A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

Introduction to Network Mathematics

Introduction to Network Mathematics provides college students with basic graph theory to better understand the Internet

School of Mathematics Computing Guide

Guide for computing in the School of Mathematics. Intended for new staff and PG students. Originally written by Anton Prowse from a number of earlier documents.

Educating an iPod generation: undergraduate attitudes, experiences and understanding of vodcast and podcast use

ognyline) There is an increasing pressure on university staff to provide ever more information and resources to students. This study investigated student opinions on (audio) podcasts and (video) vodcasts and how well they met requirements and aided learning processes. Two experiments within the Aston University looked at student opinion on, and usage of, podcasts and vodcasts for a selection of their psychology lectures.

Attitude in students of Health Sciences toward scientific knowledge

Educating health professionals implies the challenge of creating and developing an inquiring mind, ready to be in a state of permanent questioning. For this purpose, it is fundamental to generate a positive attitude toward the generation of knowledge and science. Objective: to determine the attitude toward science and the scientific method in undergraduate students of health sciences. Materials and methods: a cross-sectional study was made by applying a self-administered survey, excluding those who were transferred from other universities and repeated. The attitude toward science and the scientific method were valued using the scale validated and published by Hren, which contains three domains: value of scientific knowledge, value of scientific methodology, and value of science for health professions. Results: 362 students were included, 86,6% of them graded the attitude toward scientific knowledge above 135 points, neutral scale value. Similar scores were registered in the domains value of scientific knowlede for the human dimension of the students and value of science for health professions. 91,4% of the students graded the value of scientific methodology below 48 points. Conclusions: the favorable attitude of the students can be explained by the contact that they have with the scientific method since the beginning of their studies and its concordance with the evolution of science. The domain value of scientific methodology obtained the lowest grade on the part of the students, which could be related to the lack of knowledge about scientific methodology.

Medical Student’s Use of Time During Clinical Clerkships and the Credits Based System

Introduction: Comprehensive undergraduate education in clinical sciences is grounded on activities developed during clerkships. To implement the credits system we must know how these experiences take place. Objectives: to describe how students spend time in clerkships, how they assess the educative value of activities and the enjoyment it provides. Method: We distributed a form to a random clustered sample of a 100 students coursing clinical sciences, designed to record the time spent, and to assess the educative value and the grade of enjoyment of the activities in clerkship during a week. Data were registered and analyzed on Excel® 98 and SPSS. Results: mean time spent by students in clerkship activities on a day were 10.8 hours. Of those, 7.3 hours (69%) were spent in formal education activities. Patient care activities with teachers occupied the major proportion of time (15.4%). Of the teaching and learning activities in a week, 28 hours (56%) were spent in patient care activities and 22.4 hours (44.5%) were used in independent academic work. The time spent in teaching and learning activities correspond to 19 credits of a semester of 18 weeks. The activities assessed as having the major educational value were homework activities (4.6) and formal education activities (4.5). The graded as most enjoyable were extracurricular activities, formal educational activities and independent academic work. Conclusion: our students spend more time in activities with patients than the reported in literature. The attending workload of our students is greater than the one reported in similar studies.

A tool for mapping research skills in undergraduate curricula

There has been considerable interest recently in the teaching of skills to undergraduate students. However, existing methods for collating data on how much, where and when students are taught and assessed skills have often been shown to be time-consuming and ineffective. Here, we outline an electronic research skills audit tool that has been developed to map both transferable and discipline-specific skills teaching and assessment within individual modules, the results of which can be collated and analysed across entire degree programmes. The design and use of the audit tool is described in detail and a bioscience case study is presented to illustrate the types of data that can be collected. The audit tool has been designed as a time-effective way of collecting information on skills teaching and assessment, but also actively encourages staff to reflect on their teaching and learning practices. Conclusions are drawn about the practicalities of using the audit tool and its importance in both curriculum design and as a resource to encourage dialogue with graduate employers.

