On understanding and interpretation in mathematics: An integrative overview

For decades, understanding has been considered as a basic theme of interest and a research object in Mathematics Education. In this theoretical overview paper we present a integrative framework for organizing the diversity of results that emerge from the different studies on mathematical understanding and its interpretation. The proposal is applied onto a representation of relevant literature that has arise in the area over the last two decades. With this overview we seek to provide an useful reference for: (a) advancing towards a better insight of understanding in mathematics, (b) establishing the specific limitations and open questions that demarcate the boundaries of understanding and interpretation in mathematics, and (c) orienting its future study using a shared base of consolidated knowledge

Universality of K-Theory

We prove that graded K-theory is universal among oriented Borel-Moore homology theories with a multiplicative periodic formal group law.Comment: 12 page

Descent for algebraic cobordism

We prove the exactness of a descent sequence relating the algebraic cobordism groups of a scheme and its envelopes. Analogous sequences for Chow groups and K-theory were previously proved by Gillet.Comment: 15 page

The change towards a teaching methodology based on competences: a case study in a Spanish university

The European Higher Education Area (EHEA) has promoted the implementation of a teaching methodology based on competences. Drawing on New Institutional Sociology, the present work aims to identify and improve knowledge concerning the factors which are hindering that change in the Spanish university system. This is investigated using a case study based on a Spanish university which is a pioneer in the implementation of a competence-based curriculum. The results show that factors identified and analysed are conditioning the change and causing a ceremonial adoption of the competence-based system by the teaching staff. The results of the study may be of use as a reference and orientation for educators and administrators as well as for the regulators of those countries integrated within the EHEA. The study may prove useful in the analysis of inertia factors present when designing and implementing the policies and measures necessary to achieve a comprehensive teaching methodology; one which incorporates learning and assessment of competences in a real manner

Quality uncetainty and informative advertising.

We consider a single period model where a monopolist introduces a product of uncertain quality. Before pricing and informative advertising decisions take place, the producer observes the true quality of the good while consumers receive an independent signal which is correlated with the true quality of the product. We show that if advertising occurs in equilibrium, there must exist some pooling. We then characterize the constellations of parameters for which advertising occurs in equilibrium: For an advertising full pooling equilibrium to exist, (a) the consumers' valuation for the high quality must be high enough, (b) the informativeness of the market signal must be sufficiently low, (c) the costs of advertising must be high enough and (d) the consumers' priori probability of high quality must be sufficiently high. Existence of an advertising semi-separating equilibrium also requires the three first conditions but, in contrast, the consumers' a priori probability of high quality cannot be too large. When advertising occurs in equilibrium, the adverse selection problem is mitigated. Moreover, the lower are advertising costs, the more intense is the alleviation of that problem.Informative Advertising; Quality uncertainty; signaling;

Bivariant Algebraic Cobordism

We associate a bivariant theory to any suitable oriented Borel-Moore homology theory on the category of algebraic schemes or the category of algebraic G-schemes. Applying this to the theory of algebraic cobordism yields operational cobordism rings and operational G-equivariant cobordism rings associated to all schemes in these categories. In the case of toric varieties, the operational T-equivariant cobordism ring may be described as the ring of piecewise graded power series on the fan with coefficients in the Lazard ring.Comment: 39 page