English 125: Language, Logic, and Information -- Fall 2013

Using Mathematics to Understand Writing, Communication and Argument

This Week's Schedule
Go to: [Course Information] [Assignments and Handouts] [Schedule] [Links]

Course Information

Instructor: Rafe Kinsey
Email: rkinsey (at) umich (dot) edu (please put "English 125" in subject)
Office: East Hall 5832 (Make sure to take the stairs or elevator in the math side of the building, otherwise you will not be able to access it.)
Office Phone: 734-763-2518 (Please use email for messages.)
Course Hours: MW 2.30-4pm. School of Education 2334
Office Hours: M 1.30-2.30, W 4-5, or by appointment (email me)
Textbook: Keith Devlin, An Introduction to Mathematical Thinking. Available for $9 from Amazon. Make sure to buy this in time for the second day of class (or, ideally, before then, since there will be reading from it due by the second class).

For more info, please see the syllabus. You might also want to read my blog post from the summer introducing the course, as well as later blog posts about the course. Feel free to contact me with any questions! (This includes not just students but anyone--mathematicians, humanists, linguists, philosophers, economists, computer scientists and other educators--interested in these pedagogical ideas, since I hope others will consider teaching courses along these lines. I'll be posting more about this experiment at the end of the semester, and have been intentionally documenting what I'm doing carefully, so I'd be happy to share my thoughts, lesson plans, experiences, etc.)
This course has an audacious goal: we're going to learn a bit of pure mathematics and then apply what we've learned to understand language and writing. We'll begin with an introduction to pure math: the beauty of proofs and abstraction, not the rote calculations of high school. Some of the things we'll study will be logic, set theory, recursions, and algorithms. (Don't worry if you haven't seen these before!) The math will then lead us into theoretical linguistics, the scientific study of language. Finally, we'll use our knowledge of math and theoretical linguistics to think about writing itself, in particular how to write (and argue, and think) effectively. For example, we'll see how Venn diagrams, from set theory, are used in linguistic semantics, the study of meaning, to explain precisely when there should and shouldn't be a comma before "which."

Throughout, we'll be motivated by the premise that mathematical thinking is crucial in understanding much of the world, not only in the linguistics we'll be focusing on, but also in economics, computer science, music, medicine, sports, political science, and many other areas. (Indeed, an unofficial title for the course that represents this philosophy is "Math, Writing, and the World.") There will be lots of writing, in many different forms, throughout the semester, but we'll focus on a final project where you will get the opportunity to choose, study and then write about some interesting application of mathematical thinking to the world.

