Material Detail

The third university year of One Math Book, a free, coherent mathematics course from grade 1 to the end of a bachelor's degree, following the French Licence 3 programme. 23 chapters: group theory, rings, modules over a principal ideal domain, Galois theory and representations of finite groups; general topology, complete spaces and Banach spaces; measure theory, the Lebesgue integral, Lp and Hilbert spaces, the Fourier transform and the spectral theorem; holomorphic functions, residues and conformal maps; ordinary differential equations, submanifolds and differential forms with Stokes' theorem; probability up to the central limit theorem.

Each chapter gives definitions, theorems with proofs and methods, then graded exercises and a weekend problem: 276 exercises and 23 problems, all with full solutions. It builds on Years 1 and 2 of the same series, and individual chapters can serve as the text for an upper-division course in algebra, analysis, complex analysis, geometry or probability. Read online or download the PDF, free and without an account, in English, French, Dutch, Spanish, Portuguese, Hindi, Arabic and Indonesian.

Drafted with Anthropic's Claude models (text, exercises, solutions and translations) and reviewed by Benjamin Virrion, PhD in mathematics; every edition passes automated build and consistency checks. Sources, history and error reports: https://github.com/bvirrion/one-math-book

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