Ring Theory: Let f(x)=x^5+2x^3+2x^2 + x+2 and g(x)=x^4+2x^3+2x^2 be polynomials over Z/3. Use the Euclidean algorithm to find gcd(f,g), find the prime factorizations of f and g, and find coefficients for Bezout's Identity in this case. We also find a field in which f(x) factors into linear factors.
Includes course on Group Theory (problems and solutions at website) and Ring Theory, and Field Theory. For Prerequisites on proofs and sets, see the Math Major Basics course.