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Title : 18.702 Algebra II (MIT)

Title : 18.702 Algebra II (MIT)

Description : The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.

Description : The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.

Fromsemester : Spring

Fromsemester : Spring

Fromyear : 2003

Fromyear : 2003

Creator :

Creator :

Date : 2009-06-19T07:45:49+05:00

Date : 2009-06-19T07:45:49+05:00

Relation : 18.702

Relation : 18.702

Language : en-US

Language : en-US

Subject : Sylow theorems

Subject : Sylow theorems

Subject : Group Representations

Subject : Group Representations

Subject : definitions

Subject : definitions

Subject : unitary representations

Subject : unitary representations

Subject : characters

Subject : characters

Subject : Schur's Lemma

Subject : Schur's Lemma

Subject : Rings: Basic Definitions

Subject : Rings: Basic Definitions

Subject : homomorphisms

Subject : homomorphisms

Subject : fractions

Subject : fractions

Subject : Factorization

Subject : Factorization

Subject : unique factorization

Subject : unique factorization

Subject : Gauss' Lemma

Subject : Gauss' Lemma

Subject : explicit factorization

Subject : explicit factorization

Subject : maximal ideals

Subject : maximal ideals

Subject : Quadratic Imaginary Integers

Subject : Quadratic Imaginary Integers

Subject : Gauss Primes

Subject : Gauss Primes

Subject : quadratic integers

Subject : quadratic integers

Subject : ideal factorization

Subject : ideal factorization

Subject : ideal classes

Subject : ideal classes

Subject : Linear Algebra over a Ring

Subject : Linear Algebra over a Ring

Subject : free modules

Subject : free modules

Subject : integer matrices

Subject : integer matrices

Subject : generators and relations

Subject : generators and relations

Subject : structure of abelian groups

Subject : structure of abelian groups

Subject : Rings: Abstract Constructions

Subject : Rings: Abstract Constructions

Subject : relations in a ring

Subject : relations in a ring

Subject : adjoining elements

Subject : adjoining elements

Subject : Fields: Field Extensions

Subject : Fields: Field Extensions

Subject : algebraic elements

Subject : algebraic elements

Subject : degree of field extension

Subject : degree of field extension

Subject : ruler and compass

Subject : ruler and compass

Subject : symbolic adjunction

Subject : symbolic adjunction

Subject : finite fields

Subject : finite fields

Subject : Fields: Galois Theory

Subject : Fields: Galois Theory

Subject : the main theorem

Subject : the main theorem

Subject : cubic equations

Subject : cubic equations

Subject : symmetric functions

Subject : symmetric functions

Subject : primitive elements

Subject : primitive elements

Subject : quartic equations

Subject : quartic equations

Subject : quintic equations

Subject : quintic equations