Mathematics Education in Spain and Portugal
Spain 
Elena Ausejo 
 
This section offers a brief overview of Spanish mathematics education over the last two centuries, in the context of the educational system as a whole, which in turn depended to a very large extent on the country’s political and economic circumstances. Although political instability delayed the regulation of secondary education in Spain until 1836, the syllabi of 1845 and 1857 set up the basic structure throughout the nineteenth century. The country developed a system for preparing mathematics teachers that was relatively demanding – above all with respect to mathematical knowledge – and absorbed international experience through translations of textbooks. Later, Spain took part in the principal international movements in mathematics education, becoming involved in the ICMI and the reform movements of the 1950s–1970s.
Elementos de Matematica
El libro "Elementos de Matematica" es una obra que fue utilizada por muchos cientificos e ingenieros espanoles en su formacion basica en los anos 50-70 del pasado siglo XX. Contiene una primera parte dedicada al Algebra lineal, una segunda parte dedicada al Analisis infinitesimal y una tercera parte con las soluciones a los ejercicios propuestos en las anteriores. Ademas de por su interes como texto de introduccion a la Matematica, se hace publico en el archivo digital por su interes historico
A quantitative measure of nitrifying bacterial growth.
Nitrifying bacteria convert ammonia (NH3) to nitrate (NO3-) in a nitrification reaction. Methods to quantitatively separate the growth rate of these important bacterial populations from that of the dominant heterotrophic bacteria are important to our understanding of the nitrification process. The changing concentration of ammonia is often used as an indirect measure of nitrification but ammonification processes generate ammonia and confound this approach while heterotrophs remove nitrate via denitrification. Molecular probe methods can tell us what proportion of the microbial community is nitrifying bacteria but not their growth rate. The technique proposed here was able to quantify the growth rate of the nitrifying bacterial populations amidst complex ecological processes. The method incubates [methyl-3H] thymidine with water samples in the presence and absence of an inhibitor of nitrification-thiourea. The radioactively labeled DNA in the growing bacteria was extracted. The rate of incorporation of the label into the dividing bacterial DNA was used to determine bacterial growth rate. Total bacterial community growth rates in full-scale and pilot-scale fixed-film nitrifying reactors and an activated sludge reactor were 2.1 x 10(8), 4.1 x 10(8) and 0.4 x 10(8)cell ml(-1)d(-1), respectively; the growth rate of autotrophic-nitrifying bacteria was 0.7 x 10(8), 2.6 x 10(8) and 0.01 x 10(8)cell ml(-1)d(-1), respectively. Autotrophic-nitrifying bacteria contributed 30% and 60% of the total bacterial community growth rate in the nitrifying reactors whereas only 2% was observed in the activated sludge reactor that was not designed to nitrify. The rates of ammonia loss from the nitrifying reactors corresponded to the rate of growth of the nitrifying bacteria. This method has the potential to more often identify factors that enhance or limit nitrifying processes in both engineered and natural aquatic environments.