In the small hours of 30 May 1832, in Paris, a young man of twenty spent the night writing. Évariste Galois had a duel arranged for dawn and knew he would probably not survive it. He wrote a long letter to his friend Auguste Chevalier summarising the ideas the Academy of Sciences had rejected or lost, and asked that it be shown to Jacobi and Gauss, “not on the truth, but on the importance of these theorems”. In the margin of a manuscript he left a sentence that became famous:
Source: FUVEST – test of the 1st phase, version V and official template (rectified in 24/11/2023), available in the FUVEST collection 2024. The 1st phase of FUVEST 2024 (General Knowledge Test, 19/11/2023) had 90 questions from all disciplines. This post only contains 12 math questions. The numbering used here is that of Proof V; In versions K, Q, X and Z the same questions appear with other numbers. Template Question Subject Template 13 Matrices: product and social network B 31 Volume of cylinder and circular segment B 33 Percentage: cost variation A 34 Statistics: mode, median, mean and range A 35 Count: digital clock reflected B 48 Cobblestone Packaging D or E (both accepted) 49 Parallelogram and trigonometry C 59 Exponential and logarithmic function (inverse) D 60 Linear system and line graph E 63 Pythagorean Tree: geometric progression and logarithm C 84 Graph Reading: Homicide Rates E 85 Triangular and oblong numbers D Question 13: Matrices and connections in a social network Statement Matrices can be used to obtain information about a social network. To understand how this can be done, let’s consider as an example a small social network made up of 4 people: $P_1, P_2, P_3, P_4$. The matrix associated with this social network is the matrix $4 \times 4$: