Introduction to Group Theory

Exam questions and solutions for a second year group theory course.

Measure Theory

Exam questions, exercises and solutions for a measure theory course.

Number Theory

Lecture notes for a number theory course

Theory of Numbers

Exercises, exams and solutions for a third year maths course.

Análisis al Proceso de Titulación Minera en Colombia desde TOC (Theory Of Constraints)

El incumplimiento reiterado de la normatividad y políticas relacionadas con los tiempos de respuesta del proceso de contratación minera del país, desarrollado actualmente por la recién creada Agencia Nacional de Minería ANM, ha suscitado que la administración del recurso minero no se realice bajo los principios de eficiencia, eficacia, economía y celeridad. Estas debilidades manifiestas provocan represamientos en la resolución de trámites, congelación de áreas para contratar, sobrecostos, demoras en los tiempos de respuesta establecidos por la normatividad vigente y trae como consecuencia incertidumbre en los inversionistas mineros y pérdidas por concepto de recaudo de canon superficiario, entre otras. El objetivo del presente trabajo de investigación consiste en analizar el proceso de titulación minera de Colombia a partir de la filosofía de mejora continua desarrollado en la teoría de restricciones TOC (Theory Of Constraints), para poder identificar cuáles son los cuellos de botella que no permiten que el proceso fluya de manera adecuada y proponer alternativas de mejora, que con su implementación exploten y subordinen la limitaciones al sistema.

Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Social development: bridging the theory-practice divide, past and present

Introduces a collection of articles appearing in a special issue that reflect on social development, considering the various intellectual forms social development has taken, how development thinking has been shaped by different concepts in different periods, and how contributors' personal experiences with social development research has been applied to social development practice.

Models of understanding criminal behaviour and the sentencing process : a place for criminological theory?

The method by which a sentencing court understands the reasons for the commission of a criminal offence is crucial to the framing of the ultimate disposition imposed in all of the circumstances of the offence and the offender. Under Australian criminal law the insights of criminology are rarely. if ever. used in the discharge of the sentencing function. In particular, theories of crime causation evident in schools of criminological thought are not relied upon even though ostensibly such theories would appear to have a degree of relevance to the sentencing task. In this article, a short sketch of contemporary criminological theory is provided. This is followed by a survey of the use of criminological theory under Australian criminal law and what role, if any, it plays in contemporary  criminal justice administration. Finally, consideration is given as to whether or not criminological theory would be of assistance in the discharge of the  sentencing task in relation to not only understanding the reasons for the commission of the offence by the offender, but also in the determination of the appropriate sanction.

What have sampling and data collection got to do with good qualitative research?

Objective: To highlight the importance of sampling and data collection  processes in qualitative interview studies, and to discuss the contribution of  these processes to determining the strength of the evidence generated and  thereby to decisions for public health practice and policy.

Approach: This discussion is informed by a hierarchy-of-evidence-for-practice  model. The paper provides succinct guidelines for key sampling and data  collection considerations in qualitative research involving interview studies. The  importance of allowing time for immersion in a given community to become  familiar with the context and population is discussed, as well as the practical  constraints that sometimes operate against this stage. The role of theory in  guiding sample selection is discussed both in terms of identifying likely sources  of rich data and in understanding the issues emerging from the data. It is noted  that sampling further assists in confirming the developing evidence and also  illuminates data that does not seem to fit. The importance of reporting sampling  and data collection processes is highlighted clearly to enable others to assess  both the strength of the evidence and the broader applications of the findings.

Conclusion: Sampling and data collection processes are critical to determining  the quality of a study and the generalisability of the findings. We argue that  these processes should operate within the parameters of the research goal, be  guided by emerging theoretical considerations, cover a range of relevant   participant perspectives, and be clearly outlined in research reports with an  explanation of any research limitations.

Data quality issues in practice and theory : a cross-cultural example

Practical considerations and traditions play a substantial role in data collection exercises, often limiting the focus of study to either qualitative or quantitative issues. An industry with a particularly strong quantitative emphasis is the insurance and reinsurance industry, where actuarial decisions are based on detailed and exacting numerical analysis of data that are assumed to be reliable and valid. However, the qualitative investigation of the quality of data in one reinsurance setting reported in this paper shows that where the meanings of the questions asked and of the answers provided are subject to interpretation, the quality of data collected for entry to databases can be poor. While this can be exacerbated in cross-cultural contexts, it is also generally true. Due to the constrained nature of insurance practice, the existence of a range of techniques combining qualitative and quantitative methods is somewhat academic. Therefore, because researchers have the latitude to investigate both qualitative and quantitative factors in the industrial context, a call is made for researchers and industry to work more closely together.

Opting in and opting out: a grounded theory of nursings contribution to inpatient rehabilitation

Aim: To develop a grounded theory of nursing’s contribution to patient rehabilitation from the perspective of nurses working in inpatient rehabilitation.

Design: Grounded theory method, informed by the theoretical perspective of symbolic interactionism, was used to guide data collection and analysis, and the development of a grounded theory.

Setting: Five inpatient rehabilitation units in Australia.

Participants: Thirty-five registered and 18 enrolled nurses participated in audio-taped interviews and/or were observed during periods of their everyday practice.

