Irreducibility and the Schoenemann-Eisenstein Criterion - Famous Math Problems 20

Explore the concepts of irreducibility and the Schoenemann-Eisenstein criterion in this 30-minute mathematics lecture. Delve into the definition and computation of cyclotomic polynomials, examining Gauss's lemma and its connection between irreducibility over integers and rational numbers. Learn about T. Schoenemann's irreducibility criterion, which utilizes mod p arithmetic for prime p, and its application to cyclotomic polynomials indexed by a prime. Discover how this criterion establishes Eisenstein's criterion, gaining valuable insights into advanced mathematical concepts and their interrelationships.