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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
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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:
04/29/2019
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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.

Access also available here: http://abstract.ups.edu/contact.html

Table of Contents
Preliminaries
The Integers
Groups
Cyclic Groups
Permutation Groups
Cosets and Lagrange's Theorem
Introduction to Cryptography
Algebraic Coding Theory
Isomorphisms
Normal Subgroups and Factor Groups
Homomorphisms
Matrix Groups and Symmetry
The Structure of Groups
Group Actions
The Sylow Theorems
Rings
Polynomials
Integral Domains
Lattices and Boolean Algebras
Vector Spaces
Fields
Finite Fields
Galois Theory

Subject:
Algebra
Material Type:
Textbook
Provider:
University of Puget Sound
Author:
Thomas Judson
Date Added:
01/01/2016
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
Unrestricted Use
CC BY
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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:
04/29/2019
Unrestricted Use
CC BY
Rating

This course is oriented toward US high school students. Its structure and materials are aligned to the US Common Core Standards. Foci include: graphing, equations and inequalities.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
04/29/2019
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

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
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.

Table of Contents
1 Prerequisites
2 Equations and Inequalities
3 Functions
4 Linear Functions
5 Polynomial and Rational Functions
6 Exponential and Logarithmic Functions
7 The Unit Circle: Sine and Cosine Functions
8 Periodic Functions
9 Trigonometric Identities and Equations
10 Further Applications of Trigonometry
11 Systems of Equations and Inequalities
12 Analytic Geometry
13 Sequences, Probability, and Counting Theory

Access also available here: https://openstax.org/details/books/algebra-and-trigonometry

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
Date Added:
01/29/2015
Conditional Remix & Share Permitted
CC BY-NC-SA
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" This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Musiker, Gregg
Date Added:
01/01/2009
Conditional Remix & Share Permitted
CC BY-NC-SA
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" This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry."

Subject:
Algebra
Geometry
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kedlaya, Kiran
Date Added:
01/01/2009
Conditional Remix & Share Permitted
CC BY-NC-SA
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In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Behrens, Mark
Date Added:
01/01/2006
Conditional Remix & Share Permitted
CC BY-NC-SA
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Laszlo Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976. Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems. The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface below. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

Subject:
Algebra
Physics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Tisza, L
Date Added:
01/01/2009
Only Sharing Permitted
CC BY-NC-ND
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Arithmetic | Algebra provides a customized open-source textbook for the math developmental students at New York City College of Technology. The book consists of short chapters, addressing essential concepts necessary to successfully proceed to credit-level math courses. Each chapter provides several solved examples and one unsolved “Exit Problem”. Each chapter is also supplemented by its own WeBWork online homework assignment. The book can be used in conjunction with WeBWork for homework (online) or with the Arithmetic | Algebra Homework handbook (traditional). The content in the book, WeBWork and the homework handbook are also aligned to prepare students for the CUNY Elementary Algebra Final Exam (CEAFE).

Subject:
Algebra
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
New York City College of Technology
Author:
Holly Carley
Lin Zhou
Marianna Bonanome
Samar ElHitti
Thomas Tradler
Date Added:
01/01/2017
Only Sharing Permitted
CC BY-NC-ND
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Arithmetic | Algebra Homework book is a static version of the WeBWork online homework assignments that accompany the textbook Arithmetic | Algebra for the developmental math courses MAT 0630 and MAT 0650 at New York City College of Technology, CUNY.

Subject:
Algebra
Material Type:
Homework/Assignment
Provider:
CUNY Academic Works
Provider Set:
New York City College of Technology
Author:
Ariane Masouda
Lin Zhou
Samar ElHitti
Date Added:
01/01/2017
Unrestricted Use
CC BY
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This course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
04/29/2019
Only Sharing Permitted
CC BY-NC-ND
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In this beginning algebra course, you'll learn about
fundamental operations on real numbers
exponents
solving linear equations and inequalities
applications
functions
graphing linear equations
slope
systems of linear equations

Subject:
Algebra
Material Type:
Full Course
Lecture
Module
Provider:
Bossier Parish Community College
Author:
Gail Hendrix
Date Added:
07/15/2020
Read the Fine Print
Educational Use
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This course covers a range of algebraic topics:  Setting up and solving linear equations, graphing, finding linear relations, solving systems of equations, working with polynomials, factoring, working with rational and radical expressions, solving rational and radical equations, solving quadratic equations, and working with functions.  More importantly, this course is intended to provide you with a solid foundation for the rest of your math courses.  As such, emphasis will be placed on mathematical reasoning, not just memorizing procedures and formulas. There is enough content in this course to cover both beginning and intermediate college-level algebra.

Subject:
Algebra
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
Tyler Wallace
Date Added:
04/25/2019
Conditional Remix & Share Permitted
CC BY-NC-SA
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Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus&nbsp;and&nbsp;Multivariable Calculus) before taking this course. The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Herbert Gross
Date Added:
01/01/2011
Read the Fine Print
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This course covers relations and functions, specifically, linear, polynomial, exponential, logarithmic, and rational functions. Additionally, sections on conics, systems of equations and matrices and sequences are also available.

Subject:
Algebra
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
Carl Stitz
Jeff Zeager
Date Added:
04/25/2019
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).

Table of Contents
1 Relations and Functions
2 Linear and Quadratic Functions
3 Polynomial Functions
4 Rational Functions
5 Further Topics in Functions
6 Exponential and Logarithmic Functions
7 Hooked on Conics
8 Systems of Equations and Matrices
9 Sequences and the Binomial Theorem

Subject:
Algebra
Material Type:
Textbook
Provider:
Stitz-Zeager Open Source Mathematics
Author:
Carl Stitz
Jeff Zeager
Date Added:
07/15/2011