Math 221 Linear Algebra, Fall 2023

One of the central goals of the course is that you improve your ability to communicate mathematics clearly, both in writing and verbally. Learning to write precise and complete mathematical arguments is a challenging endeavor and may be somewhat different from your experiences in previous math courses. However, the process will not only aid your mathematical development but can also greatly improve your clarity of thought in other disciplines as well.

The Problem Set exercises are usually more conceptual and less straight-forward than the problems you will work on during the class meetings. I firmly believe that one of the best ways to build your understanding of mathematics is to explore the ideas with other students. Therefore, you will work on the Problem Sets in groups of two (or possibly three), and each group will turn in a single set of solutions. I will randomly assign new groups for every problem set.

- You should think about each problem on your own before you get together with the other members of your group, and then you can compare approaches and work through the harder problems together.
- Each member of the group is responsible for the content of the entire problem set and the quality of the writeup.
- Each group will turn in a single assignment through Canvas. You should upload any written work as a single pdf. I've had good luck with Genius Scan, which is a free app for both an iOS and Android. When you are on campus, you can also use the public multipupose printers to scan and email a copy to yourself.
- All members of the group should sign the Honor Code statement.
- You will evaluate your partner's willingness to be an effective member of the team by filling out a confidential form on Canvas at the same time the Problem Set is due. Part of your individual grade on the problem set is based on whether or not you fill out the Peer Evaluation(s).
- I will take these evaluations from your peers into account in determining your final Problem Set grade for the semester.
- Here is a suggested timeline for working on the Problem Sets:

- Friday: Start working on Problem Set due next week
- Sunday/Monday: Meet with your partner(s) to discuss your ideas
- Monday-Thursday: Come to Office Hours if have questions
- Wednesday: Meet with your partner(s) to finish write-up
- Thursday: Submit Problem Set (one per group) & Partner Evaluation (each student)

Format for the Write-ups

I have high expectations for the organization and presentation of your Problem Sets. I am not being unnecessarily annoying about this. Learning to carefully organize your thoughts and clearly communicate them is one of the most important skills you will learn in college.

- You and your partner should put your name and date on the first page of each assignment.
- Clearly label each problem, and the problems should appear in order in your solutions.
- Leave enough empty space on your solutions for the grader or me to make comments.
- Your writing must be clear and legible. Use complete sentences to justify your arguments where appropriate.
- Do not turn in the first draft of your solutions. Expect to rewrite and polish your Problem Sets. I strongly suggest you write up your solutions using pencil so that you can more easily correct mistakes, but if you do use a pen, there should be no scratch-outs.
- A list of answers without explanation is not acceptable and will be graded accordingly.
- All of this may be summarized by what I have come to identify as the transitive property of happiness in grading: The neater and better organized your assignment is, the happier the grader is while grading it, and therefore, the happier you will be when it is returned.
- Remember that we are operating under the Wheaton Honor Code. You must cite your sources, and if you are ever uncertain if something is allowed, then please ask me!

You should always have a target audience in mind whenever you write. Here is a good rule of thumb to follow for your Problem Sets:

Write your solutions so that you could hand them to a student who previously took Linear Algebra and she would be persuaded that your solution is correct and that your conclusions are believable.

There are three types of errors* that frequently occur:

- A computational error occurs when a mathematical computation is carried out incorrectly, either by hand or by computer. For example, solving \( x^3 = 8\) to obtain \(x=3\) is a computational error.
- A conceptual error occurs when one of the concepts from the course is applied incorrectly or the solution/proof is not complete.
- An error in communication occurs when the solution is not well-organized or fully justified for the target audience. In particular,
- The solution should not omit any parts that contribute to the solution and would not be obvious to the target audience. If you are in doubt about what counts as "obvious" relative to the target audience, please ask me!
- The solution should be concise and not include any information that is not relevant to the solution.

* Thanks to Robert Talbert at Grand Valley State University for this classification of types of errors.

Each problem will be graded on a scale of 0-5 with the following criteria:

- 5: Exceptional. Shows complete conceptual understanding. May contain a minor computational error.
- 4: Essentially complete with no significant errors of any of the above kinds and the number of minor errors is minimal. That is, a small number of minor errors can be tolerated as long as they do not cast doubt on your understanding of the concepts.
- 2: Significant conceptual or communication errors.
- 1: Needs substantial improvement in all areas.

In addition, 2 points on your individual problem set are based on whether or not you fill out the Peer Evaluation(s).

Remember that the purpose of all of the assignments and activities in the course is to help you learn Linear Algebra and develop as a mathematician!