# 30-Day Math Rating Climb

> Like chess ratings: you start near 1500, solve drills matched to your level, and harder problems appear as you improve. Four weeks through the foundations that underpin ML, search evals, and systems reasoning.

Canonical: https://learn.significanthobbies.com/curriculum/roadmaps/math-rating-climb-30d

Like chess ratings: you start near 1500, solve drills matched to your level, and harder problems appear as you improve. Four weeks through the foundations that underpin ML, search evals, and systems reasoning.

- Horizon: 30d
- Outcome: Raise your per-roadmap ELO by climbing from linear algebra through statistics to calculus — each week unlocks harder drills at your edge.
- Tracks: Mathematics

Work each milestone as a claim that needs evidence. Predict the mechanism and
failure mode first, study the linked concepts, complete the drills without
copying an answer, and preserve the resulting code, measurements, or design.

## Milestone 1: Week 1 — Linear algebra

Vectors, matrices, and the geometric picture behind embeddings and layers.

### Concepts

- [Vectors & Vector Spaces](https://learn.significanthobbies.com/curriculum/concepts/vectors-and-spaces) — Vectors as ordered lists, dot products, norms, orthogonality, and the geometric picture of n-dimensional space.
- [Matrices & Linear Transformations](https://learn.significanthobbies.com/curriculum/concepts/matrices-and-transformations) — Matrix multiplication as composing linear maps: rotation, scaling, projection, and change of basis.
- [Eigenvalues & Matrix Decomposition](https://learn.significanthobbies.com/curriculum/concepts/eigenvalues-decomposition) — Eigenvectors as directions preserved by a transformation; eigenvalues as stretch factors; SVD as the universal factorization.



## Milestone 2: Week 2 — Probability & description

Uncertainty bookkeeping and summarizing data without lying.

### Concepts

- [Probability Fundamentals](https://learn.significanthobbies.com/curriculum/concepts/probability-fundamentals) — Sample spaces, conditional probability, independence, and Bayes' rule for updating beliefs.
- [Random Variables & Distributions](https://learn.significanthobbies.com/curriculum/concepts/random-variables) — Discrete and continuous distributions, expectation, variance, and the law of large numbers.
- [Descriptive Statistics](https://learn.significanthobbies.com/curriculum/concepts/descriptive-statistics) — Summarizing data: mean, median, variance, correlation, and when each summary lies.



## Milestone 3: Week 3 — Inference

Confidence intervals and hypothesis tests — the math behind A/B readouts.

### Concepts

- [Estimation & Confidence Intervals](https://learn.significanthobbies.com/curriculum/concepts/estimation-confidence) — Point estimates, standard error, confidence intervals, and what '95% confident' actually means.
- [Hypothesis Testing](https://learn.significanthobbies.com/curriculum/concepts/hypothesis-testing) — Null and alternative hypotheses, p-values, significance, power, and Type I/II errors.
- [Linear Regression](https://learn.significanthobbies.com/curriculum/concepts/regression-basics) — Fitting a line (or hyperplane) by least squares; residuals, R², and the geometry of projection.



## Milestone 4: Week 4 — Calculus bridge

Gradients and optimization — the runway into gradient descent and training.

### Concepts

- [Derivatives & Gradients](https://learn.significanthobbies.com/curriculum/concepts/derivatives-and-gradients) — Partial derivatives, the gradient vector, and reading a loss surface for descent direction.
- [Multivariable Optimization](https://learn.significanthobbies.com/curriculum/concepts/multivariable-optimization) — Convexity, critical points, constrained optimization, and why SGD works on non-convex losses anyway.
- [Information & Entropy](https://learn.significanthobbies.com/curriculum/concepts/information-entropy) — Entropy as surprise, cross-entropy as a loss, KL divergence as a distributional distance.