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Abstract Algebra
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This module aims to acquaint you with the mathematical aspects of rings and groups and the underlying algebraic structures and when they are looked at as non-empty sets, how their elements are combined by binary operations as well as how those elements behave under transformations such finding inverses. Some non-empty sets, under the operation of addition or multiplication do not include the inverses of their elements as members of the set and they are called semi-groups. The non-empty sets that include the inverses of their elements are full fledged groups. This module fills the gap arising from basic mathematics.

Subject:
Algebra
Material Type:
Module
Provider:
African Virtual University
Provider Set:
OER@AVU
Author:
Othow Onak Giel
Date Added:
03/10/2018
Abstract Algebra Course Content
Conditional Remix & Share Permitted
CC BY-NC
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The Abstract Algebra course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in September 2019. Team LeadAnna Davis                                         Ohio Dominican UniversityContent ContributorsMatt Davis                                          Muskingum UniversityRob Kelvey                                        College of WoosterLibrarianDaniel Dotson                                    Ohio State University                     Review TeamJim Cottrill                                          Ohio Dominican UniversityBart Snapp                                          Ohio State University

Subject:
Mathematics
Algebra
Material Type:
Full Course
Provider:
Ohio Open Ed Collaborative
Date Added:
05/06/2021
Abstract Algebra II
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CC BY
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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)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
10/24/2019
Abstract Algebra: Theory and Applications
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This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

Subject:
Algebra
Material Type:
Textbook
Provider:
University of Puget Sound
Author:
Thomas Judson
Date Added:
01/01/2016
Advanced Partial Differential Equations with Applications, Fall 2009
Conditional Remix & Share Permitted
CC BY-NC-SA
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" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Rosales, Rodolfo R.
Date Added:
01/01/2009
Algebra
Unrestricted Use
CC BY
Rating

This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
10/24/2019
Algebra II, Spring 2011
Conditional Remix & Share Permitted
CC BY-NC-SA
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This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Artin, Michael
Date Added:
01/01/2011
Algebra and Trigonometry
Unrestricted Use
CC BY
Rating

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

Subject:
Algebra
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
David Lippman
Jay Abramson
Jean-Marie Magnier
Melonie Rasmussen
Nicholas Belloit
Rachael Gross
Rick Norwood
Valeree Falduto
Date Added:
01/29/2015