Takane studied mathematics at UNAM, earning a bachelor's degree in 1986, master's degree in 1988, and PhD in 1992.[2] Her doctoral dissertation, Propiedades espectrales de las matrices de Coxeter y las matrices de adyacencia de las algebras hereditarias de tipo salvaje, was supervised by José Antonio de la Peña [es].[3]
She has been a faculty member at UNAM since 1991 and a researcher in the Mathematical Institute since 1992. She was also a postdoctoral researcher at the University of Bielefeld and University of Trondheim, and has also taught in the Autonomous University of Mexico State since 2006.[2][4]
She has also been active in encouraging women in mathematics in Mexico, and co-founded a center for gender studies at UNAM.[5]
