Abstract Algebra

Rutgers MATH 451, Fall 2020.
Abstract Algebra

An Element of the Braid Group
Lecture 1: The concept of a group in some context.
Lecture 2: Subgroups, particular of the additive integers.
Lecture 3: Some groups. Isomorphisms and automorphisms.
Lecture 4: Actions!
Lecture 5: More actions! Introduction to normal subgroups.
Lecture 6: Quotients!
Lecture 7: Quotients of sets and groups and an isomorphism theorem.
Lecture 8: Yet more quotients, the (acutal) first isomorphism theorem, and introduction to symmetries.
Lecture 9: Symmetries of Euclidean space in general.
Lecture 10: Symmetries of the plane.
Lecture 11: Symmetries of the plane, final chapter.
Lecture 12: The wild world of higher dimensional symmetries.
Lecture 13: Permutations.
Lecture 14: Conjugacy classes.
Lecture 15: Conjugacy classes: finishing with the icosahedron, p-groups.
Lecture 16: The long march to Sylow, part 1: Cauchy's Theorem.
Lecture 17: The long march quick sprint to Sylow, part 2: Almost all the Sylow Theorems.
Lecture 18: Sylow recap, and some small groups.
Lecture 19: Sylow recap, and some tricks.
Lecture 20: More Sylow tricks.
Lecture 21: Semidirect products.
Lecture 22: Field Theory.
Lecture 23: Bilinear forms on vector spaces, part 1.
Lecture 24: Bilinear forms on vector spaces, part 2.
Lecture 25: Matrix groups and finite groups of Lie type.
Lecture 26: Matrix groups, Lie algebras, and quasi-legal algebraic differentiation.
Lecture 27: Mostly SU(2) and SO(3).