History and Alternate Names
The history of the term "freshman's dream" is somewhat unclear. In a 1940 article on modular fields, Saunders Mac Lane quotes Stephen Kleene's remark that a knowledge of (a + b)2= a2 + b2 in a field of characteristic 2 would corrupt freshman students of algebra. This may be the first connection between "freshman" and binomial expansion in fields of positive characteristic. Since then, authors of undergraduate algebra texts took note of the common error. The first actual attestation of the phrase "freshman's dream" seems to be in Hungerford's undergraduate algebra textbook (1974), where he quotes McBrien. Alternative terms include "freshman exponentiation", used in Fraleigh (1998). The term "freshman's dream" itself, in non-mathematical contexts, is recorded since the 19th century.
Since the expansion of (x + y)n is correctly given by the binomial theorem, the freshman's dream is also known as the "Child's Binomial Theorem" or "Schoolboy Binomial Theorem".
Read more about this topic: Freshman's Dream
Famous quotes containing the words history, alternate and/or names:
“The whole history of civilisation is strewn with creeds and institutions which were invaluable at first, and deadly afterwards.”
—Walter Bagehot (1826–1877)
“It might become a wheel spoked red and white
In alternate stripes converging at a point
Of flame on the line, with a second wheel below,
Just rising, accompanying, arranged to cross,
Through weltering illuminations, humps
Of billows, downward, toward the drift-fire shore.”
—Wallace Stevens (1879–1955)
“If goodness were only a theory, it were a pity it should be lost to the world. There are a number of things, the idea of which is a clear gain to the mind. Let people, for instance, rail at friendship, genius, freedom, as long as they will—the very names of these despised qualities are better than anything else that could be substituted for them, and embalm even the most envenomed satire against them.”
—William Hazlitt (1778–1830)