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.
The Frenet trihedron on a helix
Authors
Educational level
Higher Education
Level
medium
Description
This applet shows the behavior of the Frenet trihedron along a helix. It also allows visualizing the normal plane, the osculating plane, and the rectifying plane. A list of activities is provided. GeoGebra is required.
Licence
CC-BY
Type
Applets
Category
Differential geometry – Differential geometry of curves
Keywords
Differential Geometry, 3D Curves, Frenet trihedron, GeoGebra
Tags
UPC, Gate2Math
File
UPC-054-APL-EN.zip
The Joy of Playful Matrices
Authors
Educational level
Secondary School, Higher Education
Level
easy
Description
This PowerPoint presentation is designed to motivate and facilitate learning with an approach close to “gamification” through experimentation as a pleasure for discovery. It explores the use of simple orthogonal matrices and their product with others, taking the opportunity to delve into the world of cryptography: “The Joy of Playful Matrices”. It does not use the standard notation of the permutation group, nor does it aim to provide rigorous proofs. The goal is to play and enjoy mathematical reasoning. It can serve as a good starting point for other topics: the theorem of permutation decomposition into transpositions, working with determinant properties to prove that these matrices always have a determinant of +1 or -1, proving that these matrices are orthogonal, encrypting and decrypting, studying a known plaintext attack (how many plaintext-ciphertext pairs are needed to break the cryptographic system?), etc.
Licence
CC-BY
Type
Game/Online Exercise
Category
Linear algebra – Matrix calculus
Keywords
Permutation matrices, Cryptography, Gamification
Tags
UPC, Gate2Math
File
UPC-063-GAM-EN.pptx
Mosaics
Authors
Educational level
Higher Education
Level
medium
Description
A mathematical presentation of mosaics. It describes the basic concepts of mosaics and their classes. It includes some techniques to design mosaics. A number of references and a link to an applet provide further information about the topic.
Licence
CC-BY
Type
Tutorial
Category
Linear Geometry – Affinities
Keywords
Affine geometry, Mosaics
Tags
UPC, Gate2Math
File
UPC-055-PRE-EN.pptx
Learning affinities by designing mosaics
Authors
Educational level
Higher Education
Level
medium
Description
This exercice sheet allows the experimentation with the basic planar affine maps (translation, rotation, symmetries) by elaborating several types of mosaics. GeoGebra is required.
Licence
CC-BY
Type
Excercises
Category
Linear Geometry – Affinities
Keywords
Affine geometry, Mosaics, GeoGebra
Tags
UPC, Gate2Math
File
UPC-056-EXE-EN.docx
Basic differential properties of the ellipse
Authors
Educational level
Higher Education
Level
medium
Description
This applet is designed to understand the basic properties of the ellipse related to differential geometry: normal vector, curvature, offset curve… A list of activities is provided. GeoGebra is required.
Licence
CC-BY
Type
Applets
Category
Differential geometry – Differential geometry of curves
Keywords
Ellipse, Normal vector, Offset curve, Curvature, GeoGebra
Tags
UPC, Gate2Math
File
UPC-057-APL-EN.zip
Calculus on a basketball
Authors
Josefina Antonijuan, Jordi Guàrdia, Joana Prat
Educational level
Higher Education
Level
medium
Description
In this project, the student can work simultaneously on several fundamental mathematical concepts: the parameterization of the sphere, longitude and latitude, the tangent vector to a parametric curve, and rotations in space. GeoGebra is required but the educational resource is also available online at https://www.geogebra.org/m/rp8rtrhn
Licence
CC-BY
Type
Applets
Category
Multivariable calculus – Parametric curves and surfaces
Keywords
Sphere, Parameterization, Surface, Tangent vector, GeoGebra
Tags
UPC, Gate2Math
File
UPC-058-APL-EN.zip
Complex roots of a cubic polynomial
Authors
Educational level
Higher Education
Level
medium
Description
This applet allows the visualization of the complex roots of a cubic polynomial, and the impact of the coefficients on them. GeoGebra is required but the educational resource is also available online a htttps://www.geogebra.org/m/dpw7wt2n#material/dn7mzjwe
Licence
CC-BY
Type
Applets
Category
Numerical methods – Computation of roots
Keywords
Polynomials, Complex numbers, Roots, GeoGebra
Tags
UPC, Gate2Math
File
UPC-059-APL-EN.zip
Curvature. Osculating circle
Authors
Josefina Antonijuan, Jordi Guàrdia
Educational level
Higher Education
Level
medium
Description
This activity is focused on a practical understanding of the curvature and the osculating circle of a plane curve. GeoGebra is required but the educational resource is available online at https://www.geogebra.org/m/vqxy6jrd
Licence
CC-BY
Type
Applets
Category
Differential geometry – Differential geometry of curves
Keywords
2D curves, Curvature, Osculating circle, GeoGebra
Tags
UPC, Gate2Math
File
UPC-060-APL-EN.zip
Simple 2D Vector Field
Authors
Educational level
Higher Education
Level
medium
Description
A GeoGebra applet to visualize two-dimensional vector fields. Geogebra is required but the educational resource is also available online at https://www.geogebra.org/classic/up2e8tcv
Licence
CC-BY
Type
Applets
Category
Multivariable calculus – Vector calculus
Keywords
Vector calculus, Vector fields, 2D, GeoGebra
Tags
UPC, Gate2Math
File
UPC-061-APL-EN.zip
Simple 3D Vector Field
Authors
Educational level
Higher Education
Level
medium
Description
A Geogebra applet to visualize three-dimensional vector fields. GeoGebra is required but the educational resource is also available online at https://www.geogebra.org/m/rqxxfvb2
Licence
CC-BY
Type
Applets
Category
Multivariable calculus – Vector calculus
Keywords
Vector calculus, Vector fields, 3D, GeoGebra
Tags
UPC, Gate2Math
File
UPC-062-APL-EN.zip
