Akademik Dersler - İçerik

Will be able to define the concepts of Ring, Integral Domain, and the characteristic of an integral domain, provide examples, and perform related proofs.
Defines the concepts of subring and ideal, provides examples, and performs related proofs.
Defines the concept of quotient ring, provides examples, and performs related proofs.
Defines the concept of principal ideal domain (PID), provides examples, and performs related proofs.
Defines the concepts of homomorphism and isomorphism, provides examples, and performs related proofs.
Will be able to define the concepts of maximal and prime ideals, provide examples, and perform related proofs.
Will be able to define the concepts of polynomials and polynomial rings, provide examples, and perform related proofs.
Learns how to factor a polynomial into primes (prime factors) and provides examples.
Will be able to define the structure and axioms of a field, and prove whether a given abstract algebraic structure is a field.
Will be able to define the concept of a vector space not only over familiar fields such as the real or complex numbers, but over any abstract field, including finite fields.