Mathematical Foundations Roadmap (for AI/ML)
This roadmap provides the mathematical backbone for understanding machine learning and artificial intelligence. It is designed for beginners who may not have a formal math background but want to go deep enough to understand, not just use, ML algorithms.
We start with Linear Algebra (11 lessons already detailed), then expand into Calculus, Probability/Statistics, Core ML Math, and Advanced Topics.
Module 1: Linear Algebra (Data Representation & Transformation)
(Already written: Lessons 1–11)
- Scalars, Vectors, and Matrices: The Language of Data
- Vector Operations: Dot Product, Norms, and Distances
- Matrices: Multiplication, Transpose, and Inverse
- Special Matrices: Identity, Diagonal, Orthogonal
- Rank, Determinant, and Inverses
- Eigenvalues & Eigenvectors
- Singular Value Decomposition (SVD)
- Positive Semi-Definite Matrices and Covariance
- Linear Transformations and Geometry
- Subspaces and Basis
- Linear Independence and Orthogonality
- Linear Independence and Orthogonality
Module 2: Calculus (Optimization & Learning)
- Functions and Limits
- Derivatives and Rules (Product, Quotient, Chain)
- Partial Derivatives & Gradients
- Chain Rule & Backpropagation in Neural Networks
- Gradient Descent (Batch, Stochastic, Mini-batch)
- Convexity and Optimization Landscapes
- Hessian and Second-order Methods (Newton’s Method)
- Constrained Optimization (Lagrange Multipliers, KKT)
Module 3: Probability & Statistics (Uncertainty & Data)
- Probability Axioms and Rules
- Random Variables & Probability Distributions
- Expectation, Variance & Covariance
- Conditional Probability & Bayes’ Theorem
- Independence & Correlation
- Law of Large Numbers & Central Limit Theorem
- Estimation & Confidence Intervals
- Hypothesis Testing & p-values
- Maximum Likelihood Estimation (MLE)
- Maximum A Posteriori (MAP) Estimation
- Bayesian Inference Basics
Module 4: Core Math for ML Algorithms
- Linear Regression Math Recap
- Logistic Regression Math
- Softmax & Cross-Entropy Loss
- Probability Meets Information Theory (Entropy, KL-Divergence)
- Regularization (L1, L2, Elastic Net)
- Matrix Calculus for ML
- Optimization in Neural Networks (Adam, RMSProp, Momentum)
Module 5: Advanced & Applied Math (Optional Deep Dives)
- Information Theory in Depth: Mutual Information & Cross-Entropy
- Markov Chains & Probabilistic Graphical Models
- Optimization Tricks for Deep Learning
- Numerical Stability in ML (conditioning, exploding/vanishing gradients)
- Tensors & Tensor Operations (beyond matrices)
- Bias-Variance Decomposition in ML
- Manifold Learning & Nonlinear Dimensionality Reduction
- Spectral Methods in ML (Graph Laplacians, Spectral Clustering)