The HPM notes of J. Vicente Gonçalves
J. Vicente Gonçalves (1896-1985) was an important Portuguese mathematician
of the first half of the twentieth century. He taught at Coimbra University
for almost twenty-five years. In 1940, he went to Lisbon University, where he
worked until his retirement in 1966. One of his contributions to the improvement,
development and dissemination of Portuguese mathematics research was the foundation,
in 1950, of the Mathematics Section of Revista da Faculdade de Ciências
da Universidade de Lisboa (2nd series). He was its editor until 1966. Vicente
Gonçalves published almost 100 papers in several scientific journals.
A part of his work can be found in the section "Historiae ac Pedagogiae
de Minutiis" (as he called it) of the Revista da Faculdade de Ciências
de Lisboa (2nd series) -- the following 26 HPM notes of J. Vicente Gonçalves:
1. La limite de Walsh, vol. I, 1:187-188 (1950)
2. Calcul abrégé d’une suite de Sturm, vol. I, 1:189-200
(1950)
3. Calcul abrégé d’un résultant, vol. I, 1:201-204
(1950)
4. Remarque sur le calcul abrégé d’un résultant, vol.
I, 2:403-404 (1951)
5. Une idée de Cauchy, vol. I, 2:405-408 (1951)
6. Les formules de Ruffini, vol. I, 2:408-409 (1951)
7. Sur le reste de la formule de Taylor, vol. II, 1:89-90 (1952)
8. Sur un développement de f(x,y), vol. II, 1:91-92 (1952)
9. Une matrice régulière, vol. II, 2:349 (1953)
10. Les matrices à termes nuls, vol. II, 2:350 (1953)
11. L’interpolatrice de Newton, vol. II, 2:351-352 (1953)
12. La continuité uniforme, vol. II, 2:353-360 (1953)
13. Sur la nième formule de Taylor, vol. III, 1:187-190 (1953/54)
14. Sur la méthode de Newton, vol. III, 1:191-196 (1953/54)
15. Un raffinement des séries de Pringsheim, vol. III, 1:197-199 (1953/54)
16. Sur la décomposition de cotg x, vol. III, 1:200-202 (1953/54)
17. Démonstration du théorème de Binet-Cauchy, vol. III,
2:327-329 (1954/55)
18. Démonstration du théorème de Hamilton-Cayley, vol.
III, 2:330 (1954/55)
19. Les développements de tg x et cotg x, vol. III, 2:331-332 (1954/55)
20. Sur la décomposition des fractions rationnelles, vol. V, 1:171-176
(1955/56)
21. Quelque remarques sur la série alternée décroissante,
vol.VI, 2:331-335 (1957/58)
22. Amélioration des approximations newtoniennes, vol. VII, 1:133-136
(1959)
23. Une retouche dans la méthode de Newton, vol. VII, 1:137-139 (1959)
24. La règle de Newton pour les racines rationnelles, vol. VII, 1:140
(1959)
25. Deux critères de convergence, vol. VII, 2:371-372 (1959)
26. Suite à une note sur la série alternée, vol. VIII,
1:121-123 (1960).
These notes, in the areas of analysis, algebra and history, are essentially improvements, remarks or short demonstrations of well-known mathematical results. That is why this work fits perfectly in a section of History and Pedagogy.
Professor Vicente Gonçalves also used to introduce these
notes in his lessons (to first year university students). He was a brilliant
teacher and a prolific mathematician with a penchant for introducing his research
results in his lessons and finding mathematical inspiration in the mathematical
topics he taught.
References
C. Costa and J. Vitória, Nótula sobre zeros de polinómios,
Boletim da SPM, 37:21-34 (1997) [Zb 923.01021]
C. Costa, José Vicente Gonçalves: Matemático... porque
Professor!, (PhD thesis), Universidade de Trás-os-Montes e Alto Douro,
Portugal, 2000.
Cecília Costa
Universidade de Trás-os-Montes e Alto Douro
Portugal
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