Math Writing

Some assignments are designated as Math Writing.   The idea is to write up a complete solution that explains in full English sentences the reasoning and steps of the problem. The point of this activity is to develop written communication skills in the use of the knowledge you learn in the course. In general, your knowledge is only as useful as your ability to communicate it, and written communication is one of the most important forms in mathematical and technical applications.

Most students are accustomed to writing problem solutions with the idea that the reader (namely, the teacher) will know how the problem is supposed to be done.  For that situation, you simply want to demonstrate that you followed the correct steps.   The math writing assignments have a different situation in mind: trying to communicate to someone an analysis you have performed to reach certain conclusions.  You cannot assume your reader already knows how to solve whatever problem is being discussed, and your goal is to make an argument that not only communicates your approach, but convinces the reader that your approach is valid.  This is a valuable life skill, and is applicable is all sorts of writing, whether or not there is any mathematics involved.  But because mathematical arguments can be made unnaturally exact and precise, it is generally clear whether they are valid or not.  So, if you want to develop your abilities to write coherently, logically, and convincingly, mathematics is a good subject to practice in.  Whether or not you agree with that conclusion, at least understand the rationale for math writing assignments, and what you are expected to do.  In particular, it will never be acceptable to say "you know what I mean."  Your job is to say exactly what you mean.  You must explain clearly what your reasoning is in a way that makes it evident that your reasoning is valid.  At times, you may cite results from the book to establish the correctness of your steps.  At other times your steps will be standard algebraic or arithmetic methods, and you may assume I know THOSE.

More on Math Writing.    Professor Adler has also prepared a discussion of math writing for his calculus 1 class.  Here is an excerpt, with some comments I added.

Format.  Each math writing problem should be started on a separate page.  You may either write out your solution longhand, or prepare it using a word processor.  In either case, leave a wide left margin for my comments.   A sample with two model solutions is given here.  Although your solution may be neatly hand written rather than typed, if you prefer, the sample will show you the proper format and the expected level of explanation in complete English sentences.

If you decide to use a word processor, you should use the same style as shown in our text.  In particular, variables should be italicized, equations that you want to refer to should be centered and numbered, and so on.  Note that there is an equation editor in MS word that is useful for formatting complicated mathematical expressions.  Instructions for accessing the equation editor are provided here.