An Update on My Math & Linguistics Freshman Writing Course

I thought I should provide a quick update on the freshman writing course I’m teaching this fall, Language, Logic and Information: Using Mathematics to Understand Writing, Communication and Argument. (For more, take a look at the website for the course, which is now full of lots of material.1 You can also check out my original post introducing the course and discussing its philosophy.) We’re six classes in, and it’s been going well—it’s been exhausting but exhilarating!

We began, in the first class, by talking a bit about the two core disciplines for the course, math and linguistics. To start, we worked through the mutilated chessboard problem as an example of what mathematical truth and proof is.2 I particularly liked how this problem—and the initial attempts one makes towards a solution—introduces themes about algorithms and computation that will become more important later in the course. Then we spent some time on ambiguity in natural language. This was a teaser for what’s to come in October, when we’ll start using the tools from linguistics to understand language more carefully.3

The following four classes, culminating in last Wednesday’s class, served as an introduction to logic. We’ve worked from the thin (and inexpensive) book Keith Devlin has self-published for his Coursera MOOC An Introduction to Mathematical Thinking. We covered the basic propositional connectives—and, or, not, and the conditional—and then moved on to existential and universal quantifiers. The propositional logic stuff seemed to go pretty well for the class. The conditional was a bit more confusing, but truth tables provide a nice and concrete way of working with these connectives. Quantifiers were not surprisingly more difficult. (Especially difficult were subtleties involving what domain we were quantifying over.) I wish we had more time, but I think I succeeded at least in introducing my students to the ideas and language of logic.

Now that we’ve finished the foundations in logic, yesterday we talked about mathematical proofs. We went over the two famous proofs from Hardy’s A Mathematician’s Apology: the infinitude of primes and the irrationality of the square root of two. The first major writing assignment will be for students to write an exposition of a basic mathematical proof. The focus of the assignment, since this is a writing course, will be on how clearly they can write about the proof, not the math. They have the option of writing about a proof they’ve seen in class, so all they have to do is understand the proof; they don’t have to prove new things.

I like the approach Devlin takes in his book, focusing on the unity between the math/logic and “softer” disciplines like linguistics and psychology. (This is no surprise, since Devlin worked at the Center for the Study of Language and Information at Stanford, the disciplinary home of the Symbolic Systems program that was foundational in my undergraduate education and has strongly influenced this course.) For example, in the logic section he has problems about Alice the bank teller, from Kahneman and Tversky’s conjunction paradox. I took advantage of this and assigned some reading about Kahneman and Tversky, highlighting this as an example of the role of mathematical thinking outside of traditionally scientific domains.

As we enter the second part of the course, we’re going to transition towards linguistics, while also addressing various topics in writing and argumentation. (I should note that I’ve been emphasizing these rhetorical aspects from the start, even as I teach the more mathematical content.) You can take a look at the course website to see the topics I’m planning on covering for the remainder of the course. I still haven’t finalized the readings for the second half of the semester; based on a lot of wise professors’ advice, I’ve taken a more flexible (albeit time-consuming and stressful) approach of adjusting the schedule and the readings class-by-class based on my students’ needs. Suggestions welcome!

I should note two other projects that we’ve done so far. The very first assignment I gave the class was to send me an intellectual self-description by email.4 I like the idea of establishing from the start a tone that celebrates ideas, as universities should; this assignment helped do that, I think. Also, this assignment helped students start thinking about audience from the beginning. As you can see in the assignment, I explicitly encouraged students to think about how they would write such introductory emails addressed to different audiences.

The other thing I’d like to mention is the extramural reading project, a weekly requirement that my students read good writing outside of the class. The idea behind the project—for more info, see the handout I gave my students about it—is that everyone needs to read lots and lots of good writing if they want to become good writers themselves.5 Each week, students have to spend two hours reading from high-quality sources of writing outside of the assigned readings, and then spend 10-30 minutes writing an email to me responding to the readings.

Please stay tuned for more! I’ll try to post an update a few more times during the semester, and you can also take a look at the course website, which will be updated more frequently. Once the semester is over, I’ll have a longer post recapping how the course went.

One last thing: I’d like to thank the numerous people who’ve offered me advice and support over the spring, summer, and fall. It’s been very helpful and greatly appreciated!

  1. Footnote aficionados will enjoy the syllabus, where Edward Tufte’s excellent designs have enabled me to make such notes far more prominent, as they deserve! 
  2. Thanks to Vladlen Koltun, whose CS 103X course almost a decade ago at Stanford introduced me to this problem, and helped me transition to studying pure mathematics. 
  3. I also briefly mentioned Gricean implicature, but I didn’t have enough time to get into it fully. In November, we’ll spend a class on it. If anyone has suggestions for good introductions to the topic for me to assign, I’d welcome them! (Is it too much to assign Grice’s original paper?) For now, I hope that priming my students with Grice will make his ideas more accessible in November. 
  4. Thanks to Chris Potts for the idea of turning what I’d planned to be a much shorter thing into a more substantial assignment. 
  5. In the next week or two, I’m going to post to the course website some thoughts expanding on this and related ideas, explaining my theory of how to become a better writer (and thus, implicitly, my pedagogical theory of how writing should be taught).