The following reading assignment was created by Susan Ruff and Peter Shor for the Undergraduate Seminar on Information Theory at MIT. The assignment below refers to text highlighted in yellow–the highlighted sentences were examples of guiding text.
Read the first 10.5 pages of A. D. Wyner’s paper The Wire-Tap Channel (stopping on p. 1365 at “We begin the proof of the direct half of Theorem 2…”). Also read the first paragraph of Section IV (starting at the bottom of p. 1367 and stopping at the statement of Lemma 5), and Section VI Acknowledgments (p. 1380). Pay attention to how the paper is crafted, and be prepared to discuss questions 0-2 briefly in class.
0. Some text throughout the paper has been highlighted in yellow. How helpful is that text? Choose a number from -3 to +3 where
-3 = Please remove the highlighted text!
0 = Most of the highlighted text could be removed or not—
it has no effect on my reading.
+3 = Please keep most of the highlighted text!
1. What is the purpose of the text highlighted in yellow?
2. In order to write similar text in your paper, what writing process do you think you’ll need to use?
3. In mathematics, paper introductions typically help the audience understand
- the object of study,
- the question or problem addressed by the paper,
- the paper’s main results,
- why these results are interesting or important, and
- the structure of the paper,
all while remaining relatively nontechnical. For “The Wire-Tap Channel,” identify each of the above. What strategies does Wyner use to help you identify them? To help you understand them? This introduction is very carefully crafted: you should be able to figure out how everything in the introduction contributes toward the goals above.
4. Because the introduction should be relatively nontechnical, mathematics papers sometimes have a second section in which notions from the introduction are formalized. Notice which details of the system and its results Wyner delays to Section II. What strategies does Wyner use to help readers understand Section II’s more precise statement of the paper’s results?
5. There are many strategies that can be used in mathematics papers to help readers follow the proof of the main result(s). Based on what you’ve read of this paper, what strategies does Wyner use?
6. Notice in Section VI Acknowledgments how precisely Wyner specifies the contributions of his colleagues. Imagine what it might feel like if you were Mr. Mallows and only the vague first sentence were included here. Collaboration is encouraged (often essential in mathematics) but treat your colleagues well: acknowledge their contributions.
7. Review the annotations in the margins of https://mathcomm.org/folder/maximum-overhang-annotated/ (Links to an external site.) Which of these conventions and strategies does Wyner follow and not follow? In what ways (if any) do Wyner’s choices affect you as reader?
8. What questions do you have about writing your own minipaper or term paper?
Prior Version of the Assignment
In the past, students have instead analyzed Shannon’s paper “A Mathematical Theory of Communication,” but although the content was a perfect fit for the seminar and illustrates effective communication strategies, it doesn’t work very well as an introduction to the norms of today’s research articles. The old reading assignment using this paper is below:
Reading Assignment
This assignment will teach you some of the conventions of mathematical writing and will start you thinking about authorial strategies for writing an effective mathematics paper. Expect the assignment to take a few hours. Start by reading the entire assignment: question 2 is most important.
A. Briefly look at the annotated article “Maximum Overhang” with an objective of understanding all of the marginal annotations.
B. Read Section 1 of Shannon’s paper “A Mathematical Theory of Communication.” Pay attention to the decisions Shannon makes as author and be prepared to answer the following questions in class.
- What is (are) the main point(s) of Section 1?
- What strategies does Shannon use to
i) help readers understand?
ii) convince readers?
iii) engage/interest/entertain readers? - What does Shannon do that doesn’t work well for you as a reader? Why do you think he did it?
- Which conventions indicated in the annotations of “Maximum Overhang” does Shannon follow? Which doesn’t he follow? Do you think these choices are effective?
- Come prepared with questions about writing your own paper.
