Predicate Logic and Popular Culture (Part 1)

This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

I’ll begin with a few simple examples to illustrate propositional logic.

Let p be the proposition “I am a crook.” Express the negation \lnot p in ordinary English.

Naturally, the negation is one of the most famous utterances in American political history.

Let p be the proposition “She’s cheer captain,” and let q be the proposition “I’m on the bleachers.” Express the conjunction

p \land q

in ordinary English.

I could have picked just about anything from popular culture to illustrate this idea, but my choice was Taylor Swift’s biggest hit as a country artist (before she switched to pop). The lyric in question is part of the song’s pre-chorus (for example, at the 39 second mark of the video below).

Let p be the proposition “I will get busy living,” and let q be the proposition “I will get busy dying.” Express the disjunction

p \lor q

in ordinary English.

Again, I could have picked almost anything to illustrate disjunctions. My choice comes from a famous scene from The Shawshank Redemption (at the 2:53 mark of the video below — warning, PG language in the rest of the video).

Let p be the proposition “You build it,” and let q be the proposition “He will come.” Express the implication

p \Longrightarrow q

in ordinary English.

Of course, this is the famous catchphrase from Field of Dreams.

One more for today:

Let p be the proposition “You want to roam,” and let q be the proposition “You roam.” Express the implication

p \Longrightarrow q

in ordinary English.

Though the order of the wording is different, this implication is part of the chorus of one of the biggest hits by the B-52s.

Lessons from teaching gifted elementary school students: Index (updated)

I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on various lessons I’ve learned while trying to answer the questions posed by gifted elementary school students. (This is updated from my previous index.)

Part 1: A surprising pattern in some consecutive perfect squares.

Part 2: Calculating 2 to a very large exponent.

Part 3a: Calculating 2 to an even larger exponent.

Part 3b: An analysis of just how large this number actually is.

Part 4a: The chance of winning at BINGO in only four turns.

Part 4b: Pedagogical thoughts on one step of the calculation.

Part 4c: A complicated follow-up question.

Part 5a: Exponentiation is multiplication as multiplication is to addition. So, multiplication is to addition as addition is to what? (I offered the answer of incrementation, but it was rejected: addition requires two inputs, while incrementation only requires one.)

Part 5b: Why there is no binary operation that completes the above analogy.

Part 5c: Knuth’s up-arrow notation for writing very big numbers.

Part 5d: Graham’s number, reputed to be the largest number ever to appear in a mathematical proof.

Another poorly written word problem (Part 3)

Textbooks have included the occasional awful problem ever since Pebbles Flintstone and Bamm-Bamm Rubble chiseled their homework on slate tablets while attending Bedrock Elementary. But even with the understanding that there have been children have been doing awful homework problems since the dawn of time (and long before the advent of the Common Core), this one is a doozy.

There’s no sense having a debate about standards for elementary mathematics if textbook publishers can’t construct sentences that can be understood by elementary students.

diecoin

Careers in Industry for Math Majors

I recently came across an excellent article promoting internships from math majors who would like to use their quantitative skills in an industrial setting (as opposed to an academic setting). The concluding paragraph:

Faculty will continue to train students for academic careers. Some will pursue tenure-track positions in the institutions of their choice, but an increasing number of our students will take positions very different from our own. Let’s learn about those options and share them with our students. Then, when a student takes a good job and enjoys a successful career, let’s call that a win.

 

Here’s the full article: http://www.americanscientist.org/blog/pub/internships-connect-math-students-to-new-career-paths