maths for AI and ML

1. Linear Algebra for Machine Learning

• Vectors and Matrices
  • Operations: addition, multiplication, transpose
  • Use in data representation
• Matrix Multiplication and Linear Transformations
• Determinants and Inverses
• Eigenvalues and Eigenvectors
  • PCA and dimensionality reduction
• Applications:
  • Word embeddings (word2vec, GloVe)
  • Neural network forward and backward propagation

2. Calculus for Optimization

• Limits and Continuity
• Derivatives and Gradients
  • Partial derivatives
  • Gradient vectors
• Chain Rule
  • Backpropagation in neural networks
• Optimization
  • Gradient descent
  • Learning rate intuition
• Applications:
  • Training deep neural networks
  • Cost/loss function minimization

3. Probability and Statistics

• Basic Probability Rules
  • Bayes’ Theorem
  • Conditional probability
• Probability Distributions
  • Gaussian, Bernoulli, Binomial, etc.
• Expectation and Variance
• Maximum Likelihood Estimation (MLE)
• Hypothesis Testing
• Applications:
  • Naive Bayes classifiers
  • Probabilistic models like HMMs, Bayesian networks

4. Discrete Mathematics & Logic

• Set Theory and Functions
• Graphs and Trees
• Boolean Logic
• Applications:
  • Decision trees
  • Knowledge representation in AI

5. Information Theory

• Entropy and Information Gain
• KL Divergence
• Cross-Entropy Loss
• Applications:
  • Decision trees, neural networks, regularization

6. Numerical Methods

• Root Finding (e.g., Newton-Raphson)
• Numerical Differentiation and Integration
• Linear Solvers (LU decomposition, etc.)
• Applications:
  • Solving equations in model training

7. Advanced Topics

• Convex Optimization
• Manifold Learning
• Topology Basics (for advanced deep learning)