Friday, April 23, 2010

Poems of Calculus

In her thoughtful poem "Calculus" mathematician-poet Sarah Glaz writes of sharing with her students some of their subject's history--a drama enacted by two different sorts of mathematician.  Here are Glaz' opening lines:

I tell my students the story of Newton versus Leibniz,
the war of symbols, lasting five generations,
between The Continent and British Isles,
involving deeply hurt sensibilities,
and grievous blows to national pride;
on such weighty issues as publication priority
and working systems of logical notation:
whether the derivative must be denoted by a "prime,"
an apostrophe atop the right hand corner of a function,
evaluated by Newton's fluxions method, Δy/Δx;
or by a formal quotient of differentials dy/dx,
intimating future possibilities,
terminology that guides the mind.

Here's a link to the full text of "Calculus."  Although lines 8-11 of the 13 lines above may puzzle readers unfamiliar with calculus, even without perfect understanding, the nature of the struggle Glaz is describing seems clear--and reading it can offer new insights.  And for students enrolled in calculus classes, awareness of the historial struggles associated with their subject may add perspective to their own labors.
Much of the poetry involving mathematical topics beyond numbers and counting is, as we find in "Calculus," about an encounter with mathematics rather than the subject itself.  Still, math folks sometimes tackle their subject head-on--perhaps softening the encounter by using parody or amusing rhyme, and thereby offer entertaining verse that addresses the subject matter.  Here, for example are the opening lines of "Calculus Advice Poem," written by two students  (Cathy Gellis and Amanda O'Connor) in a California Calculus class. 

Calculus Advice Poem

To whom it may concern,
If it is calculus that you will learn,
Take heed of our advice,
We hope it will suffice.

First some things you'll need to know,
(If you don't, well, we told you so)
Know your algebra very well
Or your life will be a living hell.

Absolute values may look silly, 'tis true,
But unless you know them you won't have a clue.
Geometry will come back to haunt you;
Know it or else this class will daunt you.

Know about functions in relation to sets
(A good thing to know for blondes and brunettes).
A silly rhyme but what else is new?
Now here's more you'll need to review.
   . . .
And here, in a similar spirit, is the first stanza of "Oh, Calculus," by  to be sung to the tune of "Oh, Christmas Tree":

Oh, Calculus; Oh, Calculus
How different seem thy branches.
Oh, Calculus; Oh, Calculus,
How different seem thy branches.
Derivatives tell us the rate.
For areas we integrate.
Oh, Calculus; Oh, Calculus,
How different seem thy branches.
 . . .
The full text of "Oh, Calculus" by Leon Hall and Ilene Morgan (Missouri University of Science and Technology) was published in the American Mathematical Monthly in January 2002 and is available here.  Another version of "Oh, Calculus" by Denis Gannon (1940-91) may be found here and was published in Math Horizons, Winter, 1993.

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