Clawdemy: Foundations

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The mathematical foundations of AI, narrated. Linear algebra, calculus, statistics, and classical machine learning, one bite-size lesson at a time. A focused track from Clawdemy.

  1. May 25

    Higher-order derivatives

    Lesson 12 of Track 8 (Visual Math: Calculus). A derivative is itself a function, so you can differentiate it again. The second derivative f'' measures how the slope is changing, which means acceleration in physics (Newton's F = ma is written in second derivatives) and curvature on a graph (cups upward when f'' > 0, downward when f'' 0). It powers the second-derivative test that sorts maxima from minima at critical points, gives the oscillation equation f'' = -f that governs springs, sound, and waves, and shows that every derivative of e^x is e^x. In machine learning, the same curvature information drives Newton's method, the Hessian, and loss-landscape analysis.

    10 min

  2. May 25

    Overfitting and the bias-variance tradeoff

    Lesson 13 of Track 10 (Classical Machine Learning), the opener of Phase 4 (Knowing whether your model is any good). We have casually mentioned overfitting many times; now we make it precise. There are two distinct ways a model can fail to generalize, and they pull in opposite directions. This lesson names them (bias and variance), shows why making one smaller usually makes the other larger, teaches the foundational diagnostic in machine learning (reading training and test error together), and folds in regularization as the standard low-variance dial.

    12 min

  3. May 25

    Reading the results: the confusion matrix, precision, recall, and ROC

    Lesson 15 of Track 10 (Classical Machine Learning), closing Phase 4 (Knowing whether your model is any good) and closing the track. Accuracy is the metric beginners reach for first, and on imbalanced data it lies catastrophically. This lesson covers the metrics that tell the truth: the confusion matrix and its derived precision and recall, the threshold tradeoff that connects to the logistic-regression dial from lesson 4, and the ROC curve with its AUC summary. With it, you can read a classifier honestly and pick the right metric for the problem in front of you.

    13 min

  4. May 25

    Seeing high-dimensional data: t-SNE

    Lesson 12 of Track 10 (Classical Machine Learning), closing Phase 3 (Finding structure without labels). PCA was great at compression but flat: its straight axes can hide curved or clustered structure. t-SNE is built for a different job, producing a 2D picture in which similar high-dimensional points end up near each other so you can see the clusters. The catch is that the picture is deceptive in specific ways. This lesson shows what t-SNE reveals, what it does not, and how to read its plots without over-reading them.

    12 min

  5. May 25

    Squeezing dimensions: PCA

    Lesson 11 of Track 10 (Classical Machine Learning), in Phase 3 (Finding structure without labels). Clustering grouped unlabeled points. The other great unsupervised job is the opposite: compression. When every data point has dozens or hundreds of features, you need to boil them down to a handful that still capture the signal. PCA does that by finding new axes along which the data varies most. This lesson builds the directions-of-maximum-variance intuition, shows the 2D-to-1D picture, names what a principal component is, and is clear about the linear assumption that the next lesson will work around.

    12 min

  6. May 25

    Taylor series

    Lesson 13 of Track 8 (Visual Math: Calculus), and the track's finale. Complicated functions like sine and the exponential are hard to compute directly; polynomials are easy. The Taylor series rebuilds any well-behaved function near a point out of its derivatives there. It works the expansion f(x) is approximately f(a) + f'(a)(x-a) + f''(a)/2! (x-a)^2 + ..., shows why the factorials are required (the matching property), builds the clean series for e^x, sin, and cos, reveals the small-angle approximation and L'Hopital as first-order Taylor in disguise, and shows that Newton's method, gradient descent, the neural tangent kernel, and the way hardware computes transcendentals are all Taylor at work. The arc that opened with a circle closes here, with a single polynomial standing in for any function.

    12 min

  7. May 25

    Train, test, and cross-validation

    Lesson 14 of Track 10 (Classical Machine Learning), in Phase 4 (Knowing whether your model is any good). The previous lesson said the diagnostic is to compare training and test error. That depends on having an HONEST test error. This lesson covers how to get one: the simple train/test split, the three-way split with a validation set for tuning, and k-fold cross-validation, the standard way to get a stable test-error estimate from limited data. It also names the data-leakage traps that quietly turn an honest evaluation into an optimistic lie.

    12 min

  8. May 24

    Asking the right questions: decision trees

    Lesson 5 of Track 10 (Classical Machine Learning), in Phase 2 (Teaching a machine to decide). Where logistic regression draws one straight boundary, a decision tree asks a sequence of yes/no questions, like a flowchart, funnelling each example to a prediction. This lesson shows how to read and trace a tree, how it is built by choosing the question that best separates the classes, why an unrestrained tree overfits, and why a single tree is powerful but unstable, the flaw random forests fix next.

    11 min
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The mathematical foundations of AI, narrated. Linear algebra, calculus, statistics, and classical machine learning, one bite-size lesson at a time. A focused track from Clawdemy.

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