Math For AI
A clean, ordered curriculum for the mathematics behind modern AI, built for students who want strong intuition and practical ML context.
One consistent path from math to ML intuition.
Each module is structured around core concepts, formulas, applied ML context, interview-style questions, exercises, and resources.
Study in sequence.
The order moves from representation and change to uncertainty, information, geometry, and dimensionality reduction.
Linear Algebra
The backbone of machine learning representations.
- Scalars, vectors, matrices, tensors
- Vector and matrix operations
- Dot product and geometric interpretation
- Matrix multiplication
- Identity, transpose, inverse
- Rank of a matrix
- Systems of linear equations
- Linear transformations
- Column space and null space (intuition)
- Eigenvalues and eigenvectors (intuition + usage)
- Orthogonality
- Norms and distances (L1, L2)
Calculus
The language of change, gradients, and learning.
- Functions and graphs
- Limits (intuition only)
- Derivatives and gradients
- Partial derivatives
- Chain rule (very important)
- Gradient as direction of steepest descent
- Local vs global minima
- Convex vs non-convex functions
Optimization
How models improve through loss and updates.
- Gradient descent
- Learning rate intuition
- Cost and loss functions
- Saddle points
- Vanishing and exploding gradients (intuition)
Probability Theory
Reasoning clearly under uncertainty.
- Random variables
- Discrete vs continuous variables
- Probability distributions
- PMF, PDF, CDF
- Expectation and variance
- Common distributions: Bernoulli, Binomial, Normal, Uniform, Poisson
- Independence and conditional probability
- Bayes' theorem
- Likelihood vs probability
Statistics
From samples and variation to decisions.
- Population vs sample
- Measures of central tendency
- Measures of dispersion
- Covariance
- Correlation
- Bias and variance
- Sampling techniques
- Central Limit Theorem (intuition)
- Law of Large Numbers
- Outliers and robustness
Information Theory
Entropy, surprise, and classification loss.
- Entropy
- Cross-entropy
- KL divergence
- Information gain
- Why cross-entropy is used in classification
Geometry and Distances
Similarity, space, and high-dimensional intuition.
- Euclidean distance
- Manhattan distance
- Cosine similarity
- Angle between vectors
- High-dimensional intuition (curse of dimensionality)
Probability + Linear Algebra
The bridge to multivariate modeling.
- Multivariate distributions
- Gaussian distribution in higher dimensions
- Covariance matrix interpretation
- Mahalanobis distance
Matrix Factorization
High-value decompositions for ML systems.
- Eigen decomposition
- Singular Value Decomposition (SVD)
- PCA math intuition
- Dimensionality reduction rationale