Year 2025-2026
We recall that numerical analysis is defined here, in the mind of Nick Trefethen, as a study of methods and algorithms for the effective resolution of continuous mathematics problems.
As part of the second year course of the APM41012EP at École polytechnique: “Introduction to Digital Analysis: From Mathematical Foundations to Experimentation with Jupyter”, students must familiarize themselves with three levels of skills:
Understanding the mathematical foundations of numerical analysis
Design and analysis of precise, robust and efficient algorithms
Implementation and experimentation leading to a detailed understanding of methods
The textbook provides a solid basis for the first point, as well as the design of algorithms and their analysis beyond the proposed history and bibliography. It is the foundation of the course. The PCs make it possible to take back these points and to help prepare the homework for which the students acquire the second and third points. The teaching team has invested a significant amount of time to provide a set of Jupyter notebooks to fully acquire the third point, that of experimentation and analysis of methods. This database was previously available on the basis of a set of notebooks provided as part of Moodle and required the implementation of a Jupyter environment on students’ computers.
We have therefore undertaken to provide a unified place, thanks to the possibilities offered by the JupyterBook, allowing a facilitated use of notebooks and a real flexibility for students.
For each chapter, the reader will find an Introduction to set the stakes of the chapter, a useful set of notebooks for the required part of the course in the Essentials section, elements to go further for the students interested, and finally a Challenge whose resolution must show that the essential notions of the course have been assimilated.
Three modes of use of the JupyterBook are then possible:
Use the JupyterBook through its url. This does not make it possible to modify the notebooks but makes it possible to understand the methods using “sliders” and therefore to understand more clearly the influence of certain parameters
Download Jupyter notebooks and run them in his personal environment
Use the JupyterHub of the École Polytechnique that we have set up specifically for this type of use. This allows you to edit the notebook directly and run it, but it should be noted that the notebook is not saved when the session ends (unless copied to the directory persist).