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Abstract Algebra:  Examples and Applications
Conditional Remix & Share Permitted
CC BY-NC-SA
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This book is designed to make "Abstract Algebra" as down-to-earth as possible. Using concrete examples such as the complex numbers, integers mod n, polynomials, symmetries, and permutations. We also introduce some of the beautifully general ideas of the theory of groups, rings, and fields. Along the way, we give applications to signal processing, cryptography and coding theory, as well as making connections with other branches of mathematics such as geometry and number theory.

The textbook is provided in three different formats: hyperlinked online version, pdf, and spiral bound copy (printme1.com is recommended for on-demand printing).

Subject:
Algebra
Material Type:
Homework/Assignment
Textbook
Author:
Christopher Thron
Justin Hill
Date Added:
06/15/2021
Abstract Algebra: Theory and Applications
Read the Fine Print
Some Rights Reserved
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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
Adding vectors algebraically & graphically
Unrestricted Use
CC BY
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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:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020
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:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Rosales, Rodolfo R.
Date Added:
01/01/2009
Algebra: Arithmetic with Polynomials and Rational Expressions
Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches Arithmetic with Polynomials and Rational Expressions to High Schoolers through a series of 4333 questions and interactive activities aligned to 26 Common Core mathematics skills.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
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:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Artin, Michael
Date Added:
01/01/2011
Algebra: Reasoning with Equations and Inequalities
Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches Reasoning with Equations and Inequalities to High Schoolers through a series of 5909 questions and interactive activities aligned to 36 Common Core mathematics skills.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Algebra: Seeing Structure in Expressions
Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches Structure in Algebraic Expressions to High Schoolers through a series of 3482 questions and interactive activities aligned to 26 Common Core mathematics skills.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Algebra Tiles
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Use tiles to represent variables and constants, learn how to represent and solve algebra problems. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.

Subject:
Algebra
Material Type:
Diagram/Illustration
Interactive
Simulation
Author:
Illuminations National Council of Teachers of Mathematics
Date Added:
06/03/2021
Algebra and Trigonometry
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 ensure 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
Author:
David Lippman
Jay Abramson
Jean-Marie Magnier
Melonie Rasmussen
Nicholas Belloit
Rachael Gross
Rick Norwood
Valeree Falduto
Date Added:
01/29/2015
Algebraic Geometry, Spring 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:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Kedlaya, Kiran
Date Added:
01/01/2009
Algebraic Techniques and Semidefinite Optimization, Spring 2006
Conditional Remix & Share Permitted
CC BY-NC-SA
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This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Subject:
Algebra
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Parrilo, Pablo
Date Added:
01/01/2006
Applied Geometric Algebra, Spring 2009
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:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Tisza, L
Date Added:
01/01/2009
Arithmetic | Algebra
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
Arithmetic | Algebra Homework
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
Beginning and Intermediate Algebra
Read the Fine Print
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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:
08/13/2020
Beginning and Intermediate Algebra
Unrestricted Use
CC BY
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Beginning and Intermediate Algebra by Tyler Wallace is a textbook licensed under a Creative Commons Attribution 3.0 Unported License. There is also a student guide and supplemental videos for each section.

Subject:
Algebra
Material Type:
Textbook
Provider:
Big Bend Community College
Author:
Tyler Wallace
Date Added:
06/03/2021
Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra, Fall 2011
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 and 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:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Herbert Gross
Date Added:
01/01/2011