Mathematical tapas... but what are tapas? Tapas is a Spanish word (in the Basque
country, one would also say pintxos) for small savory dishes typically served in bars, with
drinks, shared with friends in a relaxed ambiance. The offer is varied, it may be meat,
fish, vegetables,... Each guest of the party takes with a stick the tapas he likes best at the
moment. This is the spirit of the mathematical tapas that we offer to the reader here.
The tapas that we offer are mathematical questions to answer, exercises (more than long
problems, in spirit). They concern mathematics at the undergraduate level (roughly
speaking, from the end of high school to the end of the first three years of university); 1
they do not cover the whole spectrum of mathematics, of course. Clearly, they reflect the
mathematical interests of the author:
Real analysis, Calculus:
functions of a real variable, multivariate calculus, differential calculus;
Matrices (especially positive semidefinite matrices);
Convexity (sets and functions);
Optimization or “variational” situations...