Welcome to the Mathematics OER Smart Library! Our library offers a diverse range of materials—including videos, infographics, games, presentations, animations, and more—covering topics such as algebra, calculus, geometry, statistics, and probability. These resources are available in seven languages: English, Estonian, German, Portuguese, Romanian, Catalan, and Spanish. Additionally, our library includes materials accessible to visually impaired and color-blind individuals. These resources are designed to support educators, students, and researchers in secondary, vocational, and higher education institutions.
Random OERs:
Total number of OERs published so far:
3621To explore and utilize these materials, navigate through our categorized sections or use the search function to find specific OERs of interest.
Congruent diagonalization of symmetric real matrices
Authors
Educational level
Higher Education
Level
medium
Description
The theorem that guarantees the congruent diagonalization of a symmetric real matrix is presented, and this process of diagonalization is described from an operational point of view It is also explained how to use this process to determine if a symmetric real matrix is positive definite, negative definite, positive semidefinite, negative semidefinite, or indefinite. With examples (editable pptx).
Licence
CC-BY
Type
Tutorial
Category
Linear algebra – Diagonalization
Keywords
Elementary operation, Matrix in echelon form, Gaussian elimination, Symmetric definite matrix
Tags
UPC, Gate2Math
File
UPC-025-TUT-EN.pptx
Gram-Schmidt orthogonalization
Authors
Educational level
Secondary School, Higher Education
Level
medium
Description
The Gram-Schmidt orthogonalization procedure is presented, a procedure used to obtain orthogonal basis of finite dimensional vector subspaces in the context of an euclidean space (real or complex). Theoretical justification of the procedure is given, along with two examples that illustrate how it works in practice (editable pptx).
Licence
CC-BY
Type
Tutorial
Category
Linear algebra – Euclidean/hermitic spaces
Keywords
Inner product, Orthogonal projection, Orthogonal basis
Tags
UPC, Gate2Math
File
UPC-026-TUT-EN.pptx
Calculus for real-valued functions: Test
Authors
Educational level
Secondary School, Higher Education
Level
medium
Description
Five questions test (with a unique correct answer each) on calculus for real-valued functions, including limits, continuity and differentiablility.
Licence
CC-BY
Type
Quiz/Knowledge Control
Category
One variable calculus – Continuity
Keywords
Accumulation point, Limit, Continuity, Differentiability
Tags
UPC, Gate2Math
File
UPC-027-EXE-EN.zip
Matrices and systems of linear equations: Test
Authors
Educational level
Secondary School, Higher Education
Level
medium
Description
Five questions test (with a unique correct answer each) on matrices and systems of linear equations.
Licence
CC-BY
Type
Quiz/Knowledge Control
Category
Linear algebra – Linear systems
Keywords
Rank of a matrix, Elementary operation, Matrix in echelon form
Tags
UPC, Gate2Math
File
UPC-028-EXE-EN.zip
Matrices and systems of linear equations: Test
Authors
Educational level
Secondary School, Higher Education
Level
medium
Description
Five questions test (with a unique correct answer each) on matrices and systems of linear equations.
Licence
CC-BY
Type
Quiz/Knowledge Control
Category
Linear algebra – Linear systems
Keywords
Rank of a matrix, Elementary operation, Matrix in echelon form
Tags
UPC, Gate2Math
File
UPC-048-EXE-EN.zip
Matrices and systems of linear equations: Test
Authors
Educational level
Secondary School, Higher Education
Level
medium
Description
Five questions test (with a unique correct answer each) on matrices and systems of linear equations.
Licence
CC-BY
Type
Quiz/Knowledge Control
Category
Linear algebra – Linear systems
Keywords
Rank of a matrix, Elementary operation, Matrix in echelon form
Tags
UPC, Gate2Math
File
UPC-053-EXE-EN.zip
Analytic Geometry. Theory
Authors
Educational level
Higher Education
Level
medium
Description
This video is part of the UPC MOOC Engineering Fundamentals for Urban Mobility (https://mooc.upc.edu). This video is a theoretical overview of Analytic Geometry.
Licence
CC-BY
Type
Short Video
Category
Linear Geometry
Keywords
Geometry, Analytic Geometry, Theory, MOOC
Tags
UPC, Gate2Math, EIC Urban Mobility
File
UPC-036-VID-EN.docx
Analytic Geometry. Practical
Authors
Educational level
Higher Education
Level
medium
Description
This video is part of the UPC MOOC Engineering Fundamentals for Urban Mobility (https://mooc.upc.edu). In this video we found a practical overview with some examples of Analytic Geometry.
Licence
CC-BY
Type
Short Video
Category
Linear Geometry
Keywords
Geometry, Analytic Geometry, Practice, MOOC
Tags
UPC, Gate2Math, EIC Urban Mobility
File
UPC-037-VID-EN.docx
Linear Algebra. Vectors, Theory
Authors
Educational level
Higher Education
Level
medium
Description
This video is part of the UPC MOOC Engineering Fundamentals for Urban Mobility (https://mooc.upc.edu). This video is a theoretical overview of Vectors and Vector Operations.
Licence
CC-BY
Type
Short Video
Category
Linear algebra
Keywords
Linear Algebra, Vectors, Theory, MOOC
Tags
UPC, Gate2Math, EIC Urban Mobility
File
UPC-038-VID-EN.docx
Linear Algebra. Vectors. Exercises
Authors
Educational level
Higher Education
Level
medium
Description
This video is part of the UPC MOOC Engineering Fundamentals for Urban Mobility (https://mooc.upc.edu). In this video we found a practical overview with some examples of Vectors and Vector Operations.
Licence
CC-BY
Type
Short Video
Category
Linear algebra
Keywords
Linear Algebra, Vectors, Practice, MOOC
Tags
UPC, Gate2Math, EIC Urban Mobility
