The polynomial method over varieties

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2019, Director: Martín Sombra[en] In 2010, Guth and Katz introduced the polynomial partitioning theorem as a tool in incidence geometry and in additive combinatorics. This allowed the application of results from algebraic geometry (mainly on intersection theory and on the topology of real algebraic varieties) to the solution of long standing problems, including the celebrated Erdős distinct distances problem. Recently, Walsh has extended the polynomial partitioning method to an arbitrary subvariety. This result opens the way to the application of this method to control the point-hypersurface incidences and, more generally, of variety-variety incidences, in spaces of arbitrary dimension. This final project consists in studying Walsh’s paper, to explain its contents and explore its applications to t his kind of incidence problems

Data science for a new generation of tutors: building an academic-guidance system based on dropout and grades prediction

Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Laura Igual MuñozThis work is part of an innovative educational project which aim is to create a tool to help tutors offer more personalised and proactive guidance to the students. An analysis of the performance of different Machine Learning techniques for dropout intention prediction is presented. The approach of using Recommender Systems for final grade prediction and course ranking creation has been also assessed. Visualizations which help in the interpretation of the obtained results have been developed and a design for the tutoring tool has been outlined. The research has been performed using data from the degree studies in Law, Computer Science and Mathematics of Universitat de Barcelona

Data-driven System to Predict Academic Grades and Dropout

Nowadays, the role of a tutor is more important than ever to prevent students dropout and improve their academic performance. This work proposes a data-driven system to extract relevant information hidden in the student academic data and, thus, help tutors to offer their pupils a more proactive personal guidance. In particular, our system, based on machine learning techniques, makes predictions of dropout intention and courses grades of students, as well as personalized course recommendations. Moreover, we present different visualizations which help in the interpretation of the results. In the experimental validation, we show that the system obtains promising results with data from the degree studies in Law, Computer Science and Mathematics of the Universitat de Barcelona