Math 31: Topics in Algebra

Last updated August 10, 2012

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Course Information






Homework will be assigned most weeks, for a total of 8 assignments. Assignments will generally be given on Fridays, due the following Friday 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 there will also be many problems of my own. The assignments will be divided into three sections corresponding to the difficulty of the problems:

In general, 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. Each problem will be graded on a scale of 0 to 2, depending on whether the proof is correct, incorrect, or somewhere in between:

Since one of our goals is to truly develop proof-writing skills, I want you to have the opportunity to learn from your mistakes, and to really learn the material by eventually writing correct proofs. Therefore, you will have the chance to rewrite up to three problems from each homework assignment for full credit. You may choose any three problems on which you did not receive full credit, and you can turn in updated solutions to these problems within one week of receiving the assignment back. I will grade the rewrites according the usual guidelines, and if the rewrite merits a higher score, I will simply replace the original score on that problem with the new one.

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.

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 announcements

Homework Schedule

Assignment(s) due
6/29 Homework 1 is due today.
7/6 Homework 2 is due today.
7/9 You should be ready to tell me your groups for the project by today.
7/13 Homework 3 is due today. Here is the Latex code: Homework 3.tex
7/20 Homework 4 is due today. Latex code: Homework 4.tex
8/1 Rough outlines for the projects are due.
8/3 Homework 5 is due today. Latex code: Homework 5.tex
8/10 Homework 6 is due today. Latex code: Homework 6.tex
8/13 Detailed project outline is due.
8/17 Homework 7 is due. Latex code: Homework 7.tex
8/22 Individual reports for the projects are due, as well as rewrites for Homework 6.