$$ \newcommand{\RR}{\mathbb{R}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\EE}{\mathbb{E}} \newcommand{\HH}{\mathbb{H}} \newcommand{\SO}{\operatorname{SO}} \newcommand{\dist}{\operatorname{dist}} \newcommand{\length}{\operatorname{length}} \newcommand{\uppersum}[1]{{\textstyle\sum^+_{#1}}} \newcommand{\lowersum}[1]{{\textstyle\sum^-_{#1}}} \newcommand{\upperint}[1]{{\textstyle\smallint^+_{#1}}} \newcommand{\lowerint}[1]{{\textstyle\smallint^-_{#1}}} \newcommand{\rsum}[1]{{\textstyle\sum_{#1}}} \newcommand{\partitions}[1]{\mathcal{P}_{#1}} \newcommand{\erf}{\operatorname{erf}} \newcommand{\ihat}{\hat{\imath}} \newcommand{\jhat}{\hat{\jmath}} \newcommand{\khat}{\hat{k}} \newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}} \newcommand{\smat}[1]{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)} $$

Correction I

THIS IS AN EXTRA CREDIT OPPORTUNITY, AVAILABLE TO ANYONE (both grading scales) To earn a couple extra points added directly as extra credit to the scores of Exam I, you can do a full and thorough exam correction, producing a complete and correct solution to each problem for yourself to use as a study guide in the future. The amount of work depends on the number of questions you made errors on, and so the points available scale with your score as follows:

EC Points: The scale starts with 1pt by default, and then adds 1pt for each 10pt decrease in exam score. I’ve written out the scale for all possible score brackets below:

This is extra credit, so it’s a fair amount of work. You will not get extra credit for only minimal effort. You are not simply submitting the correct steps for each problem, but rather doing the learning and reflecting outlined below:

For every problem that you lost more than 1/2 point on: Write a study guide for the problem, addressed to your past self, (or your future self, when you review for the final). MAKE SURE TO INCLUDE BOTH THE PROBLEM STATEMENT, SO THAT IT IS USEFUL FOR SELF STUDY BEFORE THE NEXT EXAMS

You are not simply fixing the mistakes in your old solution, but writing a rather involved document teaching the mathematics necessary to succeed at questions like this. Your submission should be neatly hand written or typed and in full paragraphs with complete sentences. It should not be a rough draft, or an outline (bullet-point list of thoughts, etc). Complete submissions will be many pages in length. Below is an outline to help you structure such a lesson.

Analysis of your original solution What is the complete statement of the problem you are writing a study guide for? When you were working on the exam, what did you think about or try? If you were stuck at the beginning, or did not write much, what made it difficult to make progress?

Review the necessary techniques Before you begin writing up your correction, learn how to solve the problem in its entirety. Look at your solution, and identify the main tools you needed. List these techniques in your study guide, so that you know what the tools are.

A Full Solution of the Problem Now that you have taught your reader all of the mathematics necessary to do this problem, write up a complete, annotated solution. Start by repeating the problem statement, and then talk your reader through (in sentences) what you should be thinking about at each step. Write this as though you are truly trying to help your future self feel confident about this problem when they are reviewing this material down the road.

A similar problem Now that you have become an `expert’ at this one problem, make up a new example question that is similar (as in, it uses the same techniques to solve). To make sure it is indeed similar - you should solve it after proposing it! But you do not need to include the solution in your writeup. Instead, this problem will be waiting for you to try again next time you study.