China
Africa
Explore chapters and articles related to this topic
Algebraic Aspects
Published in Marlos A. G. Viana, Vasudevan Lakshminarayanan, Symmetry in Optics and Vision Studies, 2019
Marlos A. G. Viana, Vasudevan Lakshminarayanan
Linear or vector spaces are therefore specialized modules over a given ring with identity. In analogy with distinct linear spaces of a given field F there are distinct modules of a given ring R: F−linear spaces V,R−modules M.
Linear Operators and Matrices
Published in Wai-Kai Chen, Mathematics for Circuits and Filters, 2000
Cheryl B. Schrader, Michael K. Sain
Elements of V are referred to as vectors, whereas elements of F are scalars. Note that the terminology vector space V over the field F is used often. A module differs from a vector space in only one aspect; the underlying field in a vector space is replaced by a ring. Thus, a module is a direct generalization of a vector space.
Investigating mathematics anxiety among mature students in service mathematