Mundet i Riera, IgnasiGutiérrez von Porat, Nils2020-06-102020-06-102020-01-19https://hdl.handle.net/2445/165000Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Ignasi Mundet i Riera[en] The theory of persistence modules originated in topological data analysis, as an abstract algebraic languange for dealing with persistent homology. The goal in this work is to study this theory. Mainly, we focus on the Normal Form Theorem and the Isometry Theorem. Finally, we define the Morse persistence modules and provide an application in approximating functions on the sphere.49 p.application/pdfcatcc-by-nc-nd (c) Nils Gutiérrez von Porat, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria de mòdulsTreballs de fi de grauTopologia algebraicaHomologiaTeoria de MorseModuli theoryBachelor's thesesAlgebraic topologyHomologyMorse theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess