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Commutative Algebra, Fall 2008
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CC BY-NC-SA
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In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kleiman, Steven
Date Added:
01/01/2008
A Computational Introduction to Number Theory and Algebra
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:
Algebra
Mathematics
Material Type:
Textbook
Author:
Victor Shoup
Date Added:
01/01/2008
Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics, Fall 2009
Conditional Remix & Share Permitted
CC BY-NC-SA
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" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems."

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Etingof, Pavel
Date Added:
01/01/2009
Elementary Algebra
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.While algebra is one of the most diversely applied subjects, students often find it to be one of the more difficult hurdles in their education. With this in mind, John wrote Elementary Algebra from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. Elementary Algebra takes the best of the traditional, practice-driven algebra texts and combines it with modern amenities to influence learning, like online/inline video solutions, as well as, other media driven features that only a free online text can deliver.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
The Saylor Foundation
Provider Set:
Saylor Textbooks
Author:
John Redden
Date Added:
01/01/2011
Elementary Algebra 2e
Unrestricted Use
CC BY
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The 2nd Edition of Elementary Algebra ,Elementary Algebra 2e, is designed to meet scope and sequence requirements for a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.

Subject:
Algebra
Mathematics
Material Type:
Answer Key
Full Course
Lecture Notes
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Andrea Honeycutt Mathis
Lynn Marecek
MaryAnne Anthony-Smith
Date Added:
09/22/2020
Elementary Linear Algebra
Unrestricted Use
CC BY
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Elementary Linear Algebra was written and submitted to the Open Textbook Challenge by Dr. Kenneth Kuttler of Brigham Young University. Dr. Kuttler wrote this textbook for use by his students at BYU. According to the introduction of Elementary Linear Algebra, ĺÎĺ_ĺĚĄ_this is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.ĺÎĺ_ĺĚĺÎĺ A solutions manual for the textbook is included.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
The Saylor Foundation
Provider Set:
Saylor Textbooks
Author:
Kenneth Kuttler
Date Added:
05/22/2019
A First Course in Linear Algebra
Read the Fine Print
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A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
University of Puget Sound
Author:
Robert Beezer
Date Added:
05/22/2019
A First Course in Linear Algebra
Read the Fine Print
Some Rights Reserved
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"This text is designed to teach the concepts and techniques of basic linear algebra as a rigorous mathematical subject. Besides computational proficiency, there is an emphasis on understanding definitions and theorems, as well as reading, understanding and creating proofs. A strictly logical organization, complete and exceedingly detailed proofs of every theorem, advice on techniques for reading and writing proofs, and a selection of challenging theoretical exercises will slowly provide the novice with the tools and confidence to be able to study other mathematical topics in a rigorous fashion." -- Preface

Subject:
Algebra
Mathematics
Material Type:
Textbook
Author:
Robert A. Beezer
Date Added:
10/28/2020
Foundations of Mathematics
Unrestricted Use
CC BY
Rating
0.0 stars

This course focuses on algebraic and numerical skills in a context of applications and problem-solving to prepare students for Statistics. Topics will include quantitative relationships, patterning and algebraic reasoning, functional reasoning, probabilistic and statistical reasoning, incorporating quantitative communication skills and technology

Subject:
Algebra
Mathematics
Statistics and Probability
Material Type:
Assessment
Full Course
Homework/Assignment
Author:
Cassandra Frandsen
Date Added:
12/16/2021
Honors Differential Equations, Spring 2009
Conditional Remix & Share Permitted
CC BY-NC-SA
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"This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems."

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Hur, Vera Mikyoung
Date Added:
01/01/2009
In-Class Activity Sheets for OpenStax College Algebra
Unrestricted Use
CC BY
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0.0 stars

Activity Sheets, tightly aligned with the OpenStax College Algebra text, and designed for use in class as part of an active lecture.  During the 2020-2021 pandemic, the activity sheets were used successfully in both group and individual settings in hybrid and fully online learning environmentsThis resource includes activities formatted both as accessible Word documents, for ease of use under the CC-BY 4.0 license, and in pdf form to preserve historically the intended appearance on the page.These activity sheets align tightly with the OpenStax College Algebra textbook and an available MyOpenMath Course called the College Algebra Western MD Consortium (MOST), an inter-institutional effort comprised of mathematics faculty, instructional designers, and libriarians from Frostburg State University, Allegany College of Maryland, and Garrett College. 

Subject:
Algebra
Mathematics
Material Type:
Course Packet
Teaching/Learning Strategy
Author:
Deborah Devlin
Date Added:
04/07/2021
Integral Equations, Spring 2006
Conditional Remix & Share Permitted
CC BY-NC-SA
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Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Margetis, Dionisios
Date Added:
01/01/2006
Intermediate Algebra
Unrestricted Use
CC BY
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 Intermediate algebra is a course designed for students who have successfully completed high school algebra but who placed into pre-college level mathematics at Garrett College. This course is for refreshing math skills with a review of pre-college level algebra. After successfully completing this course, the student should be prepared to go on to College Algebra.

Subject:
Algebra
Mathematics
Material Type:
Assessment
Full Course
Homework/Assignment
Author:
Cassandra Frandsen
Date Added:
12/21/2021
Intermediate Algebra 2e
Unrestricted Use
CC BY
Rating
0.0 stars

The 2nd Edition of Intermediate Algebra, Intermediate Algebra 2e, is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses.

The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.

Subject:
Algebra
Functions
Mathematics
Material Type:
Answer Key
Full Course
Lecture Notes
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Andrea Honeycutt Mathis
Lynn Marecek
Date Added:
09/22/2020
Intermediate Algebra (MATH 9Y)
Unrestricted Use
CC BY
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0.0 stars

Students will learn to solve compound inequalities, absolute value inequalities, and systems of equations, simplify radical expressions, solve quadratic equations and applications and simplify compound fractions, solve rational equations and applications, use function notation to solve problems and use exponential and logarithmic functions.Login: guest_oclPassword: ocl

Subject:
Algebra
Mathematics
Material Type:
Full Course
Homework/Assignment
Lecture Notes
Lesson Plan
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
Date Added:
10/31/2011
Introductory Algebra/Basic Math
Conditional Remix & Share Permitted
CC BY-SA
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0.0 stars

This course will introduce basic algebra skills to students with limited background in algebra. Topics covered will include order of operations, computations with real numbers and linear equations and problem solving. The course will introduce operations with: integers, exponents, fractions, decimals, and percents. More advance algebra concepts will include model building and analysis of graphical and numerical data with an emphasis on making connections between concepts learned in the classroom and real-world applications. An emphasis will be placed on using proportions to solve real world problems. 

Subject:
Algebra
Mathematics
Material Type:
Assessment
Full Course
Homework/Assignment
Author:
Cassandra Frandsen
Date Added:
12/21/2021
Linear Algebra
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Author:
Andrew Waldon
David Cherney
Tom Denton
Date Added:
01/01/2016
Linear Algebra
Conditional Remix & Share Permitted
CC BY-SA
Rating
0.0 stars

Linear Algebra is a text for a first US undergraduate Linear Algebra course. It is Free. You can use it as a main text, as a supplement, or for independent study.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
St. Michael's College
Author:
Jim Hefferon
Date Added:
01/01/2011