 Beloch studied mathematics at the Sapienza University of Rome and wrote her undergraduate thesis under the supervision of Guido Castelnuovo.She received her degree in 1908 with Lauude and "dignita' di stampa" which means that her work was worthy of publication and in fact her thesis "Sulle trasformazioni birazionali nello spazio" (On Birational Transformations In Space) was published in the Annali di Matematica Pura ed Applicata.Guido Castelnuovo was very impressed with her talent and offer her the position of assistant which Margherita took and held until 1919, when she moved to Pavia and the successive year to Palermo to work under Michele De Franchis, an important figure of the Italian school of algebraic geometry at the time.