Course

MATH-310: Algebra

Lectures in this course (38)

Introduces integer numbers, well-ordering, induction principles, GCD, LCM, and Bezout's theorem.

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Delves into the symmetries of regular polygons, including the dihedral group and left cosets in a finite group.

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.

Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Discusses integral domains, abelian groups, invertibility, zero divisors, prime elements, and group classification.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

Explores the Chinese remainder theorem, systems of congruences, and Euclidean domains in integer numbers and polynomial rings.

Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.