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:
“Systematic philosophical and practical anti-intellectualism such as we are witnessing appears to be something truly novel in the history of human culture.”
—Johan Huizinga (1872–1945)
“Strange, that some of us, with quick alternate vision, see beyond our infatuations, and even while we rave on the heights, behold the wide plain where our persistent self pauses and awaits us.”
—George Eliot [Mary Ann (or Marian)
“I would to God thou and I knew where a commodity of good names were to be bought.”
—William Shakespeare (1564–1616)