There are discussed implementational aspects of the special-purpose computer algebra system FELIX designed for computations in constructive algebra. In particular, data types developed for the representation of and computation with commutative and non-commutative polynomials are described. Furthermore, comparisons of time and memory requirements of different polynomial representations are reported.

Made available in DSpace on 2016-04-27T16:57:02Z (GMT). No. of bitstreams: 1 David Antonio da Costa.pdf: 2686779 bytes, checksum: bbee7a009c55b69262b352babe87e6ee (MD5) Previous issue date: 2010-06-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This thesis analyzes the history of a school knowledge: the arithmetic in the Brazilian primary school. In specific, it discusses the transformations occurred with the teaching of the concept of number in the period 1890-1946. This temporal delimitation considers the time frame of the installation of school groups in Sao Paulo, going to the enactment of the Organic Law of Primary Education. The research takes as privileged sources the textbooks. The theoretical and methodological instrumental framework is rooted in cultural studies, in particular, in the field of History of School Subjects, described by André Chervel. The results of the study point to the changes with the arithmetic of primary education, and with the teaching of the concept of number, from the influences of Psychology in Education / Esta tese analisa a trajetória de um saber escolar: a Aritmética no curso primário brasileiro. Em específico, trata das transformações ocorridas com o ensino do conceito de número no período 1890-1946. Essa delimitação temporal considera o marco da instalação dos grupos escolares em São Paulo, indo à promulgação da Lei Orgânica do Ensino Primário. A investigação toma como fontes privilegiadas de pesquisa os livros didáticos. O instrumental teórico-metodológico utilizado tem origem nos estudos culturais, em particular, no campo da História das Disciplinas Escolares, inaugurado por André Chervel. Os resultados do trabalho apontam para as transformações ocorridas com a aritmética do ensino primário, e com o ensino do conceito de número, a partir das influências da Psicologia na Educação

Tidigare studier visar att det finns skillnader mellan flickor och pojkar avseende hur de upplever ämnet matematik, vilket återspeglas i utbildnings- och yrkesval. Tidigare studier visar även att det finns skillnader mellan flickor och pojkar avseende hur de lär och tänker när de löser matematiska problem och attlärare inte alltidtar hänsyn till dessa skillnader. Denna studie syftar till att undersöka hur flickor och pojkar löser aritmetiska uppgifter genom kognitiva, kroppsliga och externa strategier samt likheter och skillnader mellan flickor och pojkar. Totalt har 23 barn (11 flickor och 12 pojkar) i grundskolans årskurs ett löst nio aritmetiska och fyra andra matematiska uppgifter. Barnen instruerades att tänka högt och blev videofilmade. Resultaten visar att pojkarna oftare använder kognitiva strategier (75% av uppgifterna) än flickorna gör (66%). Särskilt ofta använder pojkarna de kognitiva strategier som kallas härledning och talfakta (62%) medan flickorna använder dessa strategier mindre ofta (40%). Flickorna använder oftare kognitiva och kroppsliga strategier där de räknar upp eller ned (49%) än pojkarna gör (20%). Flickorna använder även oftare kroppsliga strategier (30%) än pojkarna gör (13%). Dessa skillnader pekar på att lärare bör kartlägga vilka strategier eleverna använder för att därigenom kunna anpassa sin undervisning. / Previous research show there are differences between girls and boys as it comes to how they experience school mathematics, which has consequences for educational and professional career choices. Previous studies also show there are differences between girls and boys concerning how they learn and think when solving mathemtical problems and that teachers do not always take these differences into consideration. This study aims at describing and anaysing how girls and boys solve arithemtic tasks by using cognitive, bodily and external strategies and similarities and differences betweeen girls and boys. In total, 23 children (11 girls and 12 boys) first graders in elementary school solved nine arithmetic and four other mathematical tasks. The children were instructed to think aloud and they were video recorded. The results show that boys more often used cognitive strategies (in 75% of tasks) than girls did (66%). In particular, the boys tended to use the cognitive strategies that are called decomposition and direct retrieval of artithmetic facts (62%) while the girls used these strategies less often (40%). The girls more often used cognitive and bodily strategies involving counting up or down (49%) than the boys did (20%). The girls more often used bodily strategies (30%) than the boys did (13%). These differences indicate that teachers should be provided tools for mapping strategies that pupils use in order to be able to adapt their teaching to individual differences.

