In general, an attempt at writing a mathematical proof either ends with a correct proof, or it does not. In other words, the solution to a proof question is either right or wrong. This idea will inform the grading of the homework problems. Each problem will be graded on a scale of 0 to 2, depending on whether the proof is correct, incorrect, or somewhere in between:

Since one of our goals is to truly develop proof-writing skills, I want you to have the opportunity to learn from your mistakes, and to really learn the material by eventually writing correct proofs. Therefore, you will have the chance to rewrite up to three problems from each homework assignment for *full credit*. You may choose any three problems on which you did not receive full credit, and you can turn in updated solutions to these problems within one week of receiving the assignment back. I will grade the rewrites according the usual guidelines, and if the rewrite merits a higher score, I will simply replace the original score on that problem with the new one.

**Notes on collaboration:** As noted in the honor statement for the course, I encourage you to talk to your classmates when working on the homework assignments. When learning abstract mathematics, it is often quite helpful to discuss ideas with others, and it can be easier to discern what one does and does not understand when trying to explain things to others. Therefore, collaboration is a valuable learning tool. However, you should keep the following guidelines in mind when working on homework.