Foundations Projects

Build linear regression twice with nothing but NumPy: once with the closed-form normal equation and once with batch gradient descent. Then check both against scikit-learn's LinearRegression. You'll standardize features, write MSE and R² yourself, watch a loss curve converge, and read residual plots. The diabetes dataset ships with scikit-learn, so there's nothing to download.

Answer probability questions by simulation and check each answer against the exact math. You'll estimate π by throwing random darts, simulate the birthday problem, watch the Central Limit Theorem turn skewed data into a bell curve, update a Beta prior on a coin's bias, and bootstrap confidence intervals. Everything is vectorized NumPy and runs in seconds.