Course includes: In-depth study of polynomial rings and applications

Revisiting the arithmetic and algebra of the integers and the integers modulo n
Reviewing some basic ring theory (ideals, quotient rings, fields)
Defining polynomials, polynomial functions, and polynomial rings
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
Polynomial rings over commutative rings
oDivision algorithm
o Unique factorization
Polynomial applications (mathematical-real world) appropriate for the secondary curriculum (this will involve a review of the research literature)
Course overview