📘 Week 3 – Math Foundations (Linear Algebra + Statistics)

🔢 Project Overview

This project focuses on the mathematical foundations of machine learning using NumPy.
The goal is to practice:

• Matrix multiplication (basis of neural networks)
• Vector operations
• Statistical measures (mean, variance, std dev)
• Data visualization (normal vs uniform distributions)

By the end, you’ll have a stronger grasp of the math that powers AI/ML.

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🗂️ Dataset

• Synthetic Data generated using NumPy
• Normal distribution (np.random.randn)
• Uniform distribution (np.random.rand)
• Random integers for matrix practice (np.random.randint)

No external dataset was required.

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🛠️ Key Steps

1. Matrix Multiplication

   • Practiced multiplying matrices with compatible dimensions.
   • Verified shape rules: (m × n) × (n × p) → (m × p).

2. Vector Operations

   • Element-wise operations (addition, subtraction, multiplication).
   • Dot product.
   • Normalization of vectors.

3. Statistics

   • Manually computed mean, variance, and std dev.
   • Compared manual results with NumPy’s built-in functions.

4. Visualizations

   • Plotted histograms of:
     • Normal distribution (bell curve).
     • Uniform distribution (flat distribution).
   • Added vertical lines for the mean to interpret results.

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📊 Insights & Learnings

• Matrix multiplication underpins neural networks (weights × inputs).
• Statistics (mean, variance, std dev) are critical for feature scaling and data preprocessing.
• Normal distribution shows clustered data around the mean, while uniform distribution spreads values evenly.
• Understanding distributions helps in data analysis and detecting anomalies.

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📷 Plots

Below is the comparison between a Normal distribution and a Uniform distribution:

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🛠️ Requirements

Install the following dependencies before running the notebook:

numpy
matplotlib