Mathematics for AI · version 1
Learn the mathematics where you use it.
Seventeen interactive support lessons cover M01–M11 mapped to the fifteen proposed AI roadmap courses. Begin with school arithmetic, percentages and basic algebra; every lesson defines its extra symbols and gives a worked example. Optional deeper sections support implementation and research. No completion is required to open an AI topic, and these lessons do not enlarge existing course requirements.
The original five-lesson functions-and-graphs course and its transfer assessment remain separate. This support course records practice and completion, not independent mastery. 0 of 17 support lessons completed.
Build the foundations through shared mathematics courses
Use this contextual path when an AI lesson raises a question, or follow the connected courses for deeper practice. Existing support lessons remain canonical and retain their saved work.
- Algebra, functions and mathematical modeling
- Discrete mathematics: logic, proof and algorithms
- Linear algebra: directions, systems and approximation
- Probability, uncertainty and expected outcomes
- Statistics: from samples to qualified conclusions
- Calculus: local rates and accumulated change
- Optimization: feasible choices and competing goals
Contextual support topics
Each support lesson opens on its own page.
M01: Count rates and price mistakes
About this lesson
Move between counts, fractions, percentages and expected error costs.
Roadmap mappings: C01, C02, C08, C09; not completed, practice outstanding.
M02: Describe variation without inventing evidence
About this lesson
Inspect mean, variance, covariance and the assumptions behind uncertainty summaries.
Roadmap mappings: C01, C02, C09, C15; not completed, practice outstanding.
M03: Trace vectors through a matrix
About this lesson
Compute dot products, check shapes and compose transformations in order.
Roadmap mappings: C02, C03, C04, C05, C08, C11; not completed, practice outstanding.
M03: Project a cloud and inspect what is lost
About this lesson
Connect unit directions, reconstruction, covariance, eigenvectors and low-rank intuition.
Roadmap mappings: C02, C04, C05; not completed, practice outstanding.
M04: Update a belief from counts
About this lesson
Distinguish conditional directions, joint mass, expectation and posterior probability.
Roadmap mappings: C01, C05, C07, C10, C12; not completed, practice outstanding.
M04: Separate likelihood from a prior
About this lesson
Fit a Bernoulli probability and compare maximum likelihood with explicit prior assumptions.
Roadmap mappings: C05, C06, C07, C12; not completed, practice outstanding.
M05: Follow a gradient through a computation
About this lesson
Connect a derivative, chain factors, partial gradients and a numerical check.
Roadmap mappings: C03, C05, C06, C10, C14; not completed, practice outstanding.
M05: Compute probabilities without overflow
About this lesson
Use exponential ratios, logarithms, cross entropy and stable arithmetic.
Roadmap mappings: C03, C05, C06, C10; not completed, practice outstanding.
M06: Sample a signal without hiding aliasing
About this lesson
Inspect waveform samples, frequency bins, windows and lost high-frequency information.
Roadmap mappings: C04; not completed, practice outstanding.
M07: Relate a latent approximation to its evidence
About this lesson
Enumerate KL and ELBO exactly, then inspect numerical integration separately.
Roadmap mappings: C06, C12, C13; not completed, practice outstanding.
M08: Turn an angle into local motion
About this lesson
Connect trigonometry, rotations, Jacobians, least-squares motion and singularities.
Roadmap mappings: C04, C11, C13; not completed, practice outstanding.
M09: Connect dynamics estimates and constraints
About this lesson
Step a feedback system and separate numerical accuracy from stability and measurement assumptions.
Roadmap mappings: C11, C12, C13; not completed, practice outstanding.
M10: Compare paired experiments and interactions
About this lesson
Keep task identity when comparing methods and enumerate a small bootstrap.
Roadmap mappings: C14, C15; not completed, practice outstanding.
M11: Notice the winner selected by chance
About this lesson
Inspect repeated comparisons, weak signals and predeclared decision rules.
Roadmap mappings: C07, C15; not completed, practice outstanding.
M11: Separate a comparison from a causal claim
About this lesson
Change cohort composition and diagnose an aggregate reversal.
Roadmap mappings: C07, C09, C15; not completed, practice outstanding.
M04: Average future rewards with explicit assumptions
About this lesson
Compute expectation, discounted sums and support-aware importance ratios.
Roadmap mappings: C07, C10, C12, C14; not completed, practice outstanding.
M04: Read a density as probability per unit
About this lesson
Connect continuous probability, area, Gaussian scale and numerical integration.
Roadmap mappings: C05, C06, C10, C11, C12, C13; not completed, practice outstanding.
Find support by AI roadmap topic
C01 mathematical preparation
C02 mathematical preparation
C03 mathematical preparation
C04 mathematical preparation
C05 mathematical preparation
C06 mathematical preparation
C07 mathematical preparation
C08 mathematical preparation
C09 mathematical preparation
C10 mathematical preparation
C11 mathematical preparation
C12 mathematical preparation
C13 mathematical preparation
C14 mathematical preparation
C15 mathematical preparation
Open mathematics progress and backups. Existing temporary refreshers remain at Before you start.