Intro Modern Algebra II · Mathematics
Rings and Fields, as well as some advanced Linear Algebra. Towards the end, we tied it all together with Group Theory.
Proofs and theorems related to group theory, factorization and Galois
Standard introductory algebra: rings, fields, galois theory.
Very important course to learn ring, field, Galois Theory.
Basic ring theory, theory of fields, extensions, finite extensions, Galois extensions, Galois theory, insolvability of the quintic. Towards the end we covered introductory module theory.
I'll just copy and paste the syllabus topics: Rings and commutative rings. Rings of polynomials, residues modulo n and other examples. Matrix rings. Integral domains and fields. Field of fractions. Homomorphisms of rings and ideals. Quotient rings and First Isomorphism Theorem for rings. Principal ideal domains and polynomial rings over fields. Prime and maximal ideals. Irreducible polynomials. Euclidean domains and unique factorization domains. Characteristic of a field. Finite fields. Linear algebra over a field. Field extensions and splitting fields. Field extensions of field automorphisms. Galois group. Solvability by Radicals. Ruler and compass constructions. Independence of characters. Galois' Theorems. Applications. Fundamental Theorem of Algebra. Applications of finite fields.
Rings, Fields, Polynomials, and some Galois Theory
Rings, Fields, Ideals, Integral Domains, Field extensions, Algebraic vs Transcendental, Algebraic closure, Normal and Separable Extensions, Isomorphisms, Galois Theory, Quintic being unsolvable, Polynomials over different fields, Determinant, and Irreducibility. Review of Modern Algebra 1 material used throughout.
this is a great introduction all the way through Rings, fields, polynomial rings, fields extensions, Galois theory. it's a great course and well organized
I learned about how polynomials are not necessarily functions, rings, fields, field extensions, factorization of polynomials, Galois theory