# Math 4740: Problem Set Guidelines

## How to Write Good Mathematics

An essential part of mathematics is communication: expressing your mathematical ideas in such a way that others can understand and learn from them. In your problem sets, we expect solutions that are not only correct and complete but also clearly explained and well-written.

You do not have to write formal proofs (though you are certainly welcome to do so), but you do need to carefully justify your work. For instance:

• When you apply a result from class or the textbook, you should verify that its assumptions are satisfied. If you want to use a theorem that says "Every frumious bandersnatch is shunnable", you had better explain why the bandersnatch in this particular problem is actually frumious.
• A commonly asked question is "How do I know whether a step is obvious, or whether I need to explain it?" A good rule of thumb is to imagine explaining your solution to a classmate. If you think they'd be able to follow your logic without further explanation, it's probably okay. If they'd need it spelled out, then you should spell it out.
• A long chain of uninterrupted calculations is usually to be avoided. If you're doing routine algebra or something, you could just write something like "Rearranging this expression, we get ..." and skip to the result. On the other hand, if there's anything subtle about how you got from one line to the next, then it deserves an explanation.

You are welcome to use a computer or calculator to do computations where appropriate. This includes not only basic arithmetic but also algebra (simplifying nasty expressions or solving equations), calculus (computing limits, derivatives and integrals), and linear algebra (matrix computations). When you do so, you should briefly explain what tools you used and what you did. ("According to the HP-50G, this integral evaluates to 17." "Using Octave's eig command, the eigenvectors of this matrix are...")

Write your solution using complete sentences. Remember that you are writing for a human audience. Try reading your solution out loud; it should sound like something you would plausibly say to another (mathematically literate) person.

You are encouraged to type your problem sets using LaTeX (or LyX). LaTeX is very versatile and widely used for writing technical documents of all kinds. It will serve you well if you go on in math or another technical field. Besides, you will need it for your project! Neatly handwritten problem sets are also acceptable.

Here is a video tutorial to get you started with LaTeX. Another good resource is the LaTeX wikibook. The Cornell math support center can help you get LaTeX up and running. (Ask for a math major tutor!)

As with any writing, you should reread and revise your work as needed until you are really satisfied with the result. Of course, you should allow yourself enough time to be able to do this!

Group work policy: Working together with other students to solve the problems is strongly encouraged! You must list the group members at the top of your problem set and write the solutions entirely in your own words. Examples:

• Figuring out the solution together on a blackboard and consulting the blackboard while you write up your solution: kosher
• Giving your written solution to another student to copy with trivial wording changes: not kosher