Elements
Rebuild the foundations or prepare for university.
Prerequisites: School algebra and geometry; curiosity and an interest in reasoning.
See the contents and read an excerpt →▶ Watch this volume’s film · 7 min 54 sReading guide
Where should you begin?
The volume numbers suggest a progression, not an obligation to read everything. Start with the problem, level, or horizon that draws you in.
Foundations
Study undergraduate mathematics.
Prerequisites: The foundations of Volume I, especially algebraic manipulation and elementary proof.
See the contents and read an excerpt →▶ Watch this volume’s film · 7 min 31 sGraduate Mathematics
Develop graduate-level mathematics.
Prerequisites: A working knowledge of the analysis and algebra developed in Volume II.
See the contents and read an excerpt →▶ Watch this volume’s film · 7 min 23 sCorrespondences
Explore ideas from arithmetic and geometric research.
Prerequisites: Algebra, analysis, and geometry from Volume III, with reminders at key transitions.
See the contents and read an excerpt →▶ Watch this volume’s film · 8 min 14 sMathematical Physics
Connect advanced mathematics with physical theories.
Prerequisites: Advanced analysis and geometry. Volume IV illuminates some correspondences but is not required for every chapter.
See the contents and read an excerpt →▶ Watch this volume’s film · 8 min 28 sTo find your bearings
Three short films to find your bearings.
How the course is built, what an article is, and the research level: enough to choose with confidence.
Read an article, then work with it.
Begin with the question that opens the article. Follow the examples, then return to the proof. Redraw the figure. In Volumes I–III, try a method or exercise next; use the abridged course to recover the thread, and the compendium or formula handbook to check a result.