Applied Math for Data Science

15 small projects in data science maths

I built 15 small Python projects to practise the maths behind data science. Each includes simple code and a visual.

See the project guide for the formulas, methods, and results.

If this helps you learn, please ⭐ the repo!

---

Explore the projects

#	Project	What you will explore	Notebook
01	Linear Regression From Scratch	Least squares, slope, intercept, and prediction errors	Open
02	Gradient Descent Visualizer	Derivatives, learning rate, and optimization steps	Open
03	PCA From Scratch	Covariance, eigenvectors, and dimensionality reduction	Open
04	Statistical A/B Testing Engine	Conversion rates, z-scores, and p-values	Open
05	Bayesian A/B Testing	Bayes' rule, Beta distributions, and posterior probability	Open
06	Customer Churn Probability	Logistic probabilities and simple customer features	Open
07	Time-Series Forecasting	Trend, seasonality, moving averages, and forecasts	Open
08	Portfolio Optimization	Covariance, risk, return, and asset mixes	Open
09	Matrix Factorization Recommender	Low-rank factors and missing-rating predictions	Open
10	Clustering From Scratch	Distance, cluster centers, and k-means	Open
11	Logistic Regression From Scratch	Sigmoid, gradients, and decision boundaries	Open
12	Naive Bayes From Scratch	Conditional probability and word-count classification	Open
13	Monte Carlo Simulation Lab	Random sampling, area, and an estimate of pi	Open
14	Probability Anomaly Detection	Mean, standard deviation, and z-score flags	Open
15	Dynamic Pricing Optimization	Demand curves, revenue, and grid search	Open

---

Get started

Browse the notebooks

Open any .ipynb file in Jupyter Notebook, JupyterLab, or Visual Studio Code. The explanation and visualization preview are saved in the notebook, so you can browse the project before running its code.

Run a project

1. Install Python 3.

2. Install the libraries used in the projects:

   python -m pip install numpy matplotlib

3. Open a project folder and run its script. For example:

   cd 01_linear_regression
   python main.py

   Or open that folder's notebook and run the cells from top to bottom.

The scripts print key results and save generated charts in each project's output/ folder. The notebooks display charts inline. Random examples use fixed seeds where needed, so the results are repeatable.

How each project is organized

01_linear_regression/
├── 01_linear_regression.ipynb   # Explanation, code, and visualization preview
├── main.py                      # Standalone Python version
├── README.md                    # Short project guide
└── output/                      # Chart created when main.py is run

Learning approach

• Start with a small example. The data is intentionally compact and easy to inspect.
• Keep the math visible. The code uses straightforward formulas and named steps.
• Learn by changing things. Try different sample values, learning rates, or model settings and observe what changes.
• Build intuition first. These projects are practice exercises, not optimized software packages.

Tools

• Python
• NumPy
• Matplotlib
• Jupyter notebooks

About the examples

The datasets are small teaching examples, not real customer, experiment, or market data. Statistical results are simplified for learning. The portfolio example is not investment advice, and the pricing and churn examples should not be used to make real business decisions.

---