Handouts and Assignments


DateDone in ClassRead by TodayAssigned Today (in addition to reading; not official until day of the class)
Day 1: W 9/4 Introduction to the course.
  • Introduction to math: (domino tiling)
  • Themes and Logistics of the course (syllabus, etc)
  • Linguistic Awareness (ambiguity, Grice, "soft mathematics")
none (though feel free to look at the syllabus and the webpage)
Day 2: M 9/9 Logic; Reading
  • Reading. The extramural reading project.
  • Introduction to Logic: Devlin 2.1-2.2 (Propositional Connectives).
  • Carefully read the syllabus
  • Devlin, preface, What is this book about, chapter 1, chapter 2 sections 2.0-2.2. The preface and chapter 1 are relatively light reading; focus your efforts on the chapter 2 sections, which are more difficult. Try thinking about and working on some of the exercises. If you don't have the book yet, the preface and chapter 2 parts are available on ctools, and chapter 1 is available on Devlin's site. Make sure to bring your book to class, or else to bring your printout. (Optional: You might want to take a look at Keith Devlin's Coursera course, based on this book. There are free online videos, exercises, etc.)
  • James Salter, Once Upon a Time, Literature
  • G.H. Hardy, A Mathematician's Apology, section 10. (Optional: Feel free to read more! This is one of the great books about mathematics. A related essay--also optional--is Timothy Gowers's essay The Importance of Mathematics. The figures are available here. You can also watch the video here. Either of these would be good for the extramural reading project.)
  • Devlin, Soft Mathematics (October 2009).
  • For Wednesday, do the following exercises from Devlin's book: 2.1.1 #3; 2.2.1 #7; 2.2.1 #6; 2.2.3 #1, #5. You should first try to do these exercises on your own. Then you are welcome to collaborate with members of the class---except 2.2.1 #7 and 2.2.1 #6, which I want you to do completely by yourselves. [Oops---typo, I meant 2.2.2 #6 not 2.2.1 #6. Too late.] (Remember, the focus is on you understanding the material, so try to work things out on your own.) Then write your solutions by yourself, but indicate at the top who you collaborated with. Feel free to neatly handwrite or type (or use a combination). (If you're planning on studying math, you might want to learn about LaTeX, a useful program for typing math. Ask me for more info, or google it!) At the end of the assignment, tell me how difficult you found it. I'll check your work for effort, not correctness. Don't worry if something is confusing or you don't get it; if that's the case, describe your thinking process and what confuses you.
  • The Extramural Reading Project. (Read that carefully.) You can also see the page with links to good sources for your reading. This is due each Friday, starting this week.
Day 3: W 9/11 Logic Continued: Implication
  • Sweetland Presentation
  • Logic Continued
  • Feedback
  • Malcolm X, Coming to an awareness of language (excerpt)
  • Devlin 2.2 (reread) and 2.3 (read). Note that 2.3 is difficult. Even though it's only 13 pages, this is a substantial reading assignment. Trying some of the exercises can help. Come to class with questions!
  • Do the following exercises and hand them in Monday in class. Devlin 2.3.4: #5, #6, #8. Devlin 2.3.5: #2, #3, #4, #5, #12, #13, #14, #15, #18, #19. The same instructions apply as for the previous homework. You are welcome to collaborate with classmates (see contact info on ctools)---but first try to work on problems on your own, and write up your solutions independently. Again, the grading will be based on effort and engagement with the material, not correctness: the focus is on your learning. Start working on these well ahead of time. If you're struggling with them, please email me.
Day 4: Mon 9/16 Logic Continued: 2.3 and 2.4
  • Kahneman and Tversky's Conjunction Paradox
  • Conditional Continued (2.3)
  • Quantifiers (2.4)
  • Devlin 2.3 (reread) and 2.4 (read)
  • Exercise: 2.3.5 #23. 2.4.2 #3, #4, #5, #6. 2.4.5 #1 (a)-(e), due Wednesday in class. The same policy as before applies on collaboration, etc.
Day 5: W 9/18 Logic Continued: Set Theory and Predicate Logic
  • Discussion of Hanna Rosin's article, especially how it relates to writing we may do.
  • Set Theory
  • Predicate Logic Continued
  • Read Devlin, Appendix on Set Theory; and Devlin, 2.4 (reread). (These are the key readings; you'll want to read these carefully.)
  • Excerpt pp. 156-159 from Daniel Kahneman's Thinking, Fast and Slow, about the conjunction paradox. Also read this article from the Guardian for more about Daniel Kahneman. (You might want to read the Guardian article first, since it provides more context.) As you read these, think about how the authors have explained a complicated idea, since you will have to do this in your writing. (You might compare how they explain the conjunction paradox.) (Optional: Feel free to read more about Kahneman and Tversky's research for your extramural reading. You might, for example, choose to read more from his book.)
  • My blog post on judgment aggregation paradoxes. (This is less important; it's an example of the sort of applications you can talk about in your final project.)
  • Hanna Rosin, The Gender Wage Gap Lie (This is a great example of an analytical article in Slate, and it also can serve as a model for a paper pointing out a mistake in someone's argument. Take a close look at this.)
  • Exercises from Devlin. #2.4.5 #1 (f)-(n), #2, #5. A1 #8. (Hint: The basic structure of your proof should be like this: Suppose x is in A. Then try to show that x is in B.) Also, prove the following, using the formal approach I did in class as a model: (A intersection B) is a subset of (A union B). (Hint: Again, use the basic structure I did in class today.) Due in class on Monday. Same rules on collaboration, etc., apply. You might also want to look at the solutions (see ctools) for the previous HW. If this stuff with quantifiers is confusing, don't worry--this is difficult stuff!
  • Informal Writing Assignment: Email me by Monday 2:30pm with your one-paragraph summary of Rosin's article. Work on making your summary clear and concise, and make sure it's carefully edited and proofread.
Day 6: M 9/23 Mathematical Proofs; Clarity and Precision of Mathematical Exposition; Genre
  • Discussion of the reading
  • Proofs
  • Discussion of mathematical writing
  • The Proofs Writing Assignment
  • G.H. Hardy, A Mathematician's Apology, sections 12-14.
  • Devlin, 3.0-3.4. Read this carefully; it's difficult! You might compare Devlin's exposition with Hardy's. (Note: we won't cover 3.5 [mathematical induction] or chapter 4, but you're welcome to read these sections on your own, especially if you're interested in pure math. I'd be happy to talk about those sections after class.)
  • Kurt Vonnegut How to Write with Style (non-password protected version here).
  • The Wikipedia article on the Wason selection task.
Day 7: W 9/25 Rhetoric
  • Summary Activity
  • Rhetoric: Figures; Ethos, Logos, Pathos; Axioms; Fallacies; Induction and Deduction
  • Feedback
  • Reread Devlin 3.0-3.4. As you reread this, you will get a better understanding of the structure of proof, which will hopefully help you for your writing assignment!
  • Andrea Lunsford and John Ruszkiewicz, Everything's an Argument, 4th ed., excerpts pp. 38-41 on ethos, pathos, and logos.
  • Edward Corbett, Classical Rhetoric for the Modern Student, 3rd ed., excerpts pp. 70-80 on the fallacies. (Note: parts of this might be somewhat difficult. Corbett in earlier parts of the book uses different terminology for some of his logical ideas than we have done---terms like syllogism, enthymeme, etc. Think about what an effective reading strategy for this would be. Perhaps you should look up terms that you don't understand? Perhaps you can look up the subsection title? Can you relate the terminology Corbett is using to the terminology we've learned from Devlin? Think also about my purpose in assigning this: do you think I'm going to test you on every single fallacy?)
  • Sam Leith, Other Men's Flowers
  • Over the next several weeks, in your extramural readings, pay attention to the rhetorical techniques the authors are using. In your weekly responses to me, analyze some of these rhetorical aspects. For example, where is the author relying on ethos, logos, or or pathos? Is this an effective choice? When relying on logos, is the author relying on deduction, induction, or a combination of the two? Is the author committing any fallacies? You might also notice when authors use certain of the rhetorical figures, and point out a few examples. Your reading responses don't have to focus exclusively on the rhetorical aspects, but you should include some rhetorical analysis of at least four articles over the next month.
  • Optional: Over the next few weeks, if you're interested in these concepts of rhetoric, you might choose to read and learn more. (This could be part of your extramural reading.) Possible sources include: Lunsford and Ruszkiewicz's book (available in the library), Corbett's book (available in the library), Sam Leith's new book on rhetoric, Farnsworth's Classical English Rhetoric, and BYU's online guide to rhetoric. For a related topic, you might take a look at Joshua Foer's book Moonwalking with Einstein, which talks about tools for memory developed by classical orators (among other things).
Day 8: M 9/30 Productivity, Editing, and Writing; Peer Review
  • Logical Fallacies (cont'd from last time)
  • Productivity
  • How we write
  • Peer Review (handout)

