Considering the Audience When Writing Mathematics

Considering the Audience When Writing Mathematics (Writing Assignment #6)

Math 348 - October 30, 2009

Write up answers to the questions below and turn them in by Wed., Nov. 4. Typing is not required.

When you are writing mathematics, the intended audience will greatly affect how you write. In this exercise, you will compare four papers, all on the subject of the Prime Number Theorem:

"Prime Theorem of the Century" from Ivars Peterson's MathLand.
"The Prime Number Theorem" from The Mathematical Experience by Philip J. Davis and Reuben Hersh.
"Prime Number Theorem Lecture Notes" by Matt Baker and Dennis Clark.
"Simple Analytic Proof of the Prime Number Theorem" by D.J. Newman, published in the American Mathematical Monthly, Nov. 1980.

All are good, carefully written papers, but they are rather different from one another. The first two are written for a general audience. By this I mean a person with a good high school education who finds mathematics interesting but who has not necessarily studied any college-level mathematics. The third, by Baker and Clark, is written for mathematics students in college or graduate school (see the last sentence of their first paragraph). The fourth, by Newman, is a research article. It describes new work done by the author and is meant for professional mathematicians or advanced students of mathematics.

Read the articles by Peterson and by Davis & Hersh all the way through. Read the first page or two of the articles by Baker & Clark and by Newman. In these last two, don't worry about understanding all the mathematics. For each of the articles, answer the following questions.
What is the prime number theorem? How formally is it stated and to what extent does the author assume that the reader is already familiar with the theorem?
How does the author treat the background and context of the prime number theorem. In other words, how does the author explain the history of the theorem and its relation to other parts of mathematics? About what percentage of the paper is devoted to background and context?
How does the author treat definitions? How formally, how rigorously? Are terms or symbols which are used but not defined? If so, why do you think the author would do this? About what percentage of the paper is devoted to definitions?
How does the author treat proofs? Are formal proofs given, or informal explanations, or none? About what percentage of the paper is devoted to proofs?
What other similarities or differences do you notice between the papers? There are many, so come up with at least a few!