Hamilton Day

No, not that Hamilton.

Courtesy of Slate magazine and mathematics journalist Katharine Merow: Today is the anniversary of the great insight that led William Rowan Hamilton to the discovery of quaternions. Details can be found here: http://www.slate.com/articles/health_and_science/science/2016/10/we_should_celebrate_hamilton_day_a_mathematical_holiday_on_oct_16.html

Or the day can be celebrated in song:

Thoughts on Silly Viral Math Puzzles

I’ve seen silly math puzzles like this one spawn incredible flame wars on social media, and for months I’ve wanted to write an article about how much I’ve grown to loath these viral math posts.

Of course, after months of dilly-dallying, someone else beat me to it: http://horizonsaftermath.blogspot.com/2017/08/sick-of-viral-math.html. I encourage you to read the whole thing, but here’s the post’s outline of the myths perpetuated by these puzzles:

  1. Math is just a bag of tricks.
  2. Math is memorizing a set of rules.
  3. Math problems have only one right answer.
  4. Being smart means solving problems quickly.
  5. Math is not for you.

 

My Favorite One-Liners: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on my favorite one-liners.

Mathematical Wisecracks for Almost Any Occasion: Part 2Part 7, Part 8, Part 12, Part 21, Part 28, Part 29, Part 41, Part 46, Part 53, Part 60, Part 63, Part 65, Part 71, Part 79, Part 84, Part 85, Part 100, Part 101Part 108

All-Purpose Anecdotes: Part 38, Part 50, Part 64, Part 70, Part 92, Part 94

Addressing Misconceptions: Part 3Part 4Part 11, Part 14, Part 15, Part 18, Part 30, Part 32, Part 33, Part 37, Part 45, Part 59

Tricky Steps in a Calculation: Part 5, Part 6

Greek alphabet and choice of variables: Part 40, Part 43, Part 56

Homework and exams: Part 39Part 47, Part 55, Part 57, Part 58, Part 66, Part 77, Part 78, Part 91, Part 96, Part 97, Part 107

Inequalities: Part 99

Simplification: Part 10, Part 102, Part 103

Polynomials: Part 19, Part 48, Part 49, Part 81, Part 90

Inverses: Part 16

Exponential and Logarithmic Functions: Part 1, Part 42, Part 68, Part 80

Trigonometry: Part 9, Part 69, Part 76, Part 106

Complex numbers: Part 54, Part 67, Part 86

Sequences and Series: Part 20, Part 35

Combinatorics: Part 27

Statistics: Part 22, Part 23, Part 36, Part 51, Part 52, Part 61, Part 95

Probability: Part 26, Part 31, Part 62, Part 93

Calculus: Part 24, Part 25, Part 72, Part 73, Part 74, Part 75, Part 83, Part 87, Part 88, Part 104

Logic and Proofs: Part 13, Part 17Part 34, Part 44, Part 89, Part 98

Differential Equations: Part 82, Part 105

 

 

 

 

 

 

 

 

 

The Continuing Conflict Between Mathematics and Femininity

From a compelling opinion piece from Inside Higher Education:

The Continuing Conflict Between Mathematics and Femininity

Researchers have examined women’s experiences within the classroom and in professional settings in an effort to understand why and how young women become alienated from mathematics. The most interesting manifestation of this work looks specifically at how our culture constructs femininity and mathematics as mutually exclusive — in ways that ensure that girls and women have a difficult time understanding themselves as mathematical knowers.

Young female mathematics students feel forced to choose between their femininity and their identity as mathematicians. In interview transcripts, they either defend their talent as mathematicians in spite of their femininity or claim their identity as women while explaining away their mathematical achievements. But they clearly do not have the cultural tools available to reconcile both aspects of their identity. Some have argued that this may be one reason why young women who have achieved great success in the field nevertheless drop out of mathematics after secondary school.

We need to tell different stories to expand our cultural understanding of who can engage in mathematics.

I recommend reading the entire opinion piece.

Jobs in Mathematics

 

Courtesy of the Mathematical Association of America, here are some resources for finding a career in the mathematical sciences: http://www.maa.org/news/quantitative-careers-get-your-piece-of-the-math-jobs-pie

I’ll also link to the list of resources that my university provides to our math majors: http://math.unt.edu/support-math-department/careers-mathematics

A quick programming note: after 4 years (or roughly 1,500 consecutive days of posts), I’m going to be switching to posting on Mondays and Fridays. I recently moved to an administrative appointment at my university, and found through the school of hard knocks that I’m not going to be able to sustain daily posts while also doing my day job.

Predicate Logic and Popular Culture (Part 153): The Eagles

Let W(t) be the proposition “I try to walk away at time t,” and let S(x,t) be the proposition “At time t, $latex x makes me turn around and stay.” Translate the logical statement

\forall t (W(t) \rightarrow \exists x (S(x,t))).

This matches the opening lines of “I Can’t Tell You Why,” by the Eagles.

green line

Context: 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 152): Stevie Wonder

Let Z(x) be the proposition “We are amazed by x,” let A(x) be the proposition “We are amused by x, and let D(x) be the proposition “x is a thing you say you’ll do.” Translate the logical statement

\forall x (D(x) \Rightarrow Z(x) \land \lnot A(x)).

This matches the opening line of “You Haven’t Done Nothin'” by Stevie Wonder.

green line

Context: 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 151): Carly Rae Jepsen

Let L(x) be the proposition “I can have x,” and let D(x) be the proposition “You will do x.” Translate the logical statement

\lnot \exists x(\lnot L(x)) \land \lnot \exists x (\lnot D(x)).

This matches a line (complete with double negatives) from E-MO-TION by Carly Rae Jepsen.

green line

Context: 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 150): Katy Perry

Let S(x) be the proposition “I stood for x,” and let F(x) be the proposition “I fell for x.” Translate the logical statement

\forall x (\lnot S(x)) \land \forall x(F(x)).

This matches one of the lines in Katy Perry’s smash hit “Roar.”

green line

Context: 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 149): Adele

Let L(t) be the proposition “At time t, it lasts in love,” and let H(t) be the proposition “At time t, it hurts in love.” Translate the logical statement

\exists t_1 (L(t_1)) \land \exists t_2 (H(t_2)).

This matches part of “Someone Like You,” by Adele.

green line

Context: 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.