Quantum homogeneous spaces of connected Hopf algebras

Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension over an algebraically closed field k of characteristic 0. The objects of study in this paper are the left or right coideal subalgebras T of H. They are shown to be deformations of commutative polynomial k-algebras. A number of well-known homological and other properties follow immediately from this fact. Further properties are described, examples are considered, invariants are constructed and a number of open questions are listed.Comment: 26 pages; comments welcom

Self-Efficacy and Expectancy of Engineering Students in Higher Education: A Case Study of the Perceptions and Beliefs of Lecturers

Online assessment is intended to enhance the learning experiences of students and improve the manner in which feedback is delivered. This paper reports on an international project, undertaken in three countries, to examine the beliefs held by engineering mathematics lecturers about the self-efficacy, and constructs of expectancy of their students. The research provides a comparison with beliefs on these topics held by students in the first year of undergraduate Bachelor of Engineering programmes. The interviews were semi-structured to stimulate conversations around a set of pre-determined themes. The thematic inputs to the lecturer interviews resulted from interpretative phenomenological analysis of the beliefs, experiences and perceptions of 127 students, gained from a series of questionnaires, and interviews. The aims of the engineering mathematics lecturer interviews were to examine current practices in terms of assessment of mathematics, and the provision of feedback, in both online and face-to-face formats. A particular focus was to determine if the self-efficacy of students is considered within the process. The research highlights differences in understanding of the assessment process held by lecturers, and students, particularly in the early stages of the first semester. There is also evidence that students’ meta-cognitive functions evolve over the first year of study, and that this may reduce the differences identified between students’ and lecturers’ perceptions. The implications of these findings are discussed

Rhetorical relationships with students: A higher education case study of perceptions of online assessment in mathematics

Some students perceive that online assessment does not provide for a true reflection of their work effort. This article reports on a collaborative international project between two higher education institutions with the aim of researching issues relating to engineering student perceptions with respect to online assessment of mathematics. It provides a comparison between students of similar educational standing in Finland and Ireland. The students undertook to complete questionnaires and a sample of students was selected to participate in several group discussion interviews. Evidence from the data suggests that many of the students demonstrate low levels of confidence, do not display knowledge of continuous assessment processes and perceive many barriers when confronted with online assessment in their first semester. Alternative perspectives were sought from lecturers by means of individual interviews. The research indicates that perceptions of effort and reward as seen by students are at variance with those held by lecturers. The study offers a brief insight into the thinking of students in the first year of their engineering mathematics course. It may be suggested that alternative approaches to curriculum and pedagogical design are necessary to alleviate student concerns

Hopf algebras under finiteness conditions

This is a brief survey of some recent developments in the study of infinite dimensional Hopf algebras which are either noetherian or have finite Gelfand-Kirillov dimension. A number of open questions are listed.Comment: Comments welcom

Geriatric Assessment in Advanced Kidney Disease

Peer reviewe

Unimodular graded Poisson Hopf algebras

Let $A$ be a Poisson Hopf algebra over an algebraically closed field of characteristic zero. If $A$ is finitely generated and connected graded as an algebra and its Poisson bracket is homogeneous of degree $d \geq 0$, then $A$ is unimodular; that is, the modular derivation of $A$ is zero. This is a Poisson analogue of a recent result concerning Hopf algebras which are connected graded as algebras.Comment: 14 pages; preliminary version, comments welcom

Russian perspectives of online learning technologies in higher education: An empirical study of a MOOC

There has been a rapid growth of massive open online courses (MOOCs) in the global education market in the last decade. Online learning technologies are becoming increasingly widespread in the non-formal education sector and in higher and supplementary vocational education. The use of MOOCs in Russia to support the delivery of educational programmes at university level opens opportunities in terms of expanding the educational choice for students, the development of virtual academic mobility, reduction in the cost of educational services, and improvement in the accessibility of education. However, the effectiveness of using different online learning technologies at university level, and the consequences of their widespread adoption, has not been sufficiently explored. In this research study, a comparative analysis is made of the effects of different online learning models on student educational outcomes in a university setting. A study was undertaken in which different groups of students at the Ural Federal University, Russia, were encouraged to study technical and humanities disciplines using a framework of blended learning, and online learning with tutoring support. The results of the study were compared with the results of a reference (control) group of students who studied the same disciplines in a traditionally taught model. It was found that both models (blended and online) of MOOC implementation demonstrated greater learning gains, in comparison with the traditional model. For engineering and technical disciplines, there was no statistically significant difference between blended or online learning technologies. For the humanities discipline, where the communicative component of the learning process was significant, the blended learning technology produced better results. Conclusions of this empirical research may be useful for heads of educational organizations and teachers in helping them to make strategic decisions about the modernization of university courses by increasing the effectiveness of the implementation of new educational technologies. The results of this research project will be used for implementing the State Priority Project, ‘The Modern Digital Educational Environment of the Russian Federation’

Monster Fire at Minong: Wisconsin\u27s Five Mile Tower Fire of 1977

Review of: Monster Fire at Minong: Wisconsin\u27s Five Mile Tower Fire of 1977, by Bill Matthias