Math using Python

Welcome — this repository contains teaching materials, examples, and exercises that use Python to explore and teach mathematics.

About the instructor

I am ADIL MUKHTAR SHAH, a mathematics teacher with over 17 years of classroom experience. I created these materials to help students (and fellow teachers) learn mathematical concepts through interactive Python examples, clear visualisations, and hands-on exercises.

Purpose

This repo is designed to:

• Demonstrate mathematical concepts with runnable Python code and Jupyter notebooks.
• Provide classroom-ready exercises and solutions.
• Offer visualisations that make abstract ideas concrete.
• Help teachers adopt Python in their teaching practice.

Who is this for?

• Secondary and early undergraduate students learning algebra, calculus, linear algebra, probability, and statistics.
• Teachers who want ready-made Python examples and lesson material.
• Self-learners who prefer learning mathematics by doing.

Repository structure (suggested)

• notebooks/ — interactive Jupyter notebooks for lessons and demos
• examples/ — small, focused Python examples and scripts
• exercises/ — student exercises and worksheets
• solutions/ — solution notebooks and scripts
• slides/ — slide decks and lesson plans
• data/ — example datasets used in lessons
• requirements.txt — Python packages used in the repo

Requirements

Typical dependencies:

• Python 3.8+
• numpy
• scipy
• sympy
• matplotlib
• pandas
• jupyter (or jupyterlab)

Install with:

pip install -r requirements.txt

Quick start

Open a notebook from the notebooks/ folder with Jupyter, or run small examples from examples/. Here is a short Python example that solves a quadratic equation and plots the quadratic:

import numpy as np
import matplotlib.pyplot as plt
from math import sqrt

# coefficients for ax^2 + bx + c = 0
a, b, c = 1, -3, 2  # roots: 1 and 2

discriminant = b**2 - 4*a*c
roots = ((-b + np.sqrt(discriminant)) / (2*a), (-b - np.sqrt(discriminant)) / (2*a))
print("Roots:", roots)

# plot
x = np.linspace(-1, 4, 400)
y = a * x**2 + b * x + c
plt.axhline(0, color='black', linewidth=0.8)
plt.plot(x, y, label=f'{a}x^2 + {b}x + {c}')
plt.scatter(roots, [0, 0], color='red')
plt.legend()
plt.title('Quadratic: roots and curve')
plt.xlabel('x')
plt.ylabel('y')
plt.show()

Example lesson topics

• Algebra: solving equations, factorisation, polynomial behaviour
• Calculus: limits, derivatives (symbolic via sympy), numerical differentiation, integrals and area
• Linear Algebra: vectors, matrices, eigenvalues, visual intuition
• Probability & Statistics: distributions, sampling, hypothesis basics
• Geometry: coordinate geometry, transformations, plotting conic sections
• Number Theory & Sequences: modular arithmetic, recurrence relations

Teaching suggestions

• Use notebooks to present theory, then switch to hands-on exercises.
• Start with numeric examples (numpy) then introduce symbolic reasoning (sympy).
• Encourage students to modify parameters and observe changes in plots.
• Provide short, targeted exercises with immediate automated checks where possible.

Contributing

Contributions are welcome:

• Add new notebooks or exercises
• Improve explanations and visualisations
• Submit issues for errors or unclear material Please follow the repository style (clear markdown explanations, working notebooks, and minimal dependencies).

License

This repository is shared for educational use. If you have a preferred license, add a LICENSE file (e.g., MIT).

Contact

ADIL MUKHTAR SHAH
Mathematics Teacher — 17+ years experience
GitHub: ADIL8590
Email: (mash8851@gmail.com)