Math Foundations for AI

Eight interactive modules · about 3–4 hours · high-school algebra is the only prerequisite.

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This course sits between Introduction to AI (the ideas) and Machine Learning Foundations (the code). By the end you will be able to read ML notation, reason with conditional probability and Bayes, represent data as vectors and matrices, explain what a gradient is and how gradient descent minimizes error, summarize data with statistics, and see exactly where each tool shows up inside a machine-learning model.

Every module is hands-on: you will manipulate vectors, perform gradient descent on a loss curve, observe beliefs update as evidence is introduced, and trace the mathematics through a complete model. Each module concludes with a short mastery check; passing it marks the module complete.

Warm-up

Module 1

The Language and Notation of ML

Functions and variables, summation notation, subscripts, and the role of logarithms and exponentials. Activity: a notation reference that translates between plain language and mathematical notation.

Pillar 1 · Probability

Module 2

Conditional Probability

Sample spaces, events, the axioms, joint/marginal/conditional probability, and independence. Activity: a conditional-probability explorer over a population. AI anchor: spam filtering.

Module 3

Bayes & Random Variables

Prior, likelihood, posterior; base rates; expectation; the Bernoulli and normal distributions. Activity: a belief-updating demo. AI anchor: naive Bayes and adaptive testing.

Pillar 2 · Linear algebra

Module 4

Vectors & Data

Vectors, the dot product, norms, and the geometry of similarity. Activity: a 2-D vector playground. AI anchor: cosine similarity between embeddings — how LLMs represent meaning.

Module 5

Matrices & Transformations

Matrices as datasets and as transformations; matrix multiplication; transpose and identity. Activity: a matrix-multiplication visualizer. AI anchor: a neural-network layer as a matrix multiply.

Pillar 3 · Optimization

Module 6

Derivatives & Gradient Descent

Slope, rate of change, minima, the gradient, and following the slope downhill to reduce error. Activity: a gradient-descent demo with an adjustable learning rate. AI anchor: this is how models learn.

Pillar 4 · Statistics

Module 7

Statistics for Data & Evaluation

Mean, variance, standard deviation; the normal distribution; sampling; correlation versus causation; and the limitations of summary statistics. Activity: a data-summary and distribution explorer. AI anchor: interpreting evaluation metrics.

Synthesis

Module 8 · Project

The Math of a Tiny Model

A single model — logistic regression — worked end to end on a small dataset, demonstrating precisely where probability, vectors, the loss function, the gradient step, and evaluation each appear. Trace the mathematics through a complete model and explain every step.

Capstone

Build a Concept Manipulative

Put it all together: build a single-page interactive that teaches one Math Foundations concept — a slider-and-readout tool with correct math notation — then submit it in your portal for grading and your certificate.

Why this matters next Probability feeds naive Bayes and model evaluation in Course 3. Linear algebra feeds every model's data representation and the neural nets in Course 4. Optimization feeds training. Statistics feeds evaluation and data prep. None of this is a detour — it is the toolkit the rest of the track is built on.

Next course → Machine Learning Foundations — eight hands-on modules where these tools become working models: the modeling workflow, regression and classification, naive Bayes, decision trees, k-means clustering, PCA, and honest evaluation. Train every model in your browser. No coding required.

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