Volume I · William de France
Elements
From Number to Form
Calculate with confidence. Draw a figure. Understand what makes a proof work. The first volume builds the skills and language needed for everything that follows.
First edition · available
Mathematics,
one connection at a time.
From numbers to geometry, from symmetries to strings: five volumes to follow the ideas, understand the proofs, and find your own way through mathematics.
5 volumes251 chapters6,589 course pagesTwo languages. One shared journey.
1:31 · YouTubeThe collection on film
From a point to the universe.
From the first line to the equations of the sky: ninety seconds to discover the five volumes of the Articulated Course in Mathematics.
Watch the film on YouTube →Discover
Find your path →Volume II · William de France
Foundations
From Statement to Space
What makes a mathematical statement? What does convergence mean? How does a calculation reveal a structure? A course connecting analysis, algebra, geometry, and probability.
Volume III · William de France
Graduate Mathematics
From Functional Analysis to Galois Theory
Move from tools to theories. Functional spaces, measure, geometry, and algebra meet in a volume that develops the ability to change perspective without sacrificing precision.
Volume IV · William de France
Correspondences
From Class Field Theory to the Langlands Program
Why do arithmetic and analysis speak the same language? From number fields to the Langlands program, follow the correspondences that organize contemporary research.
Volume V · William de France
Mathematical Physics
From Symmetries to Strings
From mechanics to quantum fields and strings: understand what symmetries require, what geometry reveals, and what physical models actually allow us to conclude.
Volume1 / 5
The collection
Five volumes. An expanding horizon.
Volume I
Elements
From Number to Form
22 chapters · 710 p.
Explore this volume ▶ Watch the film · 7 min 54 sVolume II
Foundations
From Statement to Space
62 chapters · 1,569 p.
Explore this volume ▶ Watch the film · 7 min 31 sVolume III
Graduate Mathematics
From Functional Analysis to Galois Theory
86 chapters · 2,590 p.
Explore this volume ▶ Watch the film · 7 min 23 sVolume IV
Correspondences
From Class Field Theory to the Langlands Program
37 chapters · 648 p.
Explore this volume ▶ Watch the film · 8 min 14 sVolume V
Mathematical Physics
From Symmetries to Strings
44 chapters · 1,072 p.
Explore this volume ▶ Watch the film · 8 min 28 sReader’s guide on video
Eight short films on how to read this course.
How the course is built, how to work through an article, where to enter depending on your level: a few minutes per episode, in French and English.
The idea behind the course
One idea leads to another.
A definition means more than words to memorize. It becomes clear when you see the problem it answers.
Each article offers a way in and develops the reasoning towards the ideas that follow. Figures make structures visible, examples test intuition, and proofs explain what is true and under which assumptions.
Understand the editions →
Actual pages from the first edition. Browse →
Read, revisit, look up
One course. Three ways to return to it.
The abridged course
Revisit a chapter’s ideas and connections in a more concise narrative.
The compendium
Return to definitions, results, and the assumptions that make a method work.
The formula handbook
Look up a formula or identity quickly, together with its conditions of use.
Included with Volumes I, II, and III in your chosen language. Volumes IV and V contain the complete course.
Compare the formats →Éditions Clementinium
Mathematics opens the way.
A home for mathematics and science. An encyclopaedia taking shape, one idea at a time.
The Articulated Course opens the Clementinium Encyclopaedia: seven planned series spanning mathematics, the natural sciences, and the study of mind and society. All share one commitment: to make ideas intelligible without hiding their difficulties.
The publishing programme will extend this journey with the history of mathematics and the first publications in the Physics and Matter series.
Explore the publishing programme →