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                                            1. Mathematical Foundations for ML
 Why mathematics matters in ML
 Scalars, vectors, matrices, tensors
 Mathematical notation in ML

2. Linear Algebra for Machine Learning
 Vectors & vector spaces
 Matrix operations & properties
 Dot product, projections, and norms
 Eigenvalues & eigenvectors (intuition + ML use)
 Applications: Linear Regression, PCA


3. Calculus for Machine Learning
 Functions, limits & continuity
 Partial derivatives & gradients
 Chain rule (Backpropagation intuition)
 Directional derivatives
 Jacobian & Hessian (conceptual understanding)

4. Optimization Techniques
 Formulating optimization problems
 Convex vs non-convex functions
 Gradient Descent (Batch, SGD, Mini-batch)
 Local vs global minima
 Regularization basics

5. Distance, Norms & Similarity
 L1, L2 norms
 Euclidean, Manhattan & Minkowski distances
 Similarity measures
 Applications: KNN, Clustering, Recommendation Systems

6. Mathematical Understanding of ML Algorithms
 Linear Regression (mathematical derivation)
 Logistic Regression (decision boundary intuition)
 Support Vector Machines (geometric view)
 K-Means clustering (optimization perspective)
 PCA (variance & eigenvectors)

7. Numerical Methods & Stability
 Floating-point errors & precision issues
 Gradient vanishing & exploding
 Stability in numerical optimization

8. Practical Applications & Math Exercises
 Visualizing gradients & loss surfaces
 Connecting math to ML code
 Hands-on problem-solving exercises                                    

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