### Guidelines for Solutions to Problem Sets - Math 301 Real Analysis - Fall 2017

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 and proofs is a challenging endeavor, and this process will not only aid your mathematical development but can also greatly improve your clarity of thought in other disciplines as well.

You will have a Problem Set due most Friday mornings at 9:30 a.m. at the beginning of class. The Problem Sets will alternate between Group and Individual assignments. You will work on the Group Problem Sets in groups of two that I assign, and each group will turn in a single paper. See the Tentative Syllabus for the exact due dates.

Each homework assignment will have two categories of problems:

• Focus problems: These will consist of three or four of the more difficult problems, usually proofs, that I will grade carefully.

• Basic problems: These will be the more routine problems that are still very important in understanding the course material. Although I do not intend to grade the Basic problems, I will skim your solutions, and I reserve the right to include them in your course grade if I feel that you are not making a serious effort.

#### Evaluation of Problem Sets

Remember that the point of all of the assignments and activities in the course is to help you learn Real Analysis and develop as a mathematician!

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 Real Analysis 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 would not be obvious to the target audience that contribute to the solution. 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.

Each Focus Problem will be graded on a scale of 0--7 with the following criteria:

• 7: Exceptional. All areas perfect.

• 5: 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.

• 3: Significant conceptual or communication errors.

• 1: Needs substantial improvement in all areas.

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. If you do not follow these guidelines, I reserve the right to return your Problem Set ungraded.

Guidelines for all Problem Sets

• Put your name and date on the first page of each assignment.

• Group the Focus Problems together, in order, at the beginning of your problem set, and begin the set of Basic Problems on a new sheet of paper.

• Clearly label each problem with the chapter and exercise number.

• Leave enough empty space on your solutions for 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.

• Do not turn in paper torn from a spiral notebook with ragged edges.

• 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 I am while grading it, and therefore, the happier you will be when it is returned.

• The only outside resources that you may use are the text, your class notes, other students currently enrolled in our Real Analysis class, and me during office hours. 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!

• And remember, do not turn in the first draft of your solutions.

Additional Guidelines for Group Problem Sets

• I expect you and your partner to work together and discuss every problem.

• You may divide writing the final version as you see fit, but you must label the final author for each problem. I will keep track of this over the course of the semester.

• You will evalute the contribution of your partner on a scale of 1-10 by filling out a confidential form on onCourse. I will share your average evaluation from your peers with you at the end of the semester.

• I reserve the right to consider your contributions to the Group Problem Sets in determining your Problem Set grade at the end of the semester.

Additional Guidelines for Individual Problem Sets

• I encourage you to discuss the Individual Problem Sets with other students enrolled in Real Analysis this fall, but you must turn in separate papers that represents your own work. If you do work with someone else on an assignment or a specific problem, you must cite them on each problem where you collaborated.

Remember that the point of all of the assignments and activities in the course is to help you learn Real Analysis and develop as a mathematician!

 Maintained by: ratliff_thomas@wheatoncollege.edu