# ML Math Foundations

> Vectors, matrices, dot products, matmul, shapes.

Canonical: https://learn.significanthobbies.com/curriculum/concepts/ml-math

Vectors, matrices, dot products, matmul, shapes.

- Difficulty: intro
- Tracks: AI Systems

## Mental model

Three lenses keep coming back: linear algebra describes the data (vectors and matrices), calculus describes learning (gradients), probability describes uncertainty. Pick the lens that matches the question.



## Primary sources

- [Math Notes for ML (Alisa Wuffles)](https://alisawuffles.notion.site/math-notes) (course)
- [Neural Networks: Zero to Hero (Karpathy)](https://karpathy.ai/zero-to-hero.html) (course)
- [Essence of Linear Algebra (3Blue1Brown)](https://www.3blue1brown.com/topics/linear-algebra) (video)
- [CS231n — Linear algebra & calculus prerequisites](https://cs231n.github.io/optimization-1/) (course)

## Practice

### Dot product and matmul shapes

Vectors a=[1,2,3], b=[4,5,6]. Compute dot(a,b). Matrices A (2×3) and B (3×2): is A·B valid? What is the output shape?

**Expected evidence:** dot=32; A·B is 2×2.

## Review prompts

- A matmul fails with a shape error. What does reading the shapes tell you about what the layer is actually doing?

## Build evidence

- **Synthesize: AI Models & Training** — Move from transformer foundations through pre-training, fine-tuning, post-training, compression, and evaluation. Produce one working system, benchmark, or evidence-backed design that integrates the path.

## Prerequisites

- [Probability Fundamentals](https://learn.significanthobbies.com/curriculum/concepts/probability-fundamentals)
- [Descriptive Statistics](https://learn.significanthobbies.com/curriculum/concepts/descriptive-statistics)

## Related concepts

- [Gradient Descent](https://learn.significanthobbies.com/curriculum/concepts/ml-gradient-descent)
- [Vectors & Vector Spaces](https://learn.significanthobbies.com/curriculum/concepts/vectors-and-spaces)
- [Matrices & Linear Transformations](https://learn.significanthobbies.com/curriculum/concepts/matrices-and-transformations)
- [Derivatives & Gradients](https://learn.significanthobbies.com/curriculum/concepts/derivatives-and-gradients)
- [Maximum Likelihood Estimation](https://learn.significanthobbies.com/curriculum/concepts/maximum-likelihood)

## Learning paths

- [12-Week AI Models & Training](https://learn.significanthobbies.com/curriculum/roadmaps/ai-models-training-12w)
- [The Software Engineering Landscape (2026)](https://learn.significanthobbies.com/curriculum/roadmaps/swe-landscape)
- [12-Week Inference & Serving](https://learn.significanthobbies.com/curriculum/roadmaps/inference-serving-12w)
- [12-Week Evaluation & AI Reliability](https://learn.significanthobbies.com/curriculum/roadmaps/ai-reliability-12w)
- [12-Week Multimodal & Spatial Computing](https://learn.significanthobbies.com/curriculum/roadmaps/multimodal-spatial-12w)
- [12-Month Advanced AI Infrastructure](https://learn.significanthobbies.com/curriculum/roadmaps/ai-infra-12-month)
- [12-Week Active Math Stack](https://learn.significanthobbies.com/curriculum/roadmaps/math-stack-12w)