AI/ML Mathematics

Build a strong mathematical foundation for Artificial Intelligence and Machine Learning.

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

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