Importance of Clear Math Communication in MAT 421 Assignments: Writing Guidelines, Assignments of Mathematics

Download Importance of Clear Math Communication in MAT 421 Assignments: Writing Guidelines and more Assignments Mathematics in PDF only on Docsity! Writing Guidelines for All Assignments MAT 421-01 August 22, 2007 Einstein tells us that the whole of science is nothing more than a refinement of everyday thinking. It is easy in mathematics to bypass the “thinking” part, in favor of calculating, but to do so misses the whole point. One way to make sure you’re thinking (as opposed to just calculating) is to communicate what you’re thinking. Secondly, while most math graduates will never in their lives after graduation have to compute the cosets of a normal subgroup, almost all will be required to communicate technical information to people who don’t have the background to understand it. This is very hard to learn, but it begins with speaking and writing clearly among ourselves. For these reasons, good mathematical writing will be required and included in the grade for every assignment in this course. The remainder of this document will describe what I mean by “good mathematical writing.” 1 The Central Thing • What you write must make sense. Try reading aloud what you have written. Think about it. Have you said anything ridiculous (it’s easier to do than it sounds, and I routinely root out ridiculous statements from my writing)? If you replaced every technical term with “This one thing” or “this other thing,” would your younger sibling understand? All the rest is elaboration of this one point, that what you write must make sense, and without it, nothing else matters. 2 Language Issues • Spelling and grammar should be standard, except where good reason for a deviation exists. • The advice of Strunk and White (Elements of Style, 4ed) is to be followed religiously: Vigorous writing is concise. A sentence should contain no un- necessary words, a paragraph no unnecessary sentences, for the 1 same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all sentences short, or avoid all detail and treat subjects only in outline, but that every word tell. By like token, the same authors wisely counsel, “Avoid the elaborate, the pretentious, the coy, and the cute. Do not be tempted by a twenty-dollar word when there is a ten-center handy, ready, and able.” While over-used, under-specific words are generally less desirable, one distinguishing mark I have seen in the best-educated people I know is that they can, when they wish, talk more plainly than anyone else. • An equation is a sentence. Firmly fix this in your mind. Convinced? What is the subject? The verb? The object? The predicate nominative? Of course, it can also be used as a clause in a larger sentence: “If 2x2 +3 = 7, then . . . .” • In professional writing (as in this class), the third person is usually pre- ferred over the second, and slightly over the first, but avoiding artificial language is more important. Also, the active voice is usually preferred over the passive, but again, good expression is paramount. For instance, I could not figure out an equally honest and expressive way to write the last two sentences in the active voice, and to write the present sentence without the first person would be dishonest. • Beware the technical terms “obvious,” “clear,” “trivial,” and their ilk. A friend of mine once remarked that the mathematical meaning of “obvi- ously” was, “A human could prove it in a finite amount of time without any specialized knowledge.” You are almost always better off to either explain the conclusion or cite where you take it from (Theorem X.y in the book; Learned in MAT 312; etc.). 3 Audience Issues • You will, except when otherwise instructed, be writing with me, the teacher, as your audience. However, the level of your writing should be more that of an “open letter,”1 in the sense that your classmates should be able to read it with total understanding. You may assume that your au- dience understands the material from prerequisite courses and the present course to date (although it’s not a bad idea to remind the reader of more obscure points), but you should not assume that the reader is familiar with material later in the course, material from the book that we haven’t 1The “open letter” is a rhetorical form in which one writes a letter, ostensibly to one person (usually a high official), but which is published more broadly. Examples may sometimes be seen in the opinion section of a newspaper, where a person writes a letter to the Governor or the President, but also sends a copy to the newspaper, so that it be may be read by the broader public. 2