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 history of reform is always identical; it is the comparison of the idea with the fact. Our modes of living are not agreeable to our imagination. We suspect they are unworthy. We arraign our daily employments.”
—Ralph Waldo Emerson (1803–1882)
“In museums and palaces we are alternate radicals and conservatives.”
—Henry James (1843–1816)
“Far from being antecedent principles that animate the process, law, language, truth are but abstract names for its results.”
—William James (1842–1910)