Strongly Recommended: As you read these, think about how you would summarize them. Try writing one-paragraph summaries of each.

  • Over the course of this week, observe your productivity habits. What hurts your productivity? Your phone? The internet on your computer? People? Other things? Experiment with different techniques for improving your productivity as you work. (See some of the links at the bottom of this page for tools that might help.) In particular: try several times to block out an extended period of time without distractions to read in. Does this help? Send me an email with a paragraph or two describing the experience, by next Wednesday, October 9.
  • Remember the peer review response by Wednesday.
Day 9: W, 10/2 Prescriptivism, Norms, and Style
  • A discussion of these issues
  • Talking about how these authors make their arguments, to model in our own papers
  • Start paying attention to these issues. Think about some of the constructions mentioned in these or other readings. One of your writing assignments in a few weeks will have you address one of these specific constructions.
Day 10: M 10/7 Introduction to Theoretical Linguistics; Formal Grammars
  • Theoretical Linguistics
  • Explanation of the formal, mathematical nature of linguistics
  • Dichotomies: Isaiah Berlin's hedgehogs and foxes
Day 11: W, 10/9 Library Activity
  • Complete the Library Activity this week, and send your response via email by 8pm Friday. (This replaces extramural reading for this week.)
M, 10/14
No class
Fall Break
Day 12: W 10/16 Syntax
  • Syntax, Phrase Structure
  • Feedback
  • Reread just pp. 97-103 of the Pinker from last week.
  • Fromkin et al. (9th ed.) chapter on syntax. For today, read only pp. 117-142. Please also print out and bring pp. 168-178 (the summary and exercises), which you should at least skim. (Note: the pdf has more pages than this, so you'll only want to print a subset of the pages. We might use the other pages later on, but we might not. To help you with printing, the pages you need to have printed for today are pages 1-14 and 27-32 of the pdf file.)

