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<p>En god taluppfattning är grunden till matematisk förståelse som eleven skall bygga sina kunskaper på. Utan en god grund i taluppfattning uppstår svårigheter för den undervisning som lärare vill åstadkomma i skolan. Ett vidare begrepp av taluppfattning är <em>number sense</em> som är en känsla för talens storlek och rimligheten i matematikuppgifter. Syftet är att undersöka hur lärare arbetar med matematiksvårigheter inom området taluppfattning för att utveckla elevens lärande. Undersökningen beskriver hur lärare identifierar elever i matematiksvårigheter med tanke på grundläggande taluppfattning. Detta gjordes genom kvalitativa undersökningar i form av intervjuer samt studier av åtgärdsprogram gällande hur lärare identifierar problemen. Informanterna är sex yrkesverksamma lärare med olika matematiska utbildningar inom grundskolans årskurser. Det framkom att den vanligaste åtgärden enligt åtgärdsprogram var arbete i liten grupp, vilket enligt forskning är en handling som inte gynnar eleven, om undervisningen är oförändrad. Däremot ansåg flesta lärare att den bästa metoden för att både upptäcka och avhjälpa svårigheter med taluppfattning var resonemang i matematik med eleven. Brist på resurser gjorde att detta var svårt att organisera. Lärare angav tidbrist som orsak till att kartläggningar av elevers behov saknades i de flesta underlag till åtgärdsprogram.</p>

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, / Includes bibliographical references. Also available on the Internet.

This thesis investigates the function of number marking in Persian, within the framework of principles and parameters (P&P), and its relationship to inflectional and derivational number marking. Following the assumption in Distributed Morphology that inflectional and derivational morphology are not distinct, the distribution and properties of number marking in Persian provide evidence for both inflectional and derivational number marking. Assuming the two parameters of number marking (Wiltschko, 2007, 2008), number marking as a functional head and number marking as a modifier, I propose that number marking in Persian is mainly inflectional while number functions as a functional head; moreover, I propose that number marking in Persian can be derivational while number functions as a modifier. This explains that number morphology in Persian is not split to either inflectional or derivational. Rather, following Booij’s (1993, 1995) claim that inflectional morphology can be used contextually as well as inherently, I propose that number morphology in Persian is inflectional while number is a functional head; however, it has inherent residues as a modifier. Considering the functions of inflectional plural morphology in Persian, I argue that the functional category Number Phrase (NumP) is projected in Persian, and number is generated in the head of this functional category. Besides, Persian is a classifier language in which classifiers are in complementary distribution with plural marking. Following Borer’s (2005) discussion of the complementary distribution of plural marking and classifiers in Armenian, I argue that the head of NumP in Persian is either occupied by the plural maker or by full/empty classifiers. Moreover, I show that the presence of bare singulars/plurals in certain syntactic positions in Persian is related to the projection/non-projection of NumP.

Let $F$ be a non-Archimedean local field and $G$ be the general linear group $\mathrm{GL}_n$ over $F$. Bushnell and Henniart described the essentially tame local Langlands correspondence of $G(F)$ using rectifiers, which are certain characters defined on tamely ramified elliptic maximal tori of $G(F)$. They obtained such result by studying the automorphic induction character identity. We relate this formula to the spectral transfer character identity, based on the theory of twisted endoscopy of Kottwitz, Langlands, and Shelstad. In this article, we establish the following two main results. (i) To show that the automorphic induction character identity is equal to the spectral transfer character identity when both are normalized by the same Whittaker data. (ii) To express the essentially tame local Langlands correspondence using admissible embeddings constructed by Langlands-Shelstad $\chi$-data and to relate Bushnell-Henniart's rectifiers to certain transfer factors.

This thesis investigates the function of number marking in Persian, within the framework of principles and parameters (P&P), and its relationship to inflectional and derivational number marking. Following the assumption in Distributed Morphology that inflectional and derivational morphology are not distinct, the distribution and properties of number marking in Persian provide evidence for both inflectional and derivational number marking. Assuming the two parameters of number marking (Wiltschko, 2007, 2008), number marking as a functional head and number marking as a modifier, I propose that number marking in Persian is mainly inflectional while number functions as a functional head; moreover, I propose that number marking in Persian can be derivational while number functions as a modifier. This explains that number morphology in Persian is not split to either inflectional or derivational. Rather, following Booij’s (1993, 1995) claim that inflectional morphology can be used contextually as well as inherently, I propose that number morphology in Persian is inflectional while number is a functional head; however, it has inherent residues as a modifier. Considering the functions of inflectional plural morphology in Persian, I argue that the functional category Number Phrase (NumP) is projected in Persian, and number is generated in the head of this functional category. Besides, Persian is a classifier language in which classifiers are in complementary distribution with plural marking. Following Borer’s (2005) discussion of the complementary distribution of plural marking and classifiers in Armenian, I argue that the head of NumP in Persian is either occupied by the plural maker or by full/empty classifiers. Moreover, I show that the presence of bare singulars/plurals in certain syntactic positions in Persian is related to the projection/non-projection of NumP.

It is known that almost all numbers are transcendental in the sense of Lebesgue measure. However there is no simple rule to separate transcendental numbers from algebraic numbers. Today research in this direction is about establishing new transcendence criteria for new families of transcendental numbers. By applying a recent refinement of Subspace Theorem, Boris Adamczewski and Yann Bugeaud determined new transcendence criteria for real numbers which we shall present in this thesis. Published only three years ago, their articles explore combinatorial, algorithmic and dynamic approaches in discussing the notion of complexity of both continued fraction and b-adic expansions of a certain class of real numbers. The condition on the expansions are those of being stammering and non-eventually periodic. Taking together these articles give a well-structured picture of the interrelationships between sequence characteristics of expansion (i.e. complexity, periodicity, type of generator) and algebraic characteristics of number itself (i.e. class, transcendency).

In this thesis we focus on the investigation of the relation between the the chip-firing and fractional coloring. Since chi_{f}(G)=inf {n/k : G is homomorphic to K(n,k)}, we find that G has an (n,k)-periodic sequence for some configuration if and only if G is homomorphic to K(n,k). Then we study the periodic configurations for the Kneser graphs. Finally, we try to evaluate the number of chips of the periodic configurations for K(n,k).

This thesis studies the circular chromatic number of Kneser graphs. It was known that if m is greater than 2n^{2}(n-1), then the Kneser graph KG(m,n) has its circular chromatic number equal its chromatic number . In particular, if n = 3, then KG(m,3) has its circular chromatic number equal its chromatic number when m is greater than 36. In this thesis, we improve this result by proving that if m is greaer than 24, then chi_c(KG(m,3)) = chi(KG(m,3)).