Author: John Quintanilla

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.

Predicate Logic and Popular Culture (Part 271): Pirates of the Caribbean

Let T be the set of all times, and let D(t) be the statement “At time t, you can trust a dishonest man to be dishonest.” Translate the logical statement

\forall t \in T (D(t))

This matches a line from the movie “Pirates of the Caribbean: The Curse of the Black Pearl.”

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Context: 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.

Predicate Logic and Popular Culture (Part 270): Naruto Shippuden

Let P be the set of all places, let L(x) be the statement “There is light at x,” and let S(x) be the statement “There are shadows to be found at x.” Translate the logical statement

\forall x \in P (L(x) \Longrightarrow S(x))

This matches one of the lines from the anime “Naruto Shippuden.”

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Context: 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.

Predicate Logic and Popular Culture (Part 269): Hamilton

Let p be the statement “We lay a strong enough foundation,” let q be the statement “We’ll pass it on to you,” let r be the statement “We’ll give the world to you,” and let s be the statement “You’ll blow us all away.” Translate the logical statement

p \Longrightarrow q \land r \land s

This matches one of the lines from the lullaby “Dear Theodosia” from the hit musical “Hamilton.”

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Context: 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.

Wonderful quote from College Mathematics Journal

As a member of the Mathematical Association of America, one of the journals that I subscribe to is College Mathematics Journal. Of late, there has been a pleasant uptick in the number of articles that have been co-written by undergraduate researchers under the mentorship of faculty advisers, which is a terrific development for the field.

In the latest issue, one such article on knot theory appeared. Truth in advertising: I know next to nothing about knot theory, I do not know the authors, and I’ve only driven through Colorado College while on a recent vacation to Colorado Springs. With all that said, I love the opening paragraphs of their recent article, which are shown below.

The first sentence of the second paragraph grabbed my attention:

The other author, undeterred by the challenge of a long standing open problem, decided she wanted to look at this question for her senior thesis.

I absolutely love the moxie behind this sentiment. For the little it’s worth, I offer my congratulations to both authors.

More truth in advertising: usually, when I see a journal article that’s outside my realm of expertise, I’ll make a half-hearted stab at scanning it; with rare exceptions, I then give up and move on to the next article. For this article, however, given this wonderful introduction, I’ll do my best to read and (try to) understand the full article.

Predicate Logic and Popular Culture (Part 268): Eurhythmics

Let T be the set of all things, let D(x) be the statement “x is a sweet dream,” and let M(x) be the statement “x is made of this.” Translate the logical statement

\forall x \in T (D(x) \Longrightarrow M(x))

This matches the title and opening line of “Sweet Dreams are Made of This” by Eurythmics.

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Context: 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.

Predicate Logic and Popular Culture (Part 267): Sherlock Holmes

Let P be the set of all people, let G(x) be the statement “x possesses genius,” and let S(x) be the statement “x has a remarkable power of stimulating genius.” Translate the logical statement

\exists x \in P \exists y \in P (\sim G(x) \land \sim G(y) \land S(x) \land S(y) \land x \ne y)

This matches one of Sherlock Holmes’ back-handed compliments to Mr. Watson in Chapter 1 of The Hound of the Baskervilles.

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Context: 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.

Predicate Logic and Popular Culture (Part 266): The Beach Boys

Let P be the set of all people, let W be the set of all places, let K(x,y) be the statement “x knows y,” and let L(y) be the statement “y is a little place like Kokomo.” Translate the logical statement

\forall x \in P \exists y \in W (K(x,y) \land L(y))

This matches a line from the classic song “Kokomo” by the Beach Boys.

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Context: 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.

Predicate Logic and Popular Culture (Part 265): Paul Young

Let T be the set of all times, let G(t) be the statement “You go away at time t,” and let P(t) be the statement “You take a piece of me with you at time t.”  Translate the logical statement

\forall t \in T (G(t) \Longrightarrow P(t))

This matches the chorus from “Every Time You Go Away” by Paul Young.

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Context: 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.