Abstract Algebra II

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Subject:

Mathematics and Statistics

Institution Name:

The Saylor Foundation

Collection:

Saylor Foundation

Grade Level:

Post-secondary

Abstract:

This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)

Languages:

English

Material Type:

Assessments, Full Course, Homework and Assignments, Readings, Syllabi, Textbooks, Video Lectures

Media Format:

Text/HTML, Downloadable docs, Video

Conditions of Use:

Creative Commons Attribution-Noncommercial 3.0
You are welcome to share, remix, and adapt this course under the terms of the Creative Commons Attribution 3.0 Unported License; however, many linked materials within this course are copyright of their respective authors/owners and may not be openly-licensed. Please respect the copyright and terms of use associated with each resource.

Copyright Holder:

The Saylor Foundation