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Advanced Partial Differential Equations with Applications, Fall 2009
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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:
03/04/2019
Algebra2Go - Prealgebra
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CC BY-SA
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Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources page. Whether you are attending Saddleback College's prealgebra class (math 351), taking a prealgebra class at another school, or need to refresh your math skills for a business or science class, Professor Perez and his favorite student Charlie have the tools that can help you. We have five primary types of study materials: class notes, video worksheets, video lectures, practice problems, and practice quizzes. For some topics we have some additional tools to assist you.

Subject:
Algebra
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra2go:  Decimals
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CC BY-SA
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Part of the course for community college students featuring Professor Perez and his student Charlie, teaching about decimal concepts and operations.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lecture
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra2go- PreAlgebra - Intro to Subtraction
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CC BY-SA
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This course is for community college students featuring Professor Perez and his student Charlie. This lesson demonstrates subtraction, including when the answer is negative, on the number line.

Subject:
Algebra
Material Type:
Assessment
Full Course
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra2go: Pre-algebra Conversions
Unrestricted Use
CC BY
Rating

This is part of the course for community college students featuring Professor Perez and his student Charlie, teaching how to make conversions between different kinds of units.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Lecture
Unit of Study
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra II, Spring 2011
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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
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
Algebraic Geometry, Spring 2009
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CC BY-NC-SA
Rating

" 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
Applied Geometric Algebra, Spring 2009
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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
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:
Mathematics
Algebra
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
New York City College of Technology (City Tech)
Author:
Bonanome, Marianna
Carley, Holly
ElHitti, Samar
Tradler, Thomas
Zhou, Lin
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:
Mathematics
Algebra
Material Type:
Homework/Assignment
Provider:
CUNY Academic Works
Provider Set:
New York City College of Technology (City Tech)
Author:
ElHitti, Samar
Masuda, Ariane
Zhou, Lin
Date Added:
01/01/2017
Beginning Algebra
Unrestricted Use
CC BY
Rating

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:
03/04/2019
Beginning Algebra (BPCC Open Campus: Math 098)
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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, and systems of linear equations. This course was created by Bossier Parish Community College as part of its MOOC series "Open Campus." NOTE: Open Campus courses are non-credit reviews and tutorials and cannot be used to satisfy requirements in any curriculum at BPCC. (Beginning Algebra Course by Bossier Parish Community College is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at http://bpcc.edu/opencampus/index.html.)

Subject:
Algebra
Material Type:
Assessment
Full Course
Lecture
Lecture Notes
Provider:
Bossier Parish Community College
Author:
Gail Hendrix
Date Added:
03/04/2019
Beginning and Intermediate Algebra
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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:
03/04/2019
Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra, Fall 2011
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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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Herbert Gross
Date Added:
01/01/2011
College Algebra
Unrestricted Use
CC BY
Rating

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
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
College Algebra
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Rating

It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Farmers, cattlemen, and tradesmen used tokens, stones, or markers to signify a single quantity—a sheaf of grain, a head of livestock, or a fixed length of cloth, for example. Doing so made commerce possible, leading to improved communications and the spread of civilization.

Subject:
Algebra
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Date Added:
03/04/2019
College Algebra
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Rating

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:
03/04/2019
College Algebra (BPCC Open Campus: MATH102)
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CC BY-NC-ND
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This course is designed to take the concepts you learn in developmental math to expand your knowledge of algebra. This course will focus on two major algebraic concepts to learn - how to SOLVE equations and how to GRAPH equations. Throughout this course you will be challenged to recall ALL of your prior knowledge of operations of real numbers as well as your knowledge related to solving and graphing linear equations (which you should have already mastered from developmental algebra). You will use this prior knowledge to expand on learning the following objectives: solving linear & rational equations. operations of complex numbers, solving quadratic equations, solving radical & polynomial equations, solving equations with rational exponents, solving linear and compound inequalities, solving absolute value equations and inequalities, graphing linear equations & slope, understanding concepts of domain, range and function notation, finding compositions of functions, finding inverses of functions, solving and graphing exponential and logarithmic equations, solving and graphing systems of equations and inequalities, and graphing conics.

*Open Campus courses are non-credit tutorials and cannot, in and of themselves, be used to satisfy degree requirements at Bossier Parish Community College (BPCC). (College Algebra Course by Bossier Parish Community College is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at http://bpcc.edu/opencampus/index.html.)