The Acute Care Undergraduate TEaching (ACUTE) initiative: consensus development of core competencies in acute care for undergraduates in the United Kingdom

Background: The care of the acutely ill patient in hospital is often sub-optimal. Poor recognition of critical illness combined with a lack of knowledge, failure to appreciate the clinical urgency of a situation, a lack of supervision, failure to seek advice and poor communication have been identified as contributory factors. At present the training of medical students in these important skills is fragmented. The aim of this study was to use consensus techniques to identify the core competencies in the care of acutely ill or arrested adult patients that medical students should possess at the point of graduation. Design: Healthcare professionals were invited to contribute suggestions for competencies to a website as part of a modified Delphi survey. The competency proposals were grouped into themes and rated by a nominal group comprised of physicians, nurses and students from the UK. The nominal group rated the importance of each competency using a 5-point Likert scale. Results: A total of 359 healthcare professionals contributed 2,629 competency suggestions during the Delphi survey. These were reduced to 88 representative themes covering: airway and oxygenation; breathing and ventilation; circulation; confusion and coma; drugs, therapeutics and protocols; clinical examination; monitoring and investigations; team-working, organisation and communication; patient and societal needs; trauma; equipment; pre-hospital care; infection and inflammation. The nominal group identified 71 essential and 16 optional competencies which students should possess at the point of graduation. Conclusions: We propose these competencies form a core set for undergraduate training in resuscitation and acute care.

Students' assessment of immersive virtual reality as a pedagogic medium

Over the past few years a number of research studies, mainly involving desktop-based or head-mounted Virtual Reality (VR) systems, have been undertaken to determine what VR can contribute to the education process. In our study we have used the findings from a number of these studies to help in formulating a new study into the perceived merits and limitations of using VR in general, and immersive CAVE-like systems in particular, as an education tool. We conducted our study with a group of final year undergraduate students who were registered on a module that described VR in terms of the scientific issues, application areas, and strengths and weaknesses of the technology.

Electronic voting systems in undergraduate teaching

One of the major differences undergraduates experience during the transition to university is the style of teaching. In schools and colleges most students study key stage 5 subjects in relatively small informal groups where teacher–pupil interaction is encouraged and two-way feedback occurs through question and answer type delivery. On starting in HE students are amazed by the sizes of the classes. For even a relatively small chemistry department with an intake of 60-70 students, biologists, pharmacists, and other first year undergraduates requiring chemistry can boost numbers in the lecture hall to around 200 or higher. In many universities class sizes of 400 are not unusual for first year groups where efficiency is crucial. Clearly the personalised classroom-style delivery is not practical and it is a brave student who shows his ignorance by venturing to ask a question in front of such an audience. In these environments learning can be a very passive process, the lecture acts as a vehicle for the conveyance of information and our students are expected to reinforce their understanding by ‘self-study’, a term, the meaning of which, many struggle to understand. The use of electronic voting systems (EVS) in such situations can vastly change the students’ learning experience from a passive to a highly interactive process. This principle has already been demonstrated in Physics, most notably in the work of Bates and colleagues at Edinburgh.1 These small hand-held devices, similar to those which have become familiar through programmes such as ‘Who Wants to be a Millionaire’ can be used to provide instant feedback to students and teachers alike. Advances in technology now allow them to be used in a range of more sophisticated settings and comprehensive guides on use have been developed for even the most techno-phobic staff.

Meteorology and climate inspire secondary school students

As part of its National Science and Engineering Week activities in 2009 and 2010, the University of Reading organised two open days for 60 local key stage 4 pupils. The theme of both open days was ‘How do we predict weather and climate?’ Making use of the students’ familiarity with weather and climate, several concepts of relevance to secondary science were investigated. The open days also provided an opportunity for more than 30 research staff from the university to interact with the students. Feedback from students and teachers was extremely positive. This article shows how meteorological science can be used to illustrate elements of the secondary science and mathematics curricula.

Mathematics as a tool in the Life Sciences

Teaching mathematics to students in the biological sciences is often fraught with difficulty. Students often discover mathematics to be a very 'dry' subject in which it is difficult to see the motivation of learning it given its often abstract application. In this paper I advocate the use of mathematical modelling as a method for engaging students in understanding the use of mathematics in helping to solve problems in the Biological Sciences. The concept of mathematics as a laboratory tool is introduced and the importance of presenting students with relevant, real-world examples of applying mathematics in the Biological Sciences is discussed.

'In practice it doesn't always work out like that.' Undergraduate experiences in a research community of practice

This paper examines the extent to which a structured undergraduate research intervention, UROP, permits undergraduate students early access to legitimate peripheral participation (LPP) in a research community of practice. Accounts of placement experiences suggest that UROP affords rich possibilities for engagement with research practice. Undergraduates tread a path of gaining access to mature practice while also building their own independence, participating in work that they see matters to the community and making gains in use of a shared research repertoire. Students place UROP experiences in a contrasting frame to research exercises experienced during degree programmes; their sense of the authenticity of the research experienced through UROP emerges as a key element of these accounts. The data generate the interesting question that the degree of engagement with mature practice may account for more of the gain from UROP than simply the quantity of contact other researchers.