    As you read this, remember that your task is to try to learn the material on your own. In class, we'll use the "flipped classroom" model where you will do exercises in groups, rather than me lecturing. Please note that this is difficult stuff. As with the Devlin, you should read this multiple times. You should take a look at some of the exercises, and try them out. You could also practice exercises on your own: write out English sentences, and try to draw the tree structure. It's possible that you will find some of these ideas difficult; if so, think about effective strategies for learning---asking a friend, looking things up online, emailing me, etc. (Definitely email me ahead of class if there are concepts you are finding difficult, so I can talk more about them.) Also: think about what sorts of notes from your reading would help you learn.
Day 13: M 10/21 Syntax Continued
  • discuss first paper, writing criteria
  • use-mention distinction
  • Grammar continued: constituency; phrase structure
  • My handout on writing well.
  • Reread the Fromkin from last class; we'll be going over many more of the concepts. As you reread this, think about effective ways of mastering the material, so that if I ask questions about these concepts in class, you'll be able to answer them.
  • something on the use/mention distinction (see above from 10/16 Assigned Today about this)
  • Linguistics exercises: bring to class on Wednesday
Day 14: W, 10/23 Syntax Continued
  • more on syntax
  • peer review
  • From the remainder of Fromkin, read 142-154 (these are pages 14-20 of the pdf): "Heads and Complements" (142-149), "Structural Ambiguities" (149-151), and "More Structures" (151-154). (It's alright if pp. 145-149 are a bit confusing; focus on the other parts.) You might also want to reread earlier parts, on phrase structure. Please bring all of the Fromkin ch 4 selections (from today and earlier) to class. Optional: I'd encourage you to take a look at the other sections in this chapter, which go a bit further into linguistic theory.
  • Bill Poser, Political Correctness and the Use/Mention Distinction
  • Reread your proofs essay, looking at my comments
  • Remember that your peer review responses are due emailed to your partner and cc'd to me by Friday at 5pm. Before then, you should read the article your partner summarized, and take another look at your partner's paper to make sure it appropriately captures the article summarized. (You can count that reading time as part of your extramural reading.)
Day 15: M 10/28 Grammar, Punctuation, Etc.
  • Apposition
  • Constituency and Commas
  • Examples and Explanation
  • Dangling Modifiers
  • Arguments about Language
  • Writing Assignment: Prescriptive Construction
  • For next class: three paragraphs on prescriptive topics (see prescriptive assignment).
Day 16: W 10/30 Making Arguments; Explanation; More on Punctuation
  • working on our explanations for prescriptive paper
  • developing arguments for prescriptive paper
  • serial commas and constituency
  • comma exercise
Day 17: M 11/4 Probability: Math Background
  • finite probability
  • Bayes' Theorem
  • Rosen, Discrete Math, selections from chapter 6. From this, you can skip/skim examples 4-7 (we haven't covered that material). You also can skip the bottom of 406 and the top of 414. Please make sure to print out the exercises as well. You don't have to read and do all of them, but it could be helpful to glance at them and try a few. Remember, reading math is hard and takes time. (One piece of terminology you might not be familiar with is the notation |E|, which means the size of the set E. You might want to consult Devlin's appendix on set theory for a refresher on set theory notations.
  • Nate Silver, The Weatherman is Not a Moron
  • Do exercise 1, 7 and 8 from p. 424 of the Rosen book (i.e., the problems we were working on at the end of class). Hint: the structure for solving these problems is in the book. For the first one, there's a basic formula. For the last two, you're using Bayes' theorem; see the examples in the book to work things out. Please bring these to class on Wednesday to hand in.
Day 18: W 11/6 Probability Continued.
  • Probabilistic thinking in the world
  • peer review
The readings for this week are a bunch of different articles that address the role of probability. Think about how these authors explain probabilistic concepts to discuss real-world problems.
  • Please send me an email with an agenda for your conference with me by the night before the conference.
  • Look again at Steven Strogatz's article about calculating Bayes' Theorem using natural frequencies. Try to redo the homework from last time (exercises 7 and 8 from page 424 of Rosen) using Strogatz's technique.
Day 19: M 11/11 Pointing Out Flaws in Arguments
  • more on punctuation: series
  • Bayes' Theorem continued
  • practice in oral presentations
  • pointing out errors
  • feedback
  • For Wednesday's class, find two articles that have some sort of fundamental error. Please bring them to class and email them to me.
  • Writing Assignment: Debunking a Fallacious Argument
Day 20: W 11/13 Math and the World: The Final Project
  • The Final Project
  • More on Pointing out Errors (see here for more on the assignment)
For the final project: More about pointing out errors in arguments:
Day 21: M 11/18 Semantics.
  • Basic truth-conditional extensional semantics
  • Restrictiveness, in terms of semantics and punctuation
  • Finish the exercises on the handout given in class. You might want to look a bit more at Fromkin for this.
  • Reread your prescriptivism paper and look carefully at my feedback.
  • For Wednesday, please think more about your paper topic and do a bit of preliminary research on some potential topics. If you have one, please bring either a laptop or a tablet to class, since we'll talk a bit about internet research. (If you don't have access to one, that's fine; just let me know by email the night before.)
Day 22: W, 11/20 Pragmatics
  • How to do research
  • Presupposition
  • Peer Review
(See also the HW assigned on M 11/18 for things to bring to class)
  • Fromkin et al., Introduction to Language, excerpt on presupposition
Day 23: M, 11/25 Pragmatics
  • Gricean Implicature
  • Betty Birner, Introduction to Pragmatics, excerpts from chapter 2 on Gricean implicature, pp. 40-62. Note that this is difficult material; you'll want to read it a few times. You might also want to google "Gricean implicature" and take a look at other resources.
  • Optional: Read Grice's original paper
  • For Wednesday's class, bring in a short excerpt (anywhere from a paragraph to a few pages in length) from some great writing that you love, fiction or non-fiction, poetry or prose.
  • For students who are going to miss Wednesday's class due to Thanksgiving travels:

