# Pelegrí Viader

### Biosketch

Born in 1953. Attended University in Barcelona (UB) where I graduated in mathematics (1976).

After a few years as an Assistant Lecturer at UB I joined the Secondary School system as a Head of Mathematics at several schools. Headmaster of a British School in Barcelona for a few years (Oak House School in Barcelona, 1987-1991). Entered Pompeu Fabra University in 1991 where I am Associate Professor of Mathematics in the Department of Economy and Business.

Obtained the Lester R. Ford Award 2007 from the Mathematical Association of America (MAA) for the paper “On a Series of Goldbach and Euler”, (joint with Lluís Bibiloni, Jaume Paradís). American Mathematical Monthly, 113 (3), 2006 pp 206-220.

Achievements in two fields: History of mathematics with the recognition of the important work of Fermat in early integration (see Selected Publications below); Real Analysis with important work on Singular Functions, mainly Minkowski’s ?(x) fragenfunktion and Riesz-Nágy singular functions family. The best result is the construction of a singular function with a set of non-zero finite derivatives uncountable and dense in [0,1] with Hausdorff measure one (see last of selected papers).

### Research lines

- Real Analysis: Singular Functions
- History of Mathematics: Descartes and Fermat, XVII century
- Oligopoly Theory in microeconomics

### Selected publications

- “A Singular Function with a non-zero Finite Derivative on a Dense set” (joint with Juan Fernández, Manuel Díaz and Jaume Paradís). Nonlinear Analysis Theory Series A, 95 (2014), 703–713.
- “The derivative of Minkowski’s ?$(x)$ function”, (joint with Jaume Paradís, Lluís Bibiloni). Journal of Mathematical Analysis and Applications, 253, (2001), 107–125.
- “Fermat’s method of quadrature”, (joint with Jaume Paradís and Josep Pla). Revue d’histoire des mathématiques, 14, (2008), no. 1, 5–51.
- “Riesz-Nágy singular functions revisited”, (joint with Lluís Bibiloni, Jaume Paradís). Journal of Mathematical Analysis and its Applications, 329, (2007), no 1. 592-602.
- “A singular function with a non-zero finite derivative on a dense set with Hausdorff dimension one” (joint with Juan Fernández, Manuel Díaz and Jaume Paradís). Journal of Mathematical Analysis and Applications, 434 (2016), no. 1, 713–728.