ｷRevisiting the arithmetic and
algebra of the integers and the integers modulo *n*

ｷReviewing some basic ring theory
(ideals, quotient rings, fields)

ｷDefining polynomials, polynomial
functions, and polynomial rings

ｷArithmetic in *k*[*x*], *k* a field (comparing it with the ring
of integers)

oDivision algorithm

oUnique factorization (FT of
Arithmetic)

oIrreducibility in Q[*x*], R[*x*] and C[*x*] (FT of Algebra)

oStructure of *k*[*x*]/(*p*(*x*)) (e.g., R[x]/(x2+1) and Z2[x]/(x2+x+1))

oAlgebraic and transcendental
extensions

o Elementary
Galois theory

ｷ Polynomial
rings over commutative rings

oDivision algorithm

o Unique
factorization

ｷPolynomial applications
(mathematical-Òreal worldÓ) appropriate for the secondary curriculum (this will
involve a review of the research literature)