Welcome

Welcome to Scientific Computing with Python. This course is for learners who already know Python as a programming language and now want to use it as a mathematical instrument — a way to model the physical world, solve equations that have no closed-form solution, simulate systems that are too complex to reason about by hand, and analyze data that arrives in matrices rather than rows.

We will not teach you how to write a for-loop, how to build a Flask app, or how to fine-tune a transformer. We will teach you how to think about numbers when they are stored in 64 bits, how to choose a linear solver based on the structure of a matrix, how to integrate a differential equation that describes a planet's orbit, and how to build experiments that other scientists can reproduce a decade from now.

Why this course exists

Most modern science is computation. A biologist sequencing genomes, an economist forecasting GDP, a physicist colliding particles, an engineer designing an airfoil, a climate scientist projecting sea level rise — every one of them spends more time looking at the output of a Python kernel than at a laboratory bench. The scientific method is increasingly the computational scientific method, and the lingua franca of that method is the SciPy ecosystem.

But scientific computing has its own intellectual core. You cannot just translate textbook equations into Python and trust the result. A naive algorithm can be a million times slower than a clever one, can lose all of its accuracy to a single subtraction, can explode when integrating a stiff system, or can quietly converge to the wrong answer because of how floating-point arithmetic rounds. Learning to recognize and avoid these traps is what separates a programmer who uses NumPy from a computational scientist.

What you will learn

The course has six pillars:

1. The story. Where scientific computing came from — from Babbage to FORTRAN to MATLAB to NumPy — and why the field looks the way it does today.
2. Numerical foundations. Floating point, stability, error, condition number, and the vectorized style of thinking that NumPy makes possible.
3. Computational linear algebra. Arrays as memory, matrix factorizations as algorithms, and why nearly every scientific problem becomes a linear system in disguise.
4. Calculus and differential equations. Numerical differentiation, quadrature, and integrating ODEs that describe physical systems.
5. Optimization, signals, and probability. Root finding, minimization, FFTs, filtering, and Monte Carlo methods.
6. Workflows. Scientific visualization and the discipline of reproducible computational experiments, ending with a capstone that ties everything together.

How the interactive widgets work

Every code block runs in your browser via Pyodide — a full CPython 3.13 build compiled to WebAssembly that ships NumPy, SciPy, pandas, Matplotlib, SymPy, and Plotly. There is nothing to install.

You will see three kinds of widgets:

1. Executable code blocks. Edit any snippet and click Run. The output area shows stdout, plots, and DataFrame tables.
2. Multi-file challenge cards. Small computational problems with hidden test cases. Many use multiple files so you can practice organizing a numerical project the way a real scientist would.
3. Multiple choice questions. Quick conceptual checks at the end of most pages, with per-choice feedback.

A taste of what is coming

Here is a complete scientific computation you will be able to write and understand deeply by the end of the course — simulating a damped pendulum and visualizing its phase portrait.

Right now this code is probably mostly mysterious. By the end of the course, every line — the choice of solver, the tolerance, the phase-space plot, even the units — will feel obvious.