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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
01/09/2019
Rating

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
01/01/2016
Conditional Remix & Share Permitted
CC BY-NC-SA
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To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.​​

Subject:
Algebra
Material Type:
Lesson
Provider:
Provider Set:
Author:
Salman Khan
02/28/2018
Unrestricted Use
CC BY
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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
Trigonometry
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
01/29/2015
Conditional Remix & Share Permitted
CC BY-NC-SA
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College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended).

Subject:
Algebra
Material Type:
Textbook
Provider:
Stitz-Zeager Open Source Mathematics
Author:
Carl Stitz
Jeff Zeager
07/15/2011
Unrestricted Use
CC BY
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College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra 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:
Jay Abramson
11/09/2021
Rating

The College 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. The course is part of the Ohio Transfer Module and is also named TMM001. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadNicholas Shay                                     Central Ohio Technical College (now at Columbus State Community College)Content ContributorsRachida Aboughazi                            Ohio State UniversityEvelyn Kirschner                                Columbus State Community CollegeDavid Kish                                          Ohio Dominican UniversityLibrarianDaniel Dotson                                    Ohio State University                     Review TeamFauna Donahue                                University of Rio GrandeJared Stadden                                   Kent State University Geauga

Subject:
Mathematics
Algebra
Material Type:
Full Course
Provider:
Ohio Open Ed Collaborative
01/09/2019
Conditional Remix & Share Permitted
CC BY-NC
Rating

This material covers Chapter 2: Equations and Inequalities chapter of the OpenStax College Algebra Text. This module contains an overview of learning objectives mapped to the OTM state standards, worksheets that correspond to chapter sections, interactive Desmos Activities that pair with the chapter, and a list of supplemental videos that correspond to the chapter content.Image by Rudy and Peter Skitterians from Pixabay

Subject:
Mathematics
Algebra
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
06/16/2019
Conditional Remix & Share Permitted
CC BY-NC
Rating

This material covers Chapter 3: Functions chapter of the OpenStax College Algebra Text. This module contains an overview of learning objectives mapped to the OTM state standards, worksheets that correspond to chapter sections, interactive Desmos Activities that pair with the chapter, and a list of supplemental videos that correspond to the chapter content.

Subject:
Mathematics
Algebra
Functions
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
06/16/2019
Conditional Remix & Share Permitted
CC BY-NC-SA
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This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.

Subject:
Algebra
Trigonometry
Material Type:
Textbook
Author:
Richard W. Beveridge
04/27/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
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This book was designed as an introductory trigonometry textbook for college students with the explicit goal of reducing textbook costs.

Subject:
Algebra
Trigonometry
Material Type:
Textbook
Provider:
Stitz-Zeager Open Source Mathematics
Author:
Carl Stitz
Jeff Zeager
07/15/2011
Only Sharing Permitted
CC BY-NC-ND
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All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.

Subject:
Mathematics
Algebra
Material Type:
Textbook
Author:
Victor Shoup
01/01/2008
Conditional Remix & Share Permitted
CC BY-NC-SA
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Understanding alternate coordinate systems. Created by Sal Khan.

Subject:
Algebra
Material Type:
Lesson
Provider:
Provider Set:
Author:
Salman Khan
02/28/2018
Conditional Remix & Share Permitted
CC BY-NC-SA
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Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.

Subject:
Algebra
Material Type:
Lesson
Provider:
Provider Set:
Author:
Salman Khan
02/28/2018
Conditional Remix & Share Permitted
CC BY-SA
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This dynamic worksheet illustrates the relationship between the DETERMINANT, the Area of the pre-image, and the Area of the image.

Subject:
Algebra
Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
04/26/2012
Conditional Remix & Share Permitted
CC BY-SA
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Ana Donevska Todorova Humboldt Universitﾊt zu Berlin Mathematisch-Naturwissenschaftliche Fakultﾊt II Institut fﾟr Mathematik, Didaktik der Mathematik ??? ?????????? ?????? ???????? ?? ???????????? ????? ? ????

Subject:
Algebra
Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
03/12/2012
Conditional Remix & Share Permitted
CC BY-SA
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Ana Donevska Todorova Humboldt Universitﾊt zu Berlin Mathematisch-Naturwissenschaftliche Fakultﾊt II Institut fﾟr Mathematik, Didaktik der Mathematik

Subject:
Algebra
Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
03/12/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

Dimension of the Column Space or Rank. Created by Sal Khan.

Subject:
Algebra
Material Type:
Lesson
Provider:
Provider Set:
Author:
Salman Khan
02/28/2018
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

Dimension of the Null Space or Nullity. Created by Sal Khan.

Subject:
Algebra
Material Type:
Lesson
Provider:
Provider Set:
Author:
Salman Khan
02/28/2018
Unrestricted Use
CC BY
Rating

Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.

Subject:
Algebra
Material Type:
Full Course
Textbook
Provider:
Rice University
Provider Set:
OpenStax CNX
Author:
Denny Burzynski
08/16/2010
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.

Subject:
Algebra
Material Type:
Textbook
Provider:
The Saylor Foundation
Author:
John Redden