# 3Blue1Brown Visual Mathematics

Interactive notebooks inspired by the [3Blue1Brown](https://www.3blue1brown.com/) video series. Use these alongside the foundational notebooks for visual intuition.

This folder is best used as the intuition layer for the rest of the math section. Come here when a symbolic explanation makes sense formally but still does not feel concrete.

## Series

### [Calculus](calculus/) (12 notebooks)
*Essence of Calculus series*

| # | Notebook | Topics |
|---|---------|--------|
| 01 | Essence of Calculus | Geometric intuition for derivatives |
| 02 | Paradox of the Derivative | Instantaneous rate of change |
| 03 | Derivative Formulas | Power rule, sum rule, product rule |
| 04 | Chain & Product Rules | Composition of functions |
| 05 | Exponential Derivatives | e^x and natural logarithm |
| 06 | Implicit Differentiation | Differentiating implicit equations |
| 07 | Limits & L'Hopital | Formal definition, L'Hopital's rule |
| 08 | Integration | Fundamental theorem of calculus |
| 09 | Area and Slope | Connection between integration and differentiation |
| 10 | Higher-Order Derivatives | Second derivatives, concavity |
| 11 | Taylor Series | Polynomial approximation of functions |
| 12 | What Makes e Special | Why e is the natural base |

### [Linear Algebra](linear-algebra/) (13 notebooks)
*Essence of Linear Algebra series*

| # | Notebook | Topics |
|---|---------|--------|
| 01 | Vectors & Linear Combinations | Span, basis vectors |
| 02 | Linear Transformations & Matrices | Matrices as transformations |
| 03 | Matrix Multiplication | Composition of transformations |
| 04 | Determinants | Area/volume scaling factor |
| 05 | Eigenvalues & Eigenvectors | Invariant directions under transformation |
| 06 | Inverse Matrices & Systems | Solving Ax=b, invertibility |
| 07 | Dot Products & Duality | Geometric interpretation |
| 08 | Cross Products | 3D perpendicular vectors |
| 09 | Change of Basis | Coordinate transformations |
| 10 | 3D Transformations | Extending to three dimensions |
| 12 | Cramer's Rule | Solving systems via determinants |
| 13 | Quick Eigenvalue Trick | Fast 2x2 eigenvalue computation |
| 16 | Abstract Vector Spaces | Functions as vectors |

### [Differential Equations](differential-equations/) (8 notebooks)

| # | Notebook | Topics |
|---|---------|--------|
| 01 | Introduction | What are differential equations |
| 02 | Heat Equation | Partial differential equations |
| 03 | Solving Heat Equation | Separation of variables |
| 04 | Fourier Series | Decomposing periodic functions |
| 05 | Laplace Transforms | Algebraic approach to ODEs |
| 06 | Understanding Laplace | Intuition for the transform |
| 07 | Resonance | Driven oscillators |
| 08 | Matrix Exponents | e^(At) and systems of ODEs |

### [Neural Networks](neural-networks/) (9 notebooks)

| # | Notebook | Topics |
|---|---------|--------|
| 01 | What is a Neural Network | Neurons, layers, activations |
| 02 | Gradient Descent | Learning by minimizing loss |
| 03 | Backpropagation | Chain rule through a network |
| 04 | Backprop Calculus | Formal derivation |
| 05 | GPT and LLMs | How large language models work |
| 06 | Attention & Transformers | Self-attention mechanism |
| 07 | Attention Deep Dive | Multi-head attention, QKV |
| 08 | How GPT Stores Facts | Knowledge in transformer weights |
| 09 | Diffusion Models | Denoising score matching |

## How to Use

These notebooks complement the [foundational/](../foundational/) course. When a concept feels abstract, find the matching 3Blue1Brown notebook for visual intuition:

- Struggling with derivatives? → `calculus/01-07`
- Matrices feel mechanical? → `linear-algebra/01-05`
- Backprop unclear? → `neural-networks/03-04`

## How To Use This Folder Well

- Use this folder to clarify concepts, not to replace the main math sequence.
- Jump into the specific series that matches the concept blocking you.
- Return to the more formal notebooks after you regain intuition.

## Prerequisites

- Python 3.8+, NumPy, Matplotlib
- No prior math prerequisites (these build intuition from scratch)

## What Comes Next

- Return to [../foundational/README.md](../foundational/README.md) after using these visual explanations.
- Continue to [../mml-book/README.md](../mml-book/README.md) if you want more rigorous formal depth.
- Continue to [../cs229-course/README.md](../cs229-course/README.md) if you want the ML-algorithm application layer next.
