| Correct (3) | Buggy (2) | Missing or very wrong (0) | |
|---|---|---|---|
| Main answer | Formula is entirely correct. ok to use factorials, fractions, etc. Simplifying to a single number is not required. | Small mistakes, e.g. off by one errors, didn't see a pair of duplicate letters in a word. (Justification/work often helps us understand why a mistake is small.) | Major mistakes, e.g. using the wrong formula. |
| Correct (1) | Missing or very wrong (0) | ||
| Work or justification | Present, seems related to answer, and appropriate length. Informal is ok as long as graders can understand it. | Missing, apparently not related to answer, very long (e.g. formal proof). |
| Correct (3) | Poor choice (1) | Missing or very wrong (0) | |
|---|---|---|---|
| Main outline | Chooses element from co-domain, constructs pre-image, shows it is a pre-image. | Somewhat clumsy but mathematically sound proof outline. | Outline is very clumsy and/or mathematically unsound. |
| Correct (2) | Missing or very wrong (0) | ||
| Flow of Logic | Each step follows from previous information. | Significant sections are in backwards order. Preliminary work to figure out the pre-image formula is mixed into final proof. | |
| Correct (2) | Buggy (1) | Missing or very wrong (0) | |
| Definitions and Details | Key concepts, definitions, properties of helper functions are stated correctly when needed and used correctly. Algebra details are correct. | Minor errors in definitions or algebra. | Fundamental errors or significant missing sections |
| Correct (3) | Buggy (2) | Missing or very wrong (0) | |
| Style and clarity | Written with good style using mathematical English and Latex equations. Variables are declared (with their types) when introduced. | Slightly hard to follow, Latex not used or not displaying properly, missing some needed words, excessive use of abbreviations, very long paragraphs, or excessive detail/wordiness. Missing or incomplete variable declarations. | Very hard to follow. For example, very few connector works and justifications. Multiple smaller problems. |
| Correct (3) | Poor choice (2) | Missing or very wrong (0) | |
|---|---|---|---|
| Main outline | Chooses two elements of domain, assumes their images are equal, proves the two elements are equal. The contrapositive of this outline is ok only if it results in a similarly straightforward proof. | Clumsy but mathematically sound proof outline. | Outline is very clumsy and/or mathematically unsound. Significant steps lack justification due to poor choice of outline. |
| Correct (2) | Missing or very wrong (0) | ||
| Flow of Logic | Each step follows from previous information. | Significant sections are in backwards order. | |
| Correct (2) | Buggy (1) | Missing or very wrong (0) | |
| Definitions and Details | Key concepts, definitions, properties of helper functions are stated correctly when needed and used correctly. Algebra details are correct. | Minor errors in definitions or algebra. | Fundamental errors or significant missing sections |
| Correct (3) | Buggy (2) | Missing or very wrong (0) | |
| Style and clarity | Written with good style using mathematical English and Latex equations. Variables are declared (with their types) when introduced. | Slightly hard to follow, Latex not used or not displaying properly, missing some needed words, excessive use of abbreviations, very long paragraphs, or excessive detail/wordiness. Missing or incomplete variable declarations. | Very hard to follow. For example, very few connector works and justifications. Multiple smaller problems. |