0

(

ratings

)

2

students

Created by:

Profile Photo

Last updated:

September 23, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Math E-222 - Abstract Algebra (Fall 2003, Harvard Extension School). Instructor: Professor Benedict Gross. Algebra is the language of modern mathematics.

This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields. Topics include: Review of Linear Algebra; Permutations; Quotient Groups, First Isomorphism Theorem; Abstract Linear Operators and How to Calculate with Them; Orthogonal Groups; Isometrics of Plane Figures; Group Actions; A5 and the Symmetries of an Icosahedron; Rings; Euclidean Domains, PIDs, UFDs; and Structure of Ring of Integers in a Quadratic Field.

Course Curriculum

    • Lecture 01 – Introduction to the Course; Review: Linear Algebra; Definition of Groups Unlimited
    • Lecture 02 – Generalities on Groups; Examples of Groups Unlimited
    • Lecture 03 – Isomorphisms; Homomorphisms; Images Unlimited
    • Lecture 04 – Review, Kernels, Normality; Examples; Centers and Inner Autos Unlimited
    • Lecture 05 – Equivalence Relations; Cosets; Examples Unlimited
    • Lecture 06 – Congruence Mod n; (Z/nZ)* Unlimited
    • Lecture 07 – Quotients Unlimited
    • Lecture 08 – More on Quotients; Vector spaces Unlimited
    • Lecture 09 – Vector spaces (cont.) Unlimited
    • Lecture 10 – Bases and Vector spaces; Matrices and Linear Transformations Unlimited
    • Lecture 11 – Bases; Matrices Unlimited
    • Lecture 12 – Eigenvalues and Eigenvectors Unlimited
    • Lecture 13 – Review for Midterm; Orthogonal Group Unlimited
    • Lecture 14 – Orthogonal Group and Geometry Unlimited
    • Lecture 15 – Finite Groups of Motions Unlimited
    • Lecture 16 – Discrete Groups of Motions Unlimited
    • Lecture 17 – Discrete Groups of Motions; Abstract Group Actions Unlimited
    • Lecture 18 – Group Actions Unlimited
    • Lecture 19 – Group Actions (cont.) Unlimited
    • Lecture 20 – Group Actions: Sylow Theorems Unlimited
    • Lecture 21 – Group Actions: Sylow Theorems (continued), Classification Theorems Unlimited
    • Lecture 22 – Group Actions: The Symmetric Group, Conjugation, S5 Classes Unlimited
    • Lecture 23 – Alternating Group Structure Unlimited
    • Lecture 24 – Rings Unlimited
    • Lecture 25 – Rings (cont.) Unlimited
    • Lecture 26 – R Commutative Ring, Quotient Rings and Isomorphisms Unlimited
    • Lecture 27 – Examples of Rings Unlimited
    • Lecture 28 – Rings: Review Unlimited
    • Lecture 29 – Quotient Rings, Integral Domains, Fields of Fractions Unlimited
    • Lecture 30 – Domains and Factorization in Z, Euclidean Algorithm Unlimited
    • Lecture 31 – Domains and Factorization in Z (cont.), Gauss’ Lemma Unlimited
    • Lecture 32 – Gaussian Integers Unlimited
    • Lecture 33 – Gauss’ Lemma, Eisenstein’s Criterion, Algebraic Integers Unlimited
    • Lecture 34 – Gauss’ Lemma, Eisenstein’s Criterion, Algebraic Integers (cont.) Unlimited
    • Lecture 35 – Prime and Maximal Ideals, Dedekind Domains, Class Groups Unlimited
    • Lecture 36 – Dedekind Domains, Ideal Class Groups Unlimited
    • Lecture 37 – Review 1 Unlimited
    • Lecture 38 – Review 2 Unlimited

About the instructor

5 5

Instructor Rating

6

Reviews

4637

Courses

24151

Students

Profile Photo
OpenCoursa
We are an educational and skills marketplace to accommodate the needs of skills enhancement and free equal education across the globe to the millions. We are bringing courses and trainings every single day for our users. We welcome everyone woth all ages, all background to learn. There is so much available to learn and deliver to the people.