Correct I
This is an extra credit opportunity, available to everyone on both grading scales.
By doing a full and thorough exam correction, you can earn back up to 40% of the points you missed on Exam 1, added directly to your exam score. If you scored 40 out of 60, for example, you missed 20 points, and a correction of the highest quality earns up to 8 of them back.
That percentage is generous on purpose. The point of a correction is to turn the exam into a learning experience, and I want to encourage you to put real effort into this one. On Exam 2 the percentage available will drop, and on Exam 3 it will drop again.
This is extra credit, and you can only earn it through excellent work. Mediocre work will receive a zero, and generally acceptable work will receive few points. You are not simply submitting the correct steps for each problem, but doing the learning and writing outlined below.
The assignment
Start by reading carefully through the feedback on your exam. Then, for every problem on which you lost more than one point, write a short lesson on that problem, addressed to your future self when you review for the final. Each lesson has four parts.
What the problem was asking. Restate the problem in your own words. What was given, what had to be found, and what would count as a complete answer?
Analysis of your original solution. When you were working on it during the exam, what did you think about, or try? Where did it go wrong? If you were stuck at the beginning, or did not write much, what made it difficult to make progress?
The mathematics the problem is about. Describe the techniques, definitions, or theorems the problem depends on. Does it need the hypotheses of the existence-and-uniqueness theorem, and what they let you conclude? Separating variables, or undoing the product rule? Reading a phase line, or turning a description into a differential equation? Explain each idea in your own words, and say where it lives in the notes, so that future you can find it quickly when studying for the final.
A full solution. Now that you have reviewed the relevant ideas, write a complete, fully annotated solution in full sentences. Talk your reader through what you should be thinking about at each step. Write it as though you are truly trying to help your future self feel confident about this problem when reviewing the material months from now.
For a problem on which you lost exactly one point, a full lesson is not required. Instead, discuss your solution: say what went wrong, and correct it.
Your submission should be neatly handwritten or typed, in full paragraphs with complete sentences, and not a rough draft or an outline. Make sure to include the statement of each problem, so that the document is useful for self-study before the next exams.
Getting help
In general you are allowed to use AI tools to help you study and learn in this class. But just as you are not allowed to put in homework questions and ask for the answers, you are not allowed to put in the exam questions and ask for answers. You can talk with me, talk with friends, read the notes, and read things online, but you cannot ask an AI "what is this problem asking for," "critique my solution," or "give a full solution." Those are exactly the learning goals for you that this extra credit is supposed to reward.
It is fine to work with friends on thinking through and solving the problems. But then go by yourself and write your own solution, not a copy of theirs with more words added. It is okay to share ideas, but you have to do the writing and the thinking yourself if you want to grow.
Why do this?
If you do this after every exam, you will end the term with a complete set of solutions, written by you, to every exam problem you missed. That is a better study guide for the final than anything I could write for you, and a better record of what you learned in the course.