Machine Learning, From the Math Up

# Read, reason about, and build modern neural networks, understanding why each layer and training trick works instead of treating them as magic.

# a suggested order, not a lock: jump anywhere, checkpoints track what you finish

1. start here

   Linear Algebra6 posts · 1h 10m

   Vectors, linear maps, matrices, change of basis and eigenvalues are the alphabet every model is written in.

   1. The Geometry of Linearity: Why Vector Spaces MatterWant to Learn10 min
   2. Linear Transformations: The Language of ChangeWant to Learn11 min
   3. Matrices as Transformations: Rank, Span, and the Geometry of SolutionsDeep Dive12 min
   4. Change of Basis: Seeing Transformations Through New EyesDeep Dive12 min
   5. The Anatomy of Linear Maps: Injectivity, Surjectivity, and IsomorphismDeep Dive12 min
   6. Eigenvalues and Eigenvectors: The DNA of Linear TransformationsDeep Dive13 min scheduled
2. Linear Algebra10 mindemo

   optional

   Play with transformations and eigenvectors before they reappear as weight matrices.

3. Foundations of Machine Learning10 posts · 1h 39m 1 self-checks

   The full arc: from classical models through CNNs and sequence models to representation, generative and reinforcement learning.

   1. Understanding Machine Learning: From Classic Algorithms to Modern Neural NetworksDeep Dive9 min scheduled
   2. From Abstract Problems to Concrete Models: Classical Algorithms in PracticeDeep Dive10 min scheduled
   3. Deep Neural Networks: Architecture, Layers, and Activation FunctionsDeep Dive11 min scheduled
   4. Training Neural Networks: Backpropagation, Gradient Descent, and OptimizationDeep Dive9 min scheduled
   5. Convolutional Neural Networks: Deep Learning for ImagesDeep Dive10 min scheduled
   6. Recurrent and Transformer Networks: Deep Learning for SequencesDeep Dive11 min scheduled
   7. Unsupervised and Representation Learning: Discovering Patterns Without LabelsDeep Dive9 min scheduled
   8. Generative Models: GANs, Diffusion Models, and BeyondDeep Dive10 min scheduled
   9. Reinforcement Learning: Concepts, Value Functions, and Policy OptimizationDeep Dive11 min scheduled
   10. Integrating Modern Machine Learning: From Classical Foundations to Advanced AIDeep Dive9 min scheduledquiz
4. Neural Network Lab10 mindemo

   Assemble a small network by hand and watch it learn, now that you know what the matrices mean.

5. Machine Learning Foundations CapstoneDeep Dive5 minquiz

   Capstone: prove you can reason about every layer and training trick, not just name them.

6. You can build and explain a neural network from first principles