Mathematical Foundations

ML draws from multiple math areas. This topic is a roadmap: what to learn, why it matters, and how the pieces connect.

The Core Toolkit

• Linear algebra: vectors/matrices, projections, decompositions (SVD).
• Calculus: derivatives, gradients, chain rule (backprop).
• Probability: uncertainty, expectations, Bayes’ rule.
• Statistics: estimation, generalization, significance.
• Optimization: how training algorithms actually minimize loss.

A Useful “Translation Table”

• “Similarity” often means dot products / cosine similarity (linear algebra).
• “Learning” often means gradient-based optimization (calculus + optimization).
• “Uncertainty” often means distributions and expectations (probability).
• “Does it generalize?” often means statistical reasoning and careful evaluation (statistics).

Suggested Learning Order

1. Vectors, matrices, matrix multiplication, dot products.
2. Derivatives, gradients, and the chain rule.
3. Random variables, expectation, basic distributions.
4. MLE/MAP, overfitting, bias–variance, confidence intervals.
5. Gradient descent, momentum, Adam, regularization.

How To Practice

• Derive gradients for simple models (linear/logistic regression) by hand once.
• Check shapes in matrix expressions until it becomes automatic.
• Run small experiments: change learning rate, batch size, weight decay, and observe effects.