Mathematics Laboratory

Ten interactive tools. Manipulate the inputs and watch the mathematics respond — the fastest way to build intuition that sticks. Each one is also embedded in the lesson where it's most relevant.

• Week 2→

  Function Explorer

  Plot linear, quadratic, exponential, logarithmic, and activation functions; adjust parameters and overlay the derivative.

  functionsactivationsderivatives
• Week 3→

  Vector Playground

  Drag two vectors, add and scale them, and read magnitude, dot product, angle, cosine similarity, and projection live.

  vectorsdot-productcosine-similarityprojection
• Week 4→

  Matrix Transformation Visualizer

  Edit a 2×2 matrix and watch it transform a grid, the basis vectors, and sample points. See determinant, rotation, shear, and singularity.

  matriceslinear-transformationdeterminant
• Week 4→

  Matrix Multiplication Explorer

  Set matrix values and step through the row-by-column computation, with the contributing entries highlighted for each output cell.

  matmulshapesdot-product
• Week 4→

  Linear-System Solver

  Enter a 2×2 or 3×3 system and step through Gaussian elimination, with the geometric picture and a unique/infinite/none diagnosis.

  linear-systemgaussian-elimination
• Week 6→

  Derivative Visualizer

  Move a point along a curve, shrink the secant interval toward the tangent, and compare the numerical slope to the analytic derivative.

  derivativetangentnumerical-derivative
• Week 7→

  Chain-Rule Visualizer

  For y = (w·x + b)², watch the forward values, local derivatives, and backward gradient flow through the computational graph.

  chain-rulebackpropcomputational-graph
• Week 8→

  Gradient-Descent Visualizer

  Pick a 1-D loss, a start point, and a learning rate; step or run, and compare convergence, slow learning, oscillation, and divergence.

  gradient-descentlearning-rateconvergence
• Week 8→

  Linear-Regression Laboratory

  Generate noisy data, fit a line by hand or by gradient descent, and watch residuals, MSE, the loss curve, and learned-vs-true parameters.

  linear-regressionmseresidualstraining
• Week 5→

  PCA Intuition Visualizer

  Generate a 2-D cloud, see the mean and principal directions, project onto the first component, and compare original vs reduced data.

  pcacovarianceprojectionvariance