title: On integers for which the sum of divisors is the square of the squarefree core

authors: Broughan, Kevin A.

subjects: mathematics

abstract: We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four distinct prime factors is n = 1782. We show that there is no solution which is fourth power free. We also show that the number of solutions up to x > 1 is at most x ⅟⁴⁺ᵉ for any ε > 0 and all x > xε. Further, call n primitive if no proper unitary divisor d of n satisﬁes σ(d) | γ(d) ² . We show that the number of primitive solutions to the equation up to x is less than xᵉ for x > xₑ.

text: On integers for which the sum of divisors is the square of the squarefree core We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four distinct prime factors is n = 1782. We show that there is no solution which is fourth power free. We also show that the number of solutions up to x > 1 is at most x ⅟⁴⁺ᵉ for any ε > 0 and all x > xε. Further, call n primitive if no proper unitary divisor d of n satisﬁes σ(d) | γ(d) ² . We show that the number of primitive solutions to the equation up to x is less than xᵉ for x > xₑ.

year: 2012

title: The creative university: Creative social development and academic entrepreneurship

authors: Besley, Tina

subjects: Education

abstract: The idea that the university needs re-imagining has gained considerable currency since the 21th century. Just why this should be needs some analysis and an examination of the functions and role(s) of universities. Some universities, especially in USA, have recently conducted exercises to achieve this in specific ways that deal with local issues (e.g. Cornell, Harvard, Minnesota, New York, Brown¹). It seems that much of the re-imagining discourse focuses on institutional financial issues, and this tends to play out as part of the crisis in universities literature, which may well be related to the crisis in schools and reform movements there as promoted by neoliberal policy agendas. Crisis discourses frequently use economic consultant advisory reports from large multinational companies (e.g. Ernst & Young and Pearson as described later in this chapter) to provide some degree of analysis. More often than not solutions offered tend to promote forms of university that such as the entrepreneurial university that emphasize research and forms of academic entrepreneurship beyond the traditional forms related to publishing. More recently teaching has become the focus in re-imagining as many universities not only become more global in their focus, but as they start to address modalities of pedagogy as presented by recent IT based systems in MOOCs.

text: The creative university: Creative social development and academic entrepreneurship The idea that the university needs re-imagining has gained considerable currency since the 21th century. Just why this should be needs some analysis and an examination of the functions and role(s) of universities. Some universities, especially in USA, have recently conducted exercises to achieve this in specific ways that deal with local issues (e.g. Cornell, Harvard, Minnesota, New York, Brown¹). It seems that much of the re-imagining discourse focuses on institutional financial issues, and this tends to play out as part of the crisis in universities literature, which may well be related to the crisis in schools and reform movements there as promoted by neoliberal policy agendas. Crisis discourses frequently use economic consultant advisory reports from large multinational companies (e.g. Ernst & Young and Pearson as described later in this chapter) to provide some degree of analysis. More often than not solutions offered tend to promote forms of university that such as the entrepreneurial university that emphasize research and forms of academic entrepreneurship beyond the traditional forms related to publishing. More recently teaching has become the focus in re-imagining as many universities not only become more global in their focus, but as they start to address modalities of pedagogy as presented by recent IT based systems in MOOCs.

