University Mathematics-Laden Education, Competencies and the Fighting of Syllabusitis

Syllabusitis is a name for a disease that consists of identifying the mastering of a subject with proficiency related to a syllabus. In this chapter I argue that using a set of mathematical competencies as the hub of mathematics-laden education can be a means to fight syllabusitis. The introduction and thorough exemplification of this idea was the main outcome of the Danish KOM Project. Furthermore, a two-dimensional structuring of the relation between subject specific competencies and subject matter was suggested. As the analytic core of this chapter I argue that such a two-dimensional structure has proven to be a crucial element when attempting to put the competency idea into educational practice, and exemplify how that can be done when it comes to mathematics-laden education at university level.

Local Spectral Properties Under Conjugations

In this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and $$T\in L(H)$$ T ∈ L ( H ) . We also study the relationship between the quasi-nilpotent part of the adjoint $$T^*$$ T ∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form $$JT^*J$$ J T ∗ J . The theory is exemplified in some concrete cases.

The Local spectral theory and surjective spectrum of linear relations

UDC 517.98 This paper initiates a study of local spectral theory for linear relations. At the beginning, we define the local spectrum and study its properties. Then we obtain results related to the correlation analytic core and quasinilpotent part of a linear relation in a Banach space . As an application, we give a characterization of the surjective spectrum in terms of the local spectrum and show that if , then does not cluster at .

Avar

This chapter provides a grammatical sketch of Avar, the largest indigenous language of Dagestan. Avar has five vowels and more than 40 consonants, among which there are a number of voiced, voiceless, ejective (glottalized), and tense (strong) obstruents. The language is agglutinative with some elements of fusion and strongly suffixing. Nouns are divided into three genders, and three inflectional classes, which largely correlate with the gender divisions. The core cases are absolutive, ergative, dative and genitive; furthermore, there are twenty spatial cases. Avar has gender and number agreement expressed by prefixes, suffixes, and occasionally infixes. Agreement targets are mainly verbs, adjectives, and certain pronouns. While agreement and case marking follow ergative alignment, no ergative patterns are found outside the realm of morphology. The rich inventory of verb forms consists of four synthetic and six analytic core tenses used in finite clauses. The non-finite verb forms include infinitive, masdar, and a wide range of participles and converbs. Noun phrases and subordinate clauses are head-final. In main clauses there is a clear tendency for A-P-V order, but other orders are also attested.

Analytic core and quasi-nilpotent part of linear relations in Banach spaces

In this paper, we investigate the notion of analytic core and quasi-nilpotent part of a linear relation. Furthermore, we are interested in studying the set of Generalized Kato linear relations to give some of their properties in connection with the analytic core and the quasi-nilpotent part. We finish by giving a perturbation result for this set of linear relations.

The Economic History of the American Economic Review: A Century's Explosion of Economics Research

Written in celebration of the 100th anniversary of the American Economic Review, this paper recounts the history of the journal. The recounting has an analytic core that sees the American Economic Association as an organization supplying goods and services to its members, one of which is the Review. Early in its history the Review was a multipurpose publication with highly disparate content. Over time the economics profession expanded and more economics research was produced, primarily in the form of journal articles. Editors accommodated this shift by allocating more resources to the refereeing and editing process and more space to research papers. (JEL A14, B19, B29)

Alfred Marshall's Idea of Progress and Sustainable Development

For a long time, Marshall's chief contribution to economic science was considered to be Book V of Principles of Economics, which is the “analytic core” of his thought. Book V, “General Relations of Demand, Supply and Value,” deals with the important theme of economic equilibrium that ipso facto rules out any possibility of coping with economic development. When Alfred Marshall describes Book V, he points out that “it is not descriptive, nor does it deal constructively with real problems. But it sets out the theoretical backbone of our knowledge of the causes that govern value” (1961, vol. 1, p. 324); in short, it “deals with abstractions” (1898, p. 52). The existence of Book V has been supposed by some scholars to be sound enough proof that Alfred Marshall was not interested in the question of economic development. More recently, however, it has been suggested that one of the main Marshallian concerns was economic development,—“the high theme of economic progress,” as he called it (Marshall 1961, vol. 1, p. 461).