Collection
Articulated Course in Mathematics
From the Pythagorean theorem to string theory
Five volumes. One thousand two hundred and seventy-two articles. From the Pythagorean theorem to the Langlands correspondence, from the brachistochrone to the amplituhedron. The Articulated Course in Mathematics is an articulated essay that develops, in pocket format, the grammar by which reality composes itself.
Method
Every article
Opens with tension or surprise, never with a definition.
Explains why before what — the reader should feel the need for the concept before seeing it.
Develops a single idea, from its motivation to its interpretation.
Interprets every formal result in plain language.
Closes with resonance — the last sentence carries beyond the article.
Threads
Ten mathematical objects run through the collection from the first to the last volume.
S1 · Z · Q(√2) · GLn · ζ(s) · L2 · k[x] · Sn · E : y²=x³+ax+b · T
The five volumes
I. Elements
From Number to Form
High school
Arithmetic, algebra, plane and space geometry, complex numbers, functions, sequences, analysis, probability, conics. 2nd edition: 64 articles rewritten, 9 new figures.
II. Undergraduate
From Statement to Space
Undergraduate
Logic, real analysis, linear algebra, polynomials, groups, series, multivariable calculus, topology, measure and Lebesgue, differential equations, Fourier, functional analysis, complex analysis, probability, optimization.
III. Graduate
From Functional Analysis to Galois Theory
Master, agrégation
Functional analysis, PDEs, distributions, Sobolev, advanced algebra, group theory, fields and Galois, topology, manifolds, algebraic geometry, numerical methods. Categories, homological algebra, representations, Lie groups.
IV. Correspondences
From Class Field Theory to the Langlands Program
Doctoral, research
Algebraic number theory, p-adic numbers, class field theory, adèles, Galois representations, modular forms, L-functions, automorphic forms, elliptic curves, schemes, étale cohomology, the Langlands program.
V. Mathematical Physics
From Symmetries to Strings
Doctoral, research
Classical mechanics and symplectic geometry, quantum mechanics, gauge theory, quantum field theory, conformal theory, string theory, supersymmetry, general relativity, integrable systems, quantum information.
Offer
All five volumes
1 271 articles · 3 077 pages · 642 figures
Instead of €84.95
Format