year: 2013

title: An evaluation of Kaupapa Māori in Psychology at the University of Waikato

authors: McAllister, Sue

abstract: The University of Waikato’s (UOW) reputation has been built on its unique commitment to Māori aspirations and the educational success of Māori students (The University of Waikato, n.d.-c). Kaupapa Māori has made a significant contribution to this commitment, including in the School of Psychology. Kaupapa Māori prioritises Māori values and a Māori worldview which is necessary in educating culturally aware practitioners. In addition, the inclusion of kaupapa Māori within the School ensures Māori psychology students are valued and their beliefs and worldviews are acknowledged and included. Through this evaluation we aspired to gain insight into how the UOW maintains its commitment to Māori aspirations and the educational success of Māori students.
This evaluation was conducted at the request of the Māori and Psychology Research Unit (MPRU). The aim of this evaluation was to investigate the presence and practice of kaupapa Māori within the School of Psychology at the UOW. Presence and practice refers to the ways in which kaupapa Māori is included, and actively engaged in, within the School of Psychology. This might include, public notices in the School of Psychology, tutorials, workshops, laboratories, support programmes, training, or the inclusion of kaupapa Māori material in the teaching curriculum. The vision for this evaluation was to help assist in shaping practitioners who are able to engage with Māori clients in a culturally appropriate way.
Our evaluation was guided by three objectives:
(1) to consider the experiences of psychology staff in integrating kaupapa Māori into their teaching and administration,
(2) to explore the barriers experienced by Māori psychology students during their programmes of study (both undergraduate and graduate level), and
(3) to identify the practices and structures that support the implementation of kaupapa Māori in the School of Psychology, and ways of expanding these. This evaluation adds to three previous evaluations of kaupapa Māori within the School (Masters & Levy, 1995; Hunt, Morgan & Teddy, 2002; MacLennan, Namwinga, Taylor, & Theodorus, 2013). In this evaluation we investigated outcomes of the past evaluations while exploring ways to further develop kaupapa Māori within the School.
Drawing on the UOW’s Charter, Strategy, Investment Plan, and Māori Advancement Plan, which all set out specific goals and commitments to provide culturally responsive research and education that meets the needs of Māori communities, this evaluation investigates whether the goals and commitments outlined in these documents are being met. In order to do this, this evaluation has aspired to provide significant information regarding the importance and experiences of kaupapa Māori for staff and students (both current and former) within the School of Psychology.
The evaluators conducted four focus groups and 13 semi-structured qualitative interviews with current undergraduate and graduate Māori students, former Māori students, and current and former Māori and non-Māori UOW staff. In total, the voices of 23 participants are reflected in this report.
The analysis of our findings resulted in the following themes relating to staff experiences integrating kaupapa Māori into their teaching and administration: inconsistent integration of kaupapa Māori across the School, cultural incompetence, and harmful University politics. Barriers that were identified by our participants were: lack of kaupapa Māori visibility, navigating two worlds, and financial and practical barriers experienced by Māori students. Various supports for kaupapa Māori were identified and suggestions were given on ways of expanding these. These supports, which included structures and people, were: the MPRU, Te Aka Matua (a mentoring service within the Faculty of Arts and Social Sciences (FASS, now the DALPSS)), kaupapa Māori tutorials, specific staff in the School of Psychology, integration of kaupapa Māori into papers, support of Māori peers, the importance of role models, and the importance of kaupapa Māori in preparing students for the workforce. Ideas often overlapped due to the interrelated nature of experiences, barriers, and supports.
Overall, participants advocated their support for increasing kaupapa Māori support and content within the School of Psychology through the recognition of Māori worldviews. However, it is clear that there is room for development and expansion of the ways kaupapa Māori is currently supported.
Based on the evaluation findings, the recommendations are:
● Recruit more Māori staff
● Further develop kaupapa Māori Tutorials
● Re-establish the Kaupapa Māori Student Advisor position
● Implement discussion of psychology pathways
● Include more bicultural knowledge in paper content
● Include workforce preparation
● Implement kaupapa Māori training for staff
● Incorporate cultural practices into teaching
● Appoint a cultural advisor for staff
● Offer scholarships to alleviate financial barriers
● Invite a kaumatua on site
● Create a whānau space
● Increase the marketing of all Māori services within FASS (DALPSS) and the School of Psychology
● Allocate funding to all Māori support services
● Incorporate more Māori culture visually on campus

text: An evaluation of Kaupapa Māori in Psychology at the University of Waikato The University of Waikato’s (UOW) reputation has been built on its unique commitment to Māori aspirations and the educational success of Māori students (The University of Waikato, n.d.-c). Kaupapa Māori has made a significant contribution to this commitment, including in the School of Psychology. Kaupapa Māori prioritises Māori values and a Māori worldview which is necessary in educating culturally aware practitioners. In addition, the inclusion of kaupapa Māori within the School ensures Māori psychology students are valued and their beliefs and worldviews are acknowledged and included. Through this evaluation we aspired to gain insight into how the UOW maintains its commitment to Māori aspirations and the educational success of Māori students.
This evaluation was conducted at the request of the Māori and Psychology Research Unit (MPRU). The aim of this evaluation was to investigate the presence and practice of kaupapa Māori within the School of Psychology at the UOW. Presence and practice refers to the ways in which kaupapa Māori is included, and actively engaged in, within the School of Psychology. This might include, public notices in the School of Psychology, tutorials, workshops, laboratories, support programmes, training, or the inclusion of kaupapa Māori material in the teaching curriculum. The vision for this evaluation was to help assist in shaping practitioners who are able to engage with Māori clients in a culturally appropriate way.
Our evaluation was guided by three objectives:
(1) to consider the experiences of psychology staff in integrating kaupapa Māori into their teaching and administration,
(2) to explore the barriers experienced by Māori psychology students during their programmes of study (both undergraduate and graduate level), and
(3) to identify the practices and structures that support the implementation of kaupapa Māori in the School of Psychology, and ways of expanding these. This evaluation adds to three previous evaluations of kaupapa Māori within the School (Masters & Levy, 1995; Hunt, Morgan & Teddy, 2002; MacLennan, Namwinga, Taylor, & Theodorus, 2013). In this evaluation we investigated outcomes of the past evaluations while exploring ways to further develop kaupapa Māori within the School.
Drawing on the UOW’s Charter, Strategy, Investment Plan, and Māori Advancement Plan, which all set out specific goals and commitments to provide culturally responsive research and education that meets the needs of Māori communities, this evaluation investigates whether the goals and commitments outlined in these documents are being met. In order to do this, this evaluation has aspired to provide significant information regarding the importance and experiences of kaupapa Māori for staff and students (both current and former) within the School of Psychology.
The evaluators conducted four focus groups and 13 semi-structured qualitative interviews with current undergraduate and graduate Māori students, former Māori students, and current and former Māori and non-Māori UOW staff. In total, the voices of 23 participants are reflected in this report.
The analysis of our findings resulted in the following themes relating to staff experiences integrating kaupapa Māori into their teaching and administration: inconsistent integration of kaupapa Māori across the School, cultural incompetence, and harmful University politics. Barriers that were identified by our participants were: lack of kaupapa Māori visibility, navigating two worlds, and financial and practical barriers experienced by Māori students. Various supports for kaupapa Māori were identified and suggestions were given on ways of expanding these. These supports, which included structures and people, were: the MPRU, Te Aka Matua (a mentoring service within the Faculty of Arts and Social Sciences (FASS, now the DALPSS)), kaupapa Māori tutorials, specific staff in the School of Psychology, integration of kaupapa Māori into papers, support of Māori peers, the importance of role models, and the importance of kaupapa Māori in preparing students for the workforce. Ideas often overlapped due to the interrelated nature of experiences, barriers, and supports.
Overall, participants advocated their support for increasing kaupapa Māori support and content within the School of Psychology through the recognition of Māori worldviews. However, it is clear that there is room for development and expansion of the ways kaupapa Māori is currently supported.
Based on the evaluation findings, the recommendations are:
● Recruit more Māori staff
● Further develop kaupapa Māori Tutorials
● Re-establish the Kaupapa Māori Student Advisor position
● Implement discussion of psychology pathways
● Include more bicultural knowledge in paper content
● Include workforce preparation
● Implement kaupapa Māori training for staff
● Incorporate cultural practices into teaching
● Appoint a cultural advisor for staff
● Offer scholarships to alleviate financial barriers
● Invite a kaumatua on site
● Create a whānau space
● Increase the marketing of all Māori services within FASS (DALPSS) and the School of Psychology
● Allocate funding to all Māori support services
● Incorporate more Māori culture visually on campus

year: 2018