‎Lang Serge‎
‎Algebra‎

‎Rekenen of algebra? Gebruik van en houding tegenover rekenkundige en algebraische oplossingswijzen bij toekomstige leerkrachten.‎

‎Leuven, Universitaire Pers, 2001 Paperback, Nederlands, originele uitgeversomslag, 16x24 cm., 218 pp. ISBN 9789058671042.‎

‎ Studia Paedagogica : 30. Bij de overgang van de lagere naar de secundaire school worden leerlingen geconfronteerd met heel wat nieuwe leergebieden. Zo worden zij bijvoorbeeld geintroduceerd in de algebraische redeneerwijze. Voor heel wat leerlingen verloopt deze introductie in de algebra echter niet probleemloos. In het verleden werd reeds heel wat onderzoek gedaan omtrent de moeilijkheden die leerlingen ondervinden bij het leren van algebra, naar de oorzaken die aan de basis van deze moeilijkheden liggen en naar mogelijke manieren om deze moeilijkheden te voorkomen en te remedieren. Verschillende auteurs halen aan dat de leerkracht een belangrijke rol bekleedt in de overgang van leerlingen van rekenkunde naar algebra, maar stellen tegelijk ook dat 'there is a grave scarcity not only of models of the teaching of algebra but also of literature dealing with the beliefs and attitudes of algebra teachers.' (Kieran, 1992, p. 394). Daarom hebben we onze aandacht in dit boek gericht op deze centrale beinvloedende factor in het leerproces van algebra: de leerkracht en de oplossingsvaardigheden en opvattingen die deze heeft omtrent rekenkundige en algebraische werkwijzen. Het grootste gedeelte van dit boek wordt besteed aan de rapportering van een empirische studie die we uitvoerden bij 97 aspirant-leerkrachten. In deze groep zaten toekomstige onderwijzers en wiskunderegenten die ofwel pas aan hun lerarenopleiding begonnen ofwel deze beeindigden. Bij hen namen we twee zelf ontwikkelde meetinstrumenten af: Eerst lieten we hen een toets oplossen waarin (willekeurig door elkaar) zes rekenkundige vraagstukken en zes algebraische vraagstukken waren opgenomen. Aan de hand van deze toets konden we het oplossingsprofiel (de gebruikte oplossingsmethoden en de prestaties) van de verschillende groepen aspirant-leerkrachten bepalen en met elkaar vergelijken. Vervolgens legden we de aspirant-leerkrachten een vragenlijst voor waarin we hen vroegen om een evaluatie toe te kennen aan (fictieve) oplossingen van leerlingen voor dezelfde vraagstukken. Zo konden we de invloed nagaan van het eigen oplossingsprofiel van de aspirant-leerkrachten op een aspect van het didactisch handelen (met name de evaluatie). Tenslotte gingen we ook na of het oplossingsprofiel op de vraagstukkentoets en de evaluaties die worden toegekend samenhangen met de wiskundige vooropleiding van de aspirant-leerkrachten. ‎

‎Lang Serge Leng. Algebra. 3rd edition. Algebra. Adapted third edition. In Russia‎

‎Lang Serge Leng. Algebra. 3rd edition. Algebra. Adapted third edition. In Russian (ask us if in doubt)/Lang Serge Leng. Algebra. 3rd edition. Algebra. Dopolnennoe trete izdanie.Springer 933 c.. SKUalbfdc3d5dcec369749.‎

‎Artin Michael Artin. Algebra. Algebra. In Russian (ask us if in doubt)/Artin Mic‎

‎Artin Michael Artin. Algebra. Algebra. In Russian (ask us if in doubt)/Artin Michael Artin. Algebra. Algebra.Pearson 1991 672 p.. SKUalb93ae1d424a21a978.‎

‎La langue des calculs, ouvrage posthume et élémentaire, imprimé sur les manuscrits autographes de l'auteur" Dans lequel des observations, faites sur les commencemens et les progrès de cette langue, démontrent les vices des langues vulgaires, et font... - [THE LANGUAGE OF ALGEBRA]‎

‎Paris, Charles Houel, an VI de la République (=1798). 8vo. Recent simple brown half cloth w. gilt title to spine. Uncut. Title-page w. large damp-stain, next few leaves w. a bit of soiling to upper corner. Occasinal brownspotting. Every gathering extended and re-inforced at hinge, probably in order to make the book open to its full extent. (2), 484, (1, -errata) pp.‎

‎The true first edition of this posthumously published major treatise, Condillac's final main work, which proved to be one of his most important and influential ones. The work was originally published both separately, as it is here, with its own errata-leaf and title-page without mentioning of volume number for the Oeuvres, and as the final volume of his ""Oeuvres philosophiques"".Having realized that other philosophers' accounts of knowledge had failed because they focused on the essences instead of the origins, Condillac, in all of his major treatises, set out to define moral and metaphysical problems as precisely as one can define the problems of geometry, and the approach that would enable this would be analytic. In the same stroke he would correct Locke's mistake of ""Internal sense"", the distinction between the process of sensation and of reflection. ""His instrument was a highly original theory of language as the analyst of experience. It is by the mind's capacity to invent and manipulate symbols of uniform and determinate significance that it passes from sensation to reflection and communication and hence to effective knowledge... By identifying the operations of language as the cause of intellectual functions, Condillac intended to be making the kind of statement Newton had made when he identified gravity as the cause of planetary motion - an exact and verifiable generalization of phenomenal effects. "" (D.S.B. III:381). It is in his last major work that Condillac deals most thoroughly with the analysis of language and the language of algebra. Algebra is the language of mathematics, and it is the only language that is well done (""bien faite""), nothing in this language is arbitrary" the analogies of this language are always precise and lead on to new sensible expressions" in this language the purpose is not to learn to speak like others, the purpose is to speak in the greater analogy in order to reach a greater precision. Algebra, the language of mathematics, is a language of analogies. Analogy, which constitute this language, also constitutes the methods. ""L'analogie: viola donc à quoi se réduit tout l'art de raisonner, comme tout l'art de parler"" et dans ce seul mot, nous voyons comment nous pouvons nous instruire des découvertes des autres, et comment nous en pouvons faire nous-mêmes.""(= ""The analogy: now, this is what the entire art of reasoning as well as the entire art of talking can be reduced to"" and with this single word we see how we can guide the discoveries of others, and how we can do them ourselves. [own translation]"" (p. 7). And thus, the objective of this work is to see how it will be possible to give to other sciences the same exactness as that which we otherwise believe exclusively to be a part of mathematics, namely the exactness of the language of algebra.""It was through his last works -""La logique"" and, especially, ""La langue des calculs""- that Condillac exercised the most decisive influence on the philosophical taste of the generation of scientists immediately following his own. Therein, like his predecessors in the rationalist tradition, he looked to mathematics as the exemplar of knowledge. He parted company with them, however, in developing the preference he had expressed in his early work for the analytic over the synthetic mode of reasoning."" (D.S.B."" III:382). Algebra, seen as both a language and as the method of analysis, in comparison to the inaccurate instrument that is ordinary language would reveal to Condillac what is the difference between the problems of science and those of society, the moral and metaphysical ones. ""And in that comparison Condillac's philosophy entered into the reforming mission of the Enlightenment, the central imperative of the rationalism then having been to reduce the imperfections of human arrangements by approximating them to the natural and to educate the human understanding in the grammar of nature. In Franceat least, the congruence of Condillac's philosophy of science with the broader commitments of progressive culture recommended it so scientists themselves as the most authoritative reading of Newtonian methodology... The terminology and symbolism of the modern science of chemistry are examples still alive in science of the practicality of this program."" (D.S.B., III:382). Condillac's philosophy of science was considered the most authoritative reading of Newtonian methodology. Among many others Lavoicier and other protagonists of the chemical revolution were influenced by his reform of nomenclature, as were and are botanists, zoologists and geometrics by his scientific explanations. His psychological empiricism is now considered the first positivist account of science.Condillac was one of the greatest French philosophers of the Enlightenment. He was friends with Rousseau and Diderot and was a forerunner in the junction between epistemology and philosophy, which was inspired by Locke and Newton, as the two sciences almost merged into one in this period. ""Condillac contibuted to the synthesis more decisively than did any other writer."" (D.S.B. III:380).‎

‎Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. - [THE FOUNDATION OF COMPUTER ALGEBRA]‎

‎(Berlin, Julius Springer, 1926). 8vo. Without wrappers. Extracted from ""Mathematische Annalen. Begründet 1868 durch Alfred Clebsch und Carl Neumann. 95. Band"". Pp. 735-788.‎

‎First publication of Hermann's seminal paper (her doctoral thesis) which founded computer algebra. It first established the existence of algorithms - including complexity bounds - for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings. Hermann's algorithm for primary decomposition is still in use today. The paper anticipates the birth of computer algebra by 39 years.""[The paper] is an intriguing example of ideas before their time. While computational aspects of mathematics were more fashionable before the abstractions of the twentieth century took hold, mathematicians of that time certainly knew nothing of computers nor of today's idea of what an algorithm is. The significance of the paper can be found on the first page, where we find (in translation):The claim that a computation can be found in finitely many steps will mean here that an upper bound for the number of necessary operations for the computation can be specified. Thus it is not enough, for example, to suggest a procedure, for which it can be proved theoretically that it can be executed in finitely many operations, if no upper bound for the number of operations is known. The fact that the author requires an upper bound suggests that there must exist an actual procedure or algorithm for doing computations. We see in this paper the first examples of procedures (with upper bounds given) for a variety of computations in multivariate polynomial ideals. Thus we have here a paper anticipating by 39 years the birth of computer algebra"". (ACM SIGSAM Bulletin, Volume 32. 1998).Not in Hook & Norman.‎