Math 31: Topics in Algebra

Summer 2013

Homework

Homework will be assigned most weeks, for a total of 8 assignments. Assignments will usually be given on Wednesdays, due the following Wednesday at the beginning of class. Homework solutions should be written legibly in pen or pencil or typed. All proofs should be written in complete sentences. I reserve the right to reject any papers that are illegible. Also, please be sure to staple all papers before handing them in.

The homework assignments will consist of both proofs and computational problems. Many of the problems will come from the textbook, but I may also take problems from other sources. The assignments will be divided into three sections corresponding to the difficulty of the problems:

• Easy: These are fairly basic problems that are intended to check your understanding of the key concepts.


• Medium: These are slightly more difficult problems that will require you to apply the concepts you have learned to more interesting situations. The problems in this range are of the type that you should expect to see on the exams.


• Hard: These are fairly difficult problems. They will either require you to explore certain concepts beyond what we have done in class, or the solutions may involve some creativity.

You will come to learn that an attempt at writing a mathematical proof either ends with a correct proof, or it does not. In other words, the solution to a proof question is either right or wrong. This idea will inform the grading of the homework problems to a certain extent. Each problem will be graded on a scale of 0 to 5, and the score will depend on both content and presentation. Roughly, the grading scheme will be as follows:

• 5: Your solution is a correct proof of the given statement, and it is written clearly, coherently, and in complete sentences.


• 4: The solution is mostly correct, but there are some small defects that keep it from being an airtight argument. It is also written clearly and in complete sentences.


• 3: The solution appears to be headed in the right direction, but there are some fundamental flaws in the argument or in the exposition. In other words, a score of 3 could result from a partially correct proof, or from cutting some corners in the written presentation of your proof.


• 2: The proof is fundamentally flawed and/or not well-written.


• 1: The proof is incorrect or incoherent.


• 0: You did not make a reasonable attempt at solving the problem.

Notes on collaboration: As noted in the honor statement for the course, I encourage you to talk to your classmates when working on the homework assignments. When learning abstract mathematics, it is often quite helpful to discuss ideas with others, and it can be easier to discern what one does and does not understand when trying to explain things to others. Therefore, collaboration is a valuable learning tool. However, you should keep the following guidelines in mind when working on homework.

• The solutions that you turn in to me should be written up by you in your own words. It is fine to discuss ideas with others, but I want each person to think individually about how to put those ideas down on paper.


• If you have worked with others on a particular problem, say so when you write up the solution. If you got a particular idea from someone else, give them the appropriate credit.

In summary, I encourage you to work on homework together, and to possibly work out ideas in groups. However, I do not want you to write up complete proofs as a group—this should be done individually. Look here for examples of what I think are acceptable levels of collaboration.

Homework Schedule