Description. Produce an expository explanation of a classical theorem and present its proof. Your write-up will contain an introduction with motivation and context, a worked example, a clear statement of the theorem, a careful proof structured through lemmas, and a brief discussion of the implications of the result. The final product will be two to three pages, and will be handed in as a TeX file through Canvas.
Rubric
Content 15 points
- 15 points
- The Paper motivates its theorem and places it in context, works an illuminating example, and discusses the implications of the result.
- 10 points
- The Paper supplies motivation, an example, and a discussion of the implications, but one of these is poorly explained or improperly chosen.
- 5 points
- The Paper presents its theorem with little sense of where it comes from, what it is good for, or how it behaves in a concrete case.
- 0 points
- The Paper offers no motivation, no example, and no discussion of the result.
Clarity 15 points
- 15 points
- The Paper is clear, concise, and carefully proofread, and introduces each idea before it is used.
- 10 points
- The Paper is clear enough for a classmate to follow, though some passages are cluttered, or use notation before introducing it.
- 5 points
- The Paper can be followed only by a reader who already knows the material, or it is written so carelessly that its meaning must be reconstructed.
- 0 points
- The Paper is not comprehensible.
Rigor 12 points
- 12 points
- The theorem is stated precisely, and the proof is correct, complete, and effectively structured through lemmas.
- 8 points
- The proof is correct and well organized, but leaves to the reader a step which ought to have been supplied, or states a hypothesis imprecisely.
- 4 points
- The proof has a genuine gap or error, or runs as a single undivided argument where lemmas were needed.
- 0 points
- No proof is given, or the argument offered does not establish the stated theorem.
Structure 8 points
- 8 points
- The Paper contains each of the five required components, in proportion to one another, and runs two to three pages.
- 4 points
- A component is missing or badly out of proportion, or the Paper falls well outside two to three pages.
- 0 points
- The Paper is not organized into the required components.
Total 50 points