2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167968This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec. 2) is devoted to the mathematical foundation of the large-scale electronic structure theory and their numerical aspects.13 page, 1 figure. A PDF file in better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htmlComputational PhysicsMaterials ScienceChemical Physicstext