Python Notebooks¶

Jupyter notebooks for hands-on implementation and computational exercises.

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Getting Started¶

Notebook 0: Python Libraries Basics Introduction to NumPy, SciPy, and Pandas — Essential libraries for this course.

Open in GitHub | Open in Google Colab | Download

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Lecture Notebooks¶

Notebook 2: Analytic Geometry¶

Norms, inner products, projections, Gram-Schmidt, and rotations — all implemented in Python with visualizations.

Open in GitHub | Open in Google Colab | Download

What's inside:

• Compute and visualize \(\ell_1\), \(\ell_2\), \(\ell_\infty\) norms and unit balls
• Inner products, cosine similarity, and angle computation
• Projection onto lines and general subspaces with 2D visualization
• Gram-Schmidt implementation from scratch (compare with scipy.linalg.qr)
• 2D rotation matrices and vector transformations

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Notebook 3: Matrix Decomposition¶

Eigenvalues, SVD, and matrix approximation — the computational workhorses of data science.

Open in GitHub | Open in Google Colab | Download

What's inside:

• Determinants, trace, and property verification
• Eigenvalue computation and eigenvector visualization
• Cholesky decomposition for positive definite matrices
• Eigendecomposition: \(A = PDP^{-1}\) reconstruction
• SVD: \(A = U\Sigma V^T\) with image compression demo
• Matrix approximation: reconstruction error vs rank

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Notebook 4: Vector Calculus¶

Gradients, Jacobians, and backpropagation — the mathematics behind training neural networks.

Open in GitHub | Open in Google Colab | Download

What's inside:

• Numerical differentiation (forward and central differences)
• Gradient computation and gradient field visualization
• Gradient descent from scratch (simple and Rosenbrock functions)
• Descent path visualization on contour plots
• Chain rule and backpropagation for a 2-layer neural network
• Hessian computation and Newton's method comparison

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Notebook 5: Probability and Distributions¶

From coin flips to Gaussians — simulate, visualize, and understand probability distributions.

Open in GitHub | Open in Google Colab | Download

What's inside:

• Discrete distributions (Bernoulli, Binomial, Geometric) with PMF plots
• Continuous distributions (Uniform, Exponential, Gaussian) with PDF/CDF plots
• Bayes' Theorem: medical test example with prior vs posterior
• Joint distributions and marginalization with heatmaps
• Covariance and correlation with scatter plots
• Multivariate Gaussian: contour plots and sampling
• Central Limit Theorem demonstration

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Quick Reference: All Notebooks¶

#	Topic	Colab	Download
0	Python Libraries Basics	Open	ipynb
2	Analytic Geometry	Open	ipynb
3	Matrix Decomposition	Open	ipynb
4	Vector Calculus	Open	ipynb
5	Probability & Distributions	Open	ipynb

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Setup & Usage¶

Option 1: Google Colab (Recommended)¶

Click any "Open in Google Colab" link above — no setup required!

Option 2: Local Jupyter¶

# Install dependencies
pip install jupyter numpy scipy matplotlib pandas

# Start Jupyter
jupyter notebook

Option 3: VS Code¶

Install Python and Jupyter extensions, then open .ipynb files directly.

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Notebook Structure¶

Each notebook includes:

1. Learning Objectives - What you'll learn
2. Theory Review - Key concepts from lectures
3. Implementation - Step-by-step code with explanations
4. Visualizations - Plots and graphs for intuition
5. Practice Exercises - 4 exercises per notebook

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Best Practices¶

Before Starting:

• Review corresponding lecture slides
• Read the matching math tutorial
• Understand the theory before coding

While Working:

• Run cells in order
• Experiment with parameters
• Add your own test cases
• Write notes in markdown cells

After Completing:

• Compare your implementations with library functions (SciPy, scikit-learn)
• Test edge cases
• Try the practice exercises

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