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 and, history, alternate and/or names:
“Modern Western thought will pass into history and be incorporated in it, will have its influence and its place, just as our body will pass into the composition of grass, of sheep, of cutlets, and of men. We do not like that kind of immortality, but what is to be done about it?”
—Alexander Herzen (1812–1870)
“The history of all previous societies has been the history of class struggles.”
—Karl Marx (1818–1883)
“I alternate between reading cook books and reading diet books.”
—Mason Cooley (b. 1927)
“Every man who has lived for fifty years has buried a whole world or even two; he has grown used to its disappearance and accustomed to the new scenery of another act: but suddenly the names and faces of a time long dead appear more and more often on his way, calling up series of shades and pictures kept somewhere, “just in case” in the endless catacombs of the memory, making him smile or sigh, and sometimes almost weep.”
—Alexander Herzen (1812–1870)