Module 1: Introduction to AI/ML Mathematics
- Importance of Mathematics in AI/ML
- Overview of Key Mathematical Concepts for AI/ML
- Mathematical Tools Used in Machine Learning
Module 2: Linear Algebra
- Vectors and Matrices
- Matrix Operations: Addition, Multiplication, Inversion
- Eigenvalues and Eigenvectors
- Singular Value Decomposition (SVD)
- Systems of Linear Equations
- Applications of Linear Algebra in Machine Learning
Module 3: Calculus for AI/ML
- Limits and Continuity
- Derivatives and Differentiation
- Partial Derivatives
- Gradient Descent and Optimization
- Chain Rule and Backpropagation in Neural Networks
- Higher-Order Derivatives and Optimization
Module 4: Probability and Statistics
- Probability Theory Basics
- Random Variables and Probability Distributions
- Expectation and Variance
- Hypothesis Testing and p-values
- Statistical Inference and Confidence Intervals
- Central Limit Theorem and Sampling
Module 5: Optimization Techniques
- Convex Optimization
- Gradient Descent and Variants (Stochastic, Mini-batch)
- Learning Rate and Convergence
- Newton's Method
- Constrained Optimization
- Optimizing Cost Functions for Machine Learning
Module 6: Information Theory for AI/ML
- Entropy and Information Gain
- Kullback-Leibler (KL) Divergence
- Cross-Entropy Loss Function
- Mutual Information and its Role in Machine Learning
Module 7: Numerical Methods and Computation
- Numerical Stability and Precision
- Numerical Integration and Differentiation
- Solving Linear and Nonlinear Equations
- Iterative Methods for Large-Scale Problems
Module 8: Graph Theory and Networks
- Graphs and Their Representation
- Graph Traversal: BFS, DFS
- Weighted Graphs and Shortest Path Algorithms
- Graph Neural Networks (GNNs)
Module 9: Matrix Factorization and Decomposition
- Principal Component Analysis (PCA)
- Non-Negative Matrix Factorization (NMF)
- LU, QR, and Cholesky Decompositions
- Applications of Matrix Decompositions in Machine Learning
Module 10: Advanced Topics in AI/ML Math
- Tensor Calculus for Deep Learning
- Advanced Optimization Algorithms (Adam, Adagrad, RMSProp)
- Deep Learning Theory: Universal Approximation Theorem
- Understanding Neural Network Complexity and Overfitting
Module 11: Capstone Project and Review
- AI/ML Mathematics Capstone Project
- Application of Mathematical Concepts to Real-World ML Models
- Final Review and Q&A