Collection
Articulated Course in Mathematics
From the Pythagorean theorem to string theory
Five volumes. One thousand three hundred and fourteen articles. From the Pythagorean theorem to the Langlands correspondence, from the brachistochrone to the amplituhedron. The Articulated Course in Mathematics 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
Behind 2 + 3 × 4 lies a hierarchy, not a sequence of arbitrary moves. This first volume starts there: computation, algebra and proof, then plane and space geometry, complex numbers, functions and sequences, probability, conics, each notion motivated by a question the previous one couldn't answer. By the end, the reader has traced the chain ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ and has the language needed for the analysis in the next volume.
II. Undergraduate
From Statement to Space
Undergraduate
The shift from high-school computation to real mathematics starts with learning to read a mathematical statement, then everything follows: real analysis, linear algebra, polynomials and groups, series, multivariable calculus, curves and differential equations, Euclidean geometry, combinatorics and probability. The longest volume in the collection, and the one where proof itself becomes the object of study.
III. Graduate
From Functional Analysis to Galois Theory
Master, agrégation
Here individual objects give way to the structures that organize them: functional analysis, measure and integration, Galois theory, algebraic geometry, differential topology, dynamical systems, distributions and Fourier analysis. Twenty-five parts, the densest volume in the collection, for readers who want to understand why modern mathematics thinks in structures before it thinks in numbers.
IV. Correspondences
From Class Field Theory to the Langlands Program
Doctoral, research
In 1967, Robert Langlands sketched in a letter a dictionary between two mathematical worlds that seemed to share nothing: number theory and automorphic forms. This volume builds that dictionary from its foundations: algebraic number theory, p-adic numbers, class field theory, modular forms, Galois representations, up to the Langlands program itself and its geometric version. The same unveiling told in The Apocalypse According to Galois, built here stone by stone.
V. Mathematical Physics
From Symmetries to Strings
Doctoral, research
From classical mechanics to string theory, by way of quantum mechanics, gauge theory, quantum field theory and general relativity: this final volume follows the same thread as the four before it, applied to the physical world itself. Fourteen parts, through to quantum gravity and quantum information, the collection's mathematical grammar tested against reality.
Offer
All five volumes
1,314 articles · 5,647 pages · 822 figures
Instead of $101.95
Format