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Algebra I
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This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Artin, Michael
Date Added:
09/01/2010
Applied Geometric Algebra
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László 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. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Tisza, László
Date Added:
02/01/2009
Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra
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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.
About the Instructor
Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers.
Acknowledgements
Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.
Other Resources by Herb Gross
Calculus Revisited: Single Variable Calculus 
Calculus Revisited: Multivariable Calculus

Subject:
Algebra
Calculus
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Gross, Herbert
Date Added:
09/01/2011
Calculus of Several Variables
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This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.
Acknowledgement
Prof. McKernan would like to acknowledge the contributions of Lars Hesselholt to the development of this course.

Subject:
Algebra
Calculus
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
McKernan, James
Date Added:
09/01/2010
Computational Science and Engineering I
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This course provides the fundamental computational toolbox for solving science and engineering problems. Topics include review of linear algebra, applications to networks, structures, estimation, finite difference and finite element solutions of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, the discrete Fourier transform, and convolution. We will also explore many topics in AI and machine learning throughout the course.

Subject:
Algebra
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Zhang, Chengzhao
Date Added:
06/01/2020
Computational Science and Engineering I
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This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Note: This course was previously called "Mathematical Methods for Engineers I."

Subject:
Algebra
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Strang, Gilbert
Date Added:
09/01/2008
Dynamic Systems and Control
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The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.
We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.

Subject:
Applied Science
Career and Technical Education
Computer Science
Electronic Technology
Engineering
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Dahleh, Munther
Frazzoli, Emilio
Date Added:
02/01/2011
Elements of Abstract and Linear Algebra
Read the Fine Print
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Elements of Abstract and Linear Algebra is a book written by Dr. Edwin Connell, a professor emeritus in the math department at the University of Miami. Published in December 2001, it can be obtained free of charge from this Web site. Dr. Connell even encourages printing and distributing the book as an inexpensive resource for college students. The text is divided into sections that can be downloaded separately or as a whole. There are many theorems, proofs, and exercises throughout the book that illustrate the underlying concepts. The book is offered in four formats; so, most computers should be able to view it with no problems.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
University of Miami
Provider Set:
University of Miami Department of Mathematics
Author:
Connell, Edwin.
Edwin H. Connell
Date Added:
02/16/2011
En avant les espaces vectoriels : une introduction à l’algèbre linéaire (première édition)
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Conçu pour un cours de première année universitaire, ce manuel en algèbre linéaire adopte une approche peu commune : il présente les espaces vectoriels dès le début et traite des systèmes linéaires qu’après une introduction approfondie aux espaces vectoriels. Cette approche est fondée sur l’expérience des auteurs ayant observé au cours des 25 dernières années que les étudiantes et étudiants ont souvent besoin davantage de temps pour maîtriser les espaces vectoriels alors que les manuels traditionnels relèguent plutôt le sujet à la fin du cours. De cette façon, ces nouvelles notions au coeur de l’algèbre linéaire qui sont souvent considérées comme abstraites et difficiles dans un cours d’introduction peuvent ensuite être utilisées dans le reste du cours ainsi que différents contextes.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
University of Ottowa
Author:
Abdelkrim El basraoui
Barry Jessup
Monica Nevins
Thierry Giordano
Date Added:
08/25/2022
Engineering Math: Differential Equations and Linear Algebra
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This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

Subject:
Algebra
Applied Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Frey, Daniel
Strang, Gilbert
Date Added:
09/01/2014
A First Course in Linear Algebra
Unrestricted Use
CC BY
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This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.
All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.
Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text.
Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.

Subject:
Mathematics
Material Type:
Homework/Assignment
Lecture Notes
Textbook
Provider:
Lyryx Learning
Author:
Adapted by Lyryx Learning
K. Kuttler
Date Added:
02/12/2015
Fundamentals of Matrix Algebra
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A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This third edition corrects several errors in the text and updates the font faces.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Author:
Gregory Hartman
Date Added:
06/28/2019
Inference from Data and Models
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This course covers the fundamental methods used for exploring the information content of observations related to kinematical and dynamical models.

Subject:
Applied Science
Engineering
Mathematics
Physical Science
Physics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Wunsch, Carl
Date Added:
02/01/2005
Inquiry Oriented Linear Algebra
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The Inquiry-Oriented Linear Algebra (IOLA) project focuses on developing student materials composed of challenging and coherent task sequences that facilitate an inquiry-oriented approach to the teaching and learning of linear algebra. The project has also developed instructional support materials to help instructors implement the IOLA tasks in their classrooms.

How to cite IOLA materials: Wawro, M., Zandieh, M., Rasmussen, C., & Andrews-Larson, C. (2013). Inquiry oriented linear algebra: Course materials. Available at http://iola.math.vt.edu. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

This material is based upon work supported by the National Science Foundation under grant numbers DUE-1245673/1245796/1246083. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Subject:
Mathematics
Material Type:
Activity/Lab
Author:
Chris Rasmussen
Christine Andrews-Larson
Michelle Zandieh
Megan Wawro
Date Added:
02/07/2020
Integrating Information Technology to study Mathematics
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CC BY-SA
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This course is is a collection of resources on OER Commons curated for Adult Education instructors and students to show the integration of math into the Information Technology Career Sector. Students will analyze and practice specific skills related to being in IT as well as develop math skills. Modules in this curriculum guide can be studied in any particular order as one does not necessarily build upon the other. Each includes the idea of building mathematical and logic skills required for programming and other IT related careers.

Subject:
Career and Technical Education
Mathematics
Material Type:
Teaching/Learning Strategy
Unit of Study
Date Added:
04/26/2018
Introduction to Functional Analysis
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Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed space that is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics include normed spaces, completeness, functionals, the Hahn-Banach Theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of Lᵖ spaces; Hilbert spaces; compact and self-adjoint operators; and the Spectral Theorem.

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Rodriguez, Casey
Date Added:
02/01/2021
Introduction to GNU Octave: A Brief Tutorial for Linear Algebra and Calculus Students
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CC BY-SA
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These notes are intended to provide a brief, noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.

Subject:
Applied Science
Engineering
Mathematics
Material Type:
Textbook
Provider:
Wytheville Community College
Author:
Jason Lachniet
Date Added:
05/12/2018
Introduction to Numerical Analysis
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CC BY-NC-SA
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This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in linear algebra.

Subject:
Algebra
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Toomre, Alar
Date Added:
02/01/2004
Introduction to Stochastic Processes
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This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree. The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix.

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Wu, Hao
Date Added:
02/01/2015
Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler
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Learn Differential Equations: Up Close with _Gilbert Strang and_ Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.
About the Instructors
Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.
Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico.
These videos were produced by The MathWorks and are also available on The MathWorks website.

Subject:
Algebra
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Moler, Cleve
Strang, Gilbert
Date Added:
09/01/2015