By adapting Mitchell's algorithm for floating-point numbers, one can efficiently perform arithmetic floating-point operations in an approximate logarithmic domain in order to perform approximate computations of functions such as multiplication, division, square root and others. This work examines how this algorithm can be improved in terms of accuracy and hardware complexity by applying a set of various methods that are parametrized and offer a large design space. Optimal coefficients for a large portion of this space is determined and used to synthesize circuits for both ASIC and FPGA circuits using the bfloat16 format\@. Optimal configurations are then extracted to create an optimal curve where one can select an acceptable error range and obtain a circuit with a minimal hardware cost.

Tato práce popisuje vznik obrazu v transmisním světelném mikroskopu s proměnnou aperturou kondenzoru. Tento způsob pořizování obrazu je výhodný při pozorování tlustých vzorků, což jsou objekty, u kterých je v mikroskopickém měřítku významná výška. Klasické transmisní mikroskopy pro tento výzkum vhodné nejsou, protože výsledný obraz, který produkují, obsahuje patrné informace z velkého objemu vzorku mimo oblast, která je vyšetřovaná. Tento problém byl vyřešen po vynálezu konfokálního mikroskopu, který je ovšem daleko dražší a má i některé nevýhody navíc. Cílem je zpracovat obrazy pořízené pomocí kondenzoru s rotující aperturou tak, aby došlo k redukci podílu nežádoucí informace a obraz se tak stal "čistším". Tato metoda zpracování obrazu nemohla být použita v minulosti, protože tehdejší počítače neměly dostatečnou paměť a výkon. Na tuto metodu se dá nahlížet jako na převod množiny výstupů z mikroskopu s vylepšenou osvětlovací soustavou na odpovídající množinu výstupů konfokálního mikroskopu.

The thesis deals with arithmetics of elliptic curves over finite fields and methods to improve those calculations. In the first part, algebraic geometry helps to define elliptic curves and derive their basic properties including the group law. The second chapter seeks ways to speed up these calculations by means of time-memory tradeoff, i.e. adding redundancy. At last, the third part introduces a wholly new curve form, which is particularly effective for such purposes.

Som lärare i grundsärskolan saknade jag ofta bra undervisningsmaterial till mina elever. Utifrån detta utkristalliserades syftet med studien som är att undersöka om kartläggningsmaterialet MRP – The Mathematic Recovery Programme från ”Early Numeracy” (Wright, Martland & Stafford, 2006) är användbart i grundsärskolan och i så fall vilka delar som lämpar sig att använda i grundsärskolan, samt att se om de uppföljande uppgifterna som rekommenderas ger någon effekt på elever i grundsärskolan. För att kunna besvara detta har 13 grundsärskoleelevers aritmetiska kunskaper kartlagts. Därefter valdes 7 elever ut, vilka utmanades utifrån uppgifter från det kompletterande materialet ”Teaching Number (Wright, Martland & Stafford, 2006), antingen enskilt eller i grupp.  Studien har genomförts med hjälp av deltagande observationer och flexibla intervjuer (Ginsburg, Jacobs & Lopez, 1998). Studiens teoretiska grund finns i det konstruktivistiska perspektivet och det sociokulturella perspektivet. Det konstruktivistiska perspektivet valdes eftersom de betonar vikten av att uppgifterna anpassas efter individens inre mognad och kognitiva förmåga, vilket väl kan kombineras med det sociokulturella perspektivet som betonar vikten av den sociala gruppens gemenskap som en förutsättning för utveckling inom den proximala utvecklingszonen. Studiens resultat visar på att materialet är lika användbart i grundsärskolan som i grundskolans tidiga år, eftersom kartläggningsmaterialet hjälpte pedagogen att finna elevens kunskapsnivå, samt därefter lyckades utmana eleven att utvidga sina kunskaper under en treveckorsperiod. Alla eleverna utökade sina matematiska kunskaper under studiens gång.  Slutsatsen blir att alla elever bör kartläggas med MRP del 1.1 och 2.1, men därefter får antalet delar anpassas efter elevernas kunskapsnivå. För att genomföra kartläggningen och de uppföljande utmaningarna rekommenderas att pedagogen är väl insatt i materialets utformning och tanke för att kunna utmana eleven utifrån dennes resultat.

The thesis deals with arithmetics of elliptic curves over finite fields and methods to improve those calculations. In the first part, algebraic geometry helps to define elliptic curves and derive their basic properties including the group law. The second chapter seeks ways to speed up these calculations by means of time-memory tradeoff, i.e. adding redundancy. At last, the third part introduces a wholly new curve form, which is particularly effective for such purposes.

With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages. Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.

<p>With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages.</p><p>Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.</p>