# Doctoral studies > PhD dissertations in progress

**Fàtima Romero Vallhonesta***The algebra in the Iberian Peninsula in the 16th century***Supervisor/s: **Maria Rosa Massa Esteve **Date of defense: **28-05-2018

This thesis analyzes how algebra was introduced in the Iberian Peninsula and how it was developed, based on the analysis of all the works with algebraic content published in this region in the 16th century, and the manuscript 2294 from the end of the century, from the library of the University of Salamanca. The study of other European algebraic works from the same period, has also allowed us to show that the status of algebra in the Iberian Peninsula was similar to that of other European countries. In the treatises analyzed, the aspects that we consider to be key, in the process of algebraization of mathematics, one of which is the idea of algebra that the authors have, which in some cases implicitly involves the idea of analysis. We have also focused on the generalization of the procedures to solve equations, as well as the creation of new algebraic objects that will define their own rules. The introduction of a second unknown is also one of the aspects that we have looked at, since it contributed to the consideration of the equations like new algebraic objects. All these aspects of the development of algebra are exemplified with excerpts from the different works analyzed, emphasizing those that are most relevant in each one. Finally, we refer to the possible sources of the Iberian works and to the relationship between them and other European algebraic treatises published in the same period.