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:
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:
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.
|6/28||Homework 1||Here is the LaTeX code: HW 1|
|7/3||Homework 2||Here is the LaTeX code: HW 2|
|7/10||Homework 3||Here is the LaTeX code: HW 3|
|7/17||Homework 4||Here is the LaTeX code: HW 4|
|7/26||Take home midterm due.|
|8/2||Homework 5||Here is the LaTeX code: HW 5|
|8/12||Homework 6 (Note the change in due date.)||Here is the LaTeX code: HW 6|
|8/19||Individual papers for the project are due.|