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Bayesian Knowledge Tracing with ASSISTments Data
- Professor Tanja Käser
- CourseCS-421
- Kernel Python3
- Type Demonstrations in class
- Language English
- DescriptionThis notebook trains Bayesian Knowledge Tracing models on student interactions from the ASSISTments platform. It uses learner-level train-test splits and evaluates predictions overall and by skill with RMSE and AUC.
- Bayesian knowledge tracing
- Student modeling
- ASSISTments
- Predictive evaluation
Regression Models for Behavioral and Time-Series Data
- Professor Tanja Käser
- CourseCS-421
- Kernel Python3
- Type Demonstrations in class
- Language English
- DescriptionThis notebook introduces linear and multivariable regression, generalized linear models, and mixed-effects models for educational data. It also covers feature scaling, pass/fail prediction, random effects, and regression with longitudinal student behavior.
- Linear regression
- Generalized linear models
- Mixed-effects models
- Longitudinal data
Learning Curves and Knowledge Tracing Model Comparison
- Professor Tanja Käser
- CourseCS-421
- Kernel Python3
- Type Demonstrations in class
- Language English
- DescriptionThis notebook derives and interprets learning curves from ASSISTments interaction data. It compares Bayesian Knowledge Tracing with the Additive Factors Model and Performance Factors Analysis using learner-separated predictions and standard performance metrics.
- Learning curves
- Bayesian knowledge tracing
- Additive Factors Model
- Performance Factors Analysis
Critère d'inversibilité par le déterminant
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook proves and applies the criterion that a square matrix is invertible exactly when its determinant is nonzero. Exercises connect zero determinants with linearly dependent rows and columns.
- Determinant
- Invertible matrix
- Linear dependence
Matrice des cofacteurs et formule de l'inverse
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines minors, cofactors, and the cofactor matrix, then derives the adjugate formula for the inverse of a nonsingular matrix. Exercises compute inverses explicitly from determinants and cofactors.
- Cofactor matrix
- Adjugate matrix
- Matrix inverse
- Determinant
Interprétation géométrique du déterminant
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook interprets the absolute determinant as the area scaling in two dimensions and volume scaling in three dimensions. Exercises connect matrix columns with parallelograms, parallelepipeds, orientation, and geometric transformations.
- Determinant
- Area scaling
- Volume scaling
- Geometric transformation
Déterminant : définition et premiers calculs
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines the determinant recursively by cofactor expansion and illustrates the definition for 2×2 and 3×3 matrices. Students also practice the Sarrus rule for three-dimensional cases.
- Determinant
- Cofactor expansion
- Sarrus rule
Propriétés du déterminant et méthodes de calcul
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook develops determinant properties under row operations, transposition, and scalar multiplication. It compares cofactor expansion with elimination-based calculations and discusses their computational cost.
- Determinant
- Elementary row operation
- Cofactor expansion
- Computational complexity
Déterminant d'un produit de matrices
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook establishes the multiplicative identity det(AB)=det(A)det(B) and contrasts it with the absence of an analogous addition rule. Exercises use the product formula to simplify determinant calculations and revisit computational complexity.
- Determinant
- Matrix multiplication
- Multiplicative property
Classification des formes quadratiques
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook classifies quadratic forms as positive definite, negative definite, semidefinite, or indefinite using eigenvalue signs. It applies the classification to two-dimensional conics after a principal-axis change of coordinates.
- Quadratic form
- Definite matrix
- Eigenvalue
- Conic classification