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Module 01
Mathematical Foundations
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Submodule 01Vectors & Geometry0/12
- 1Vector Element-wise SumEasy
- 2Dot Product CalculatorEasy
- 3Orthonormal Basis for 2D VectorsMed.
- 4The Cross Product of Two 3D VectorsEasy
- 5Orthogonal Projection of a Vector onto a LineEasy
- 6Cosine Similarity Between VectorsEasy
- 7Vector Norms (L1/L2/Frobenius)Med.
- 8Linear Independence of VectorsMed.
- 9Gradient Direction and MagnitudeMed.
- 10Hamming Distance for Kanerva CodingMed.
- 11Coarse Coding FeaturesMed.
- 12Captain Redbeard's Hidden TreasureMed.
Submodule 02Matrix Algebra0/17
- 1Matrix times MatrixMed.
- 2Matrix-Vector Dot ProductEasy
- 3Transpose of a MatrixEasy
- 4Reshape MatrixEasy
- 5Convert Vector to Diagonal MatrixEasy
- 6Scalar Multiplication of a MatrixEasy
- 7Matrix TransformationMed.
- 8Transformation Matrix from Basis B to CEasy
- 92D Translation Matrix ImplementationMed.
- 102x2 Matrix InverseMed.
- 11Mean by Row or ColumnEasy
- 12Matrix Determinant & TraceMed.
- 13Matrix RankMed.
- 14The Null Space (Kernel) of a MatrixMed.
- 15The column space of a matrixMed.
- 16If Matrix is Positive DefiniteMed.
- 17Jacobian Matrix CalculationconceptMed.
Submodule 03Linear Systems & Numerical Methods0/6
- 1Gaussian Elimination for Solving Linear SystemsMed.
- 2Solve Linear Equations using Jacobi MethodconceptMed.
- 3Gauss-Seidel Method for Solving Linear SystemsconceptMed.
- 4Solve System of Linear Equations Using Cramer's RuleMed.
- 5Reduced Row Echelon Form (RREF) FunctionMed.
- 6The Conjugate Gradient Method for Solving Linear SystemsconceptMed.
Submodule 04Decomposition & Spectral Methods0/10
- 1Eigenvalues of a MatrixMed.
- 2SVD of a 2x2 MatrixMed.
- 3Singular Value Decomposition (SVD) of 2x2 MatrixMed.
- 4LU Decomposition of a Square MatrixMed.
- 5QR DecompositionMed.
- 6Cholesky DecompositionMed.
- 7Explained Variance Ratio for PCAMed.
- 8Compressed Row Sparse Matrix (CSR) Format ConversionEasy
- 9Compressed Column Sparse Matrix Format (CSC)Easy
- 10Determinant of a 4x4 Matrix using Laplace's Expansion (hard)Hard
Submodule 05Calculus & Optimization0/26
- 1Derivative of a PolynomialEasy
- 2Partial Derivatives of Multivariable FunctionsMed.
- 3Chain Rule for Composite FunctionsMed.
- 4Product Rule for DerivativesMed.
- 5Quotient Rule for DerivativesMed.
- 6The Hessian MatrixMed.
- 7Classify Critical Points Using Hessian EigenvaluesHard
- 8Derivative of SoftmaxHard
- 9Derivative of Cross-Entropy Loss w.r.t. LogitsHard
- 10Derivatives of Activation FunctionsMed.
- 11Numerical Gradient CheckingMed.
- 12Taylor Series ApproximationMed.
- 13Gradient CheckpointingEasy
- 14Gradient Descent Variants with MSE LossMed.
- 15Nesterov Accelerated Gradient OptimizerEasy
- 16Adam Optimization AlgorithmconceptMed.
- 17CosineAnnealingLR Learning Rate SchedulerMed.
- 18Newton's Method for OptimizationconceptMed.
- 19Lagrange Multipliers for Constrained Quadratic OptimizationHard
- 20Muon Optimizer Update with Newton-Schulz IterationHard
- 21Efficient Gradient Computation for Binary FeaturesMed.
- 22Gradient Boosting Regressor StepHard
- 23T-SNE Gradient CalculationconceptMed.
- 24Warmup + Cosine Decay ScheduleMed.
- 25Linear Learning Rate DecayMed.
- 26Arithmetic Intensity and Classify BottleneckconceptEasy