My high school calculus teacher, Kathy Trier, invited our class to write math-themed versions of Christmas carols, inspired by Dennis Gagnon's parodies. I was more than happy to do so, and ever since then, I've branched out from calculus to even higher math, with more parodies every year. However, my range of available carols to plagiarize grows smaller just as my mathematical jokes grow more obscure.

This PDF file includes all the carols (with some slight edits in the intervening years, but mostly the old versions). The tracklisting to date reads as follows:

• 'Twas Just Before the Winter Break ('Twas In The Moon Of Wintertime)
• The First Derivative (The First Noel)
• We Three Dimensions (We Three Kings)
• What Function Is This? (What Child Is This)
• Hark! The AP Proctors Sing (Hark, The Herald Angels Sing)
• O Sum All Your Data (O Come, All Ye Faithful)
• O Little Open Interval (O Little Town of Bethlehem)
• Look at the Board (People, Look East)
• All the Spivak I've Forgotten (Of The Father's Love Begotten)
• Joy to the Set (Joy to the World)
• Creator Alme Siderum (Complex Analysis version)
• Infant Holy, Infant Lowly (Mathematical Logic version)
• The Friendly Beasts (Abstract Algebra version)
• The Gentzen and the Hilbert (The Holly and the Ivy)

Here are my two most recent songs, based on my first-year sequences at UCLA.

THE FRIENDLY BEASTS

Math goes beyond just humankind.
Not just I have it on my mind.
The friendly beasts do too, I find,
When I do math, so good and kind.

"I," said the cow, with rib so prime,
"Like differentiating. I'm
Able to do it in no time!
I," said the cow, with rib so prime.

"I," said the pig, with yellow snout,
"Will tell you what calc's all about!
I'll prove it all, so you won't doubt.
I," said the pig with yellow snout.

"I," said the pigeon in the hole
"Will fill things up to meet your goal.
I make things fit, since that's my role.
I," said the pigeon in the hole.

"I," said the cat, "will make you cram,
Chase arrows in a diagram
That's how generalized I am.
I," said the cat, "will make you cram."

Thus every beast said "Stop all that
You're just an abstract nonsense cat!
So be you skeletal or fat
You're just an abstract nonsense cat!"

THE GENTZEN AND THE HILBERT (The Holly and the Ivy)

The Gentzen and the Hilbert, when they are written down
Of all the trees that are used for proofs, the Gentzen bears the crown.

Chorus:
The rising of the parents that sit above an "or"
Contracting of the duplicates when many came before.
(Chorus)

The axioms bear theorems, each axiom is sound
And we need some restrictions when the variable's bound.
(Chorus)

The Gentzen bears lots of proofs, with all of its might.
The GI doesn't bear as much; it uses less on the right.
(Chorus)

The Gentzen bears midsequents in proofs that are normal
And we must grin and bear it when logic feels too formal.
(Chorus)

"Exists-elimination" will introduce "exists"
And this makes me so furious that I have to shake my fists.
(Chorus)