Benjamin Garcia
Français

Benjamin Garcia

First-year master's student in fundamental mathematics, University of Montpellier.

I write mathematics documents and make them freely available: a thesis on the distribution of the primes, course notes on integral calculus with worked exercises, lecture summaries. I also publish programming projects. The documents themselves are written in French. If you find a mistake, write to me: I correct it and republish.

Writing

2026

Asymptotics of the prime numbers

An undergraduate thesis on the prime number theorem. We first establish Chebyshev's elementary bounds, then prove the equivalence by Newman's method, which borrows only the simplest tools from complex analysis. Along the way: Mertens' theorems, the non-vanishing of zeta on the line Re(s) = 1, and a Tauberian theorem.

PDF in French, 38 pages, third-year thesis — with Gauthier Ciotta and Loan Ruble, supervised by Olivier Guichard

2025

Notions of integral calculus

A course and exercise document on integral calculus, grown out of my favourite exercises and then widened with the lecture notes behind them: Riemann sums, integration by parts, partial fraction decomposition, Bioche's rules, the tangent half-angle substitution. Seven fully worked exercises at the end.

PDF in French, 34 pages, version 1.1 — CC BY-NC-SA 4.0

Archive

2025

Continuous distributions, revision sheet

PDF in French, 17 pages, second-year level — personal notes written for a midterm, compiled largely from Bibmath and Wikipedia. Tied to the syllabus of one course, so of little use elsewhere.

2024

Pascal's triangle

PDF in French, 12 pages, first-year level — an introductory piece: binomial coefficients, Pascal's rule, the binomial theorem proved by induction, and three ways of computing "n choose k" in pseudocode and Python. Written from encyclopaedic sources; it is early undergraduate work and it shows.

Projects

2025–

LinearLab

A site of tools and lessons for linear algebra, opened in November 2025. It holds a linear system solver, a matrix calculator and theory pages.

Website in French, in development — linearlab.fr

Education

2026–2027
Master's, first year, fundamental mathematics University of Montpellier, faculty of science
2025–2026
Bachelor's, third year, fundamental mathematics University of Strasbourg — thesis on the asymptotics of the primes
2024–2025
Bachelor's, second year, mathematics University of Strasbourg, department of mathematics and computer science
2023–2024
Bachelor's, first year, mathematics and computer science Université Clermont Auvergne

Contact

E-mail
benjamin.garcia02@etu.umontpellier.fr
GitHub
github.com/benjamin-grc
YouTube
My channel
CV
Download the CV (PDF, 1 page)