Labs

Weekly Python Labs

Week 1 — Data as Mathematical Objects

• Load a real dataset (Iris / Housing)
• Identify variables, features, and targets
• Visualize relationships
• Reflection: What assumptions are embedded in the data?

Week 2 — Functions & Transformations

• Apply nonlinear feature transformations
• Visualize effects of scaling and normalization
• Explore composition of functions

Week 3 — Geometry of Data

• Compute distances between data points
• Implement k-NN classifier
• Explore impact of feature scaling
• Visualize decision boundaries

Week 4 — Matrix Transformations

• Matrix–vector multiplication
• Transform point clouds
• Understand projections geometrically

Week 5 — Linear Regression

• Implement least squares regression
• Compare closed-form vs numerical solutions
• Visualize residuals and error

Week 6 — Probability Models

• Simulate random variables
• Implement Naive Bayes classifier
• Visualize likelihoods and posteriors

Week 7 — Sampling & Estimation

• Bootstrap sampling
• Confidence intervals
• Train/test splits
• Demonstrate overfitting

Week 8 — No labs due

Week 9 — No labs due

Week 10 — Optimization Landscapes

• Visualize loss surfaces
• Implement gradient descent
• Experiment with learning rates

Week 11 — Gradients as Sensitivity

• Numerical derivatives
• Gradient descent tuning
• Sensitivity analysis

Week 12 — Backpropagation Without Fear

• Implement a simple neural network
• Track gradients layer by layer
• Relate chain rule to computation

Week 13 — PCA & Dimensionality Reduction

• Eigenvector intuition via geometry
• Implement PCA from scratch
• Reconstruction and compression

Week 14 — Capstone Lab

• Choose an ML model
• Explain the mathematics behind it
• Combine code, visuals, and narrative