record yourself present the proof on the screen (as you've seen in the videos).
  6. Make sure to speak clearly and loud enough for a listener to easily understand your words (you might have to watch to the video and re-record, accordingly).
  7. You are expected to use terminology introduced in class.
  8. Note that this is an individual presentation, so, even if you wrote the proof with someone else, the words you use must be your own.
  9. Your target audience is an imaginary student taking this class who is slightly struggling with the material, so make sure to explain all steps carefully. (Your instructors will be the only ones watching these videos.)
  10. Save the video as an .mp4 file and upload it to Gradescope.