Findings: The analysis revealed a situation whereby nurses made decisions about when to ‘opt in’ and when to ‘opt out’ of inpatient rehabilitation. This occurred on two levels: with their interaction with patients and allied health professionals, and when faced with negative system issues that impacted on their ability to contribute to patient rehabilitation. The primary contribution nurses made to inpatient rehabilitation was working directly with patients, enabling them to self-care. Nurses coached patients when their decisions about ‘opting in’ and ‘opting out’ were based on assessment of the person in their particular context. In contrast, the nurses mostly distanced themselves from system-based problems, ‘opting out’ of addressing them. They did this not to make their working lives easier, but more manageable.

Conclusion: System-based problems impacted negatively on the nurses’ ability to deliver comprehensive rehabilitation care. As a consequence, some nurses felt unable to influence the care and they withdrew professionally to make their work lives more manageable.

Grounded theory of nursing's contribution to inpatient rehabilitation

There is growing awareness of the benefits of rehabilitation both in Australia and overseas. While the provision of rehabilitation services is not new, recognition of this type of health service as an integral part of health care has been linked to changes in the provision of acute care services, advances in medical technology, improvements in the management of trauma and an ageing population. Despite this, little attention has been paid to nursing's contribution to patient rehabilitation in Australia. The aim of this grounded theory study, therefore, was to collect and analyse nurses' reports of their contributions to patient rehabilitation and to describe and analyse contextual factors influencing that contribution. Data were collected during interviews with registered and enrolled nurses working in five inpatient rehabilitation units in New South Wales and during observation of the nurses' everyday practice. A total of 53 nurses participated in the study, 35 registered nurses and 18 enrolled nurses. Grounded theory, informed by the theoretical perspective of symbolic interactionism, was used to guide data analysis, the ongoing collection of data and the generation of a substantive theory. The findings revealed six major categories. One was an everyday problem labelled incongruence between nurses' and patients' understandings and expectations of rehabilitation. Another category, labelled coaching patients to self-care, described how nurses independently negotiated the everyday problem of incongruence. The remaining four categories captured conditions in the inpatient context which influenced how nurses could contribute to patient rehabilitation. Two categories, labelled segregation: divided and dividing work practices between nursing and allied health and role ambiguity, were powerful in shaping nursing's contribution as they acted individually and synergistically to constrain nursing's contribution to patient rehabilitation. The other two categories, labelled distancing to manage systemic constraints and grasping the nettle to realise nursing's potential, represent the mutually exclusive strategies nurses used in response to segregation and role ambiguity. From exploration of the relationship between the six categories, the core category and an interactive grounded theory called opting in and opting out emerged. In turn, this grounded theory reveals nursing's contribution to inpatient rehabilitation as well as contextual conditions constraining that contribution. The significance of these findings is made manifest through their contribution to the advancement of nursing knowledge and through implications for nursing practice and education, rehabilitation service delivery and research.

Environmental attitudes of pre-service teachers : a conceptual and methodological dilemma in cross-cultural data collection

Human generated environmental problems are significant issues of global concern. Despite this, varying attitudes towards environments continue to exist across the globe, impacting on environmental decision-making and action at local, national and international levels. This paper probes some of the similarities and differences in environmental attitudes amongst pre-service teachers in Australia, Republic of Maldives and Indonesia. Data were collected using an established environmental attitude questionnaire and individual interviews. The three communities exhibited a similar range of environmental attitudes using the established questionnaire but significant differences emerged when the interview data were analysed phenomenographically. These differences reflect diversity within and across cultural groups that cannot be satisfactorily explained by the theory underpinning the established questionnaire. Consequently, a revised conceptual framework is proposed.

Exploring the global and local networks of national information system integration initiatives : a case study of national cultural collection integration from an actor-network perspective

Australian Museums Online (AMOL) was the earliest attempt to make Australia’s distributed cultural collections accessible from a single online resource. Despite early successes, significant achievements and the considerable value it offered certain groups, the project ran into operational difficulties and was eventually discontinued. By using Actor-Network Theory and analysing the global and local actor-networks, it is revealed that although the project originated from large, state museums, buy-in was restricted to individuals, rather than institutions and the most significant value was for smaller, regional institutions. Furthermore, although the global networks that governed the project could translate their visions through the local production networks, because the network’s underlying weaknesses were never addressed, over time this destablised the global networks. This case study offers advice for projects attempting to consolidate data sources from disparate sources, and highlights the importance of individual actors in championing the project.

Accessibility and autonomy preconditions to ‘our’ inclusion: a grounded theory study of the experiences of secondary students with vision impairment

In this paper, I report core findings of a small-scale qualitative study that I conducted with a group of young people with vision impairment who attended an inclusive secondary school in the Australian state of Queensland. My objective was to capture their voiced experiences of their schooling through face-to-face interviews and to develop a substantive theory that was grounded in the collected data. Relevant to the study was my status as an insider researcher, which impacted both data collection and analysis. Here, I develop the methodological process that I followed and present core findings of the study. These findings shed light on the practices within schools that are designed to promote inclusion yet perpetuate exclusion for students with impaired vision.