Guidelines for Problem Sets
Math 221 Linear Algebra, Fall 2024

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, I encourage you to discuss the Problem Sets with other students, but the assignment you turn in must represent your own work. See the Course Policies for more details on the types of collaboration that is acceptable.

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.

• 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, including if you have collaborated with other students. If you are ever uncertain if something is allowed, then please ask me!

Evaluation of Problem Sets

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 they 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.

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!