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This course develops polynomial-ring techniques including division, gcd computations, irreducibility tests, and PID structure. It also constructs a field of order 4.
Syllabus
Abstract Algebra | The division algorithm for polynomials..
Abstract Algebra | Writing the gcd of polynomials as a combination..
Abstract Algebra | Writing the gcd of polynomials as a combination..
Abstract Algebra | Irreducible polynomials.
Abstract Algebra | Eisenstein's criterion.
Abstract Algebra | Writing a polynomial gcd as a combination -- example..
Abstract Algebra | Constructing a field of order 4..
Abstract Algebra | k[x] is a PID.
Taught by
Michael Penn