    (a) Send me an excerpt of great writing (from the above), along with a paragraph about why you like it. (b) For each of the three readings for Wednesday's class, write a paragraph or two explaining what you think the author was trying to accomplish in the essay. This isn't necessarily easy; you'll have to read carefully. Do a good job on this to show your engagement! (c) Write a few sentences reflecting on these articles. Did you like them? Why or why not?

    Please make sure that your responses are carefully proofread, and send them to me by email by Tuesday, 12/3, at 5pm at the latest. I'd strongly recommend you do these this week, since next week will be busy.
Day 24: W 11/27 Style
  • discussion of great writing
Note: These remaining classes are some of the last opportunities to show strong engagement with the readings in class. I do notice who seems to have been engaged with the reading. My main metric for assessing this is noticing who seems to be engaged in the classroom discussion, so make sure to speak up!

Today, we're going to take a break from what we've been doing all semester and simply read and discuss some examples of great writing. While we've emphasized Orwell's windowpane theory of prose this semester, great prose writing of course does do more than that metaphor suggests. I hope you enjoy these samples of great prose, and think about what sorts of models you want to aspire to as a writer. We'll also share some of the writings you have brought in. As you do these readings, think about what makes them distinctively stylistically.
  • Fill out the course evals by the end of the semester. Please be detailed in your comments; they are very helpful. To ensure that you all fill these out, I'm requiring that you email me a copy of your confirmation page. (Don't worry, the evals are completely anonymous, and I can't see them until after I submit your grades.) The evals close December 12. It's fine if you want to hold off filling them out until closer to the end of the semester, but please fill them out by December 11 at the latest.
Day 25: M 12/2 Math in Society
  • Course evals
  • Work on final projects!
Day 26: W 12/4 Economic Reasoning
Day 27: M 12/9 Peer Review
  • peer review of final projects
None. (Work on your projects!)
  • Course evals
  • Peer review response (by Thursday--email me by then if both partners agree to do it later)
Day 28: W 12/11 Conclusion: On College; On The Good Life
  • Conclusion
  • Remember to fill out course evals by tonight
  • Final Self-Reflection
  • Once you have free time/are done with finals, read the Zadie Smith essay
  • Good luck on finals, in the rest of college, and beyond!

An incomplete list of miscellaneous things I hope to fit in at some point and/or would think about including in a future iteration:

Go back to my homepage.
All material copyright (c) 2013, Rafe Kinsey.
Last modified: Thu Dec 19 16:02:35 EST 2013