Subject:
Mathematics
Algebra
Material Type:
Full Course
Provider:
Bossier Parish Community College
Author:
Stacey Black
Date Added:
03/04/2019
College Algebra Through Problem Solving (2018 Edition)
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CC BY-NC-SA
Rating

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

Subject:
Mathematics
Algebra
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
Queensborough Community College
Author:
Cifone, Danielle
Dabkowska, Ewa
Maslanko, Debra
Puri, Karan
Date Added:
01/25/2018
College Algebra Through Problem Solving (2018 Edition)
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

Subject:
Mathematics
Algebra
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
Queensborough Community College
Author:
Cifone, Danielle
Dabkowska, Ewa
Masklanko, Debra
Puri, Karan
Date Added:
01/01/2018
College Algebra Through Problem Solving (2021 Edition)
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CC BY-NC-SA
Rating

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

Subject:
Mathematics
Algebra
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
Queensborough Community College
Author:
Cifone, Danielle
Maslanko, Debra
Puri, Karan
Stelmach, Ewa
Date Added:
08/22/2021
College Algebra and Trigonometry
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

An OER for MAT1275, an intermediate and advanced algebra course. Topics include quadratic equations, systems of linear equations, exponential and logarithmic functions; topics from trigonometry, including identities, equations and solutions of triangles

Subject:
Algebra
Trigonometry
Material Type:
Full Course
Provider:
CUNY
Provider Set:
New York City College of Technology
Author:
Lucie Mingla
Date Added:
12/10/2018
College Algebra through Problem Solving
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

Subject:
Algebra
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
Queensborough Community College
Author:
Cifone, Danielle
Dabkowska, Ewa
Maslanko, Debra
Puri, Karan
Date Added:
01/01/2017
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
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kleiman, Steven
Date Added:
01/01/2008
A Concise Workbook for College Algebra
Conditional Remix & Share Permitted
CC BY-NC
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This workbook is mainly based on the author‰Ûªs worksheets for the college algebra course (MAD-119) at QCC of CUNY. It is intended as a concise introduction to college algebra at the intermediate level.
It contains 25 lessons. Each lesson, corresponding to roughly one class meeting, starts with a page on concepts, formulas and examples, and ends with a list of practice problems that students are expected to be able to solve and complete in class.

Subject:
Mathematics
Algebra
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
Queensborough Community College
Author:
Ye, Fei
Date Added:
06/01/2018
Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics, Fall 2009
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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
Geometry
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Etingof, Pavel
Date Added:
01/01/2009
Honors Differential Equations, Spring 2009
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

"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
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Hur, Vera Mikyoung
Date Added:
01/01/2009
Inquiry into Saving [Mathematics]
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CC BY-SA
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‰Û÷Inquiry Into Saving‰Ûª is an assignment originally designed for MAT117, which is a course for students who have been placed in basic skills mathematics and who can apply a college level course in Algebra and Trigonometry to their program. These students should, ideally, be early in their LaGuardia career, though that is frequently not the case. All, however, are novices of mathematics. The assignment was vetted and revised based on feedback from the Inquiry and Problem Solving in STEM CTL seminar and a charrette not affiliated with the seminar. Revisions addressed connections to the Inquiry and Problem Solving/Written competency/ability pair, as well as general assignment design.
The ‰Û÷Inquiry Into Saving‰Ûª assignment is scaffolded into three parts. The first part is a brief reflection on investment goals; the second requires students to find information about investment options and use a provided formula to calculate how much they would need to invest to meet their goals; the third is a written piece that pulls the first two parts together into a rudimentary investment plan. The assignment draws on calculational topics from early in the semester (eg ‰ÛÒ linear equations), as well as later topics related to exponential functions and modeling. It also addresses effective use of calculators for ‰Û÷complex‰Ûª calculations.
LaGuardia‰Ûªs Core Competencies and Communication Abilities
Main Course Learning Objectives:
The following are addressed by Part 2 (Exploring Options) of the project: Introduce students to the concept of function and its application in modeling (exponential case). Introduce students to exponential functions Enable students to identify and apply appropriate mathematical methods to solve problems in real-world contexts.

Subject:
Computer Science
Algebra
Material Type:
Homework/Assignment
Provider:
CUNY Academic Works
Provider Set:
LaGuardia Community College
Author:
Funk, Jeanne
Date Added:
10/01/2017
Integral Equations, Spring 2006
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

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
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Margetis, Dionisios
Date Added:
01/01/2006
Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra
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Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra is a typed revision that was originally published by Plenum Press in 1976 as Volume 1 in a series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.

Subject:
Engineering
Algebra
Material Type:
Textbook
Provider:
Texas A&M University
Author:
C.-C. Wang
Ray M. Bowen
Date Added:
03/07/2019
Linear Algebra - Communications Intensive, Spring 2004
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CC BY-NC-SA
Rating

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Lachowska, Anna (liakhovskaia)
Date Added:
01/01/2004
Linear Algebra, Fall 2011
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Strang, Gilbert
Date Added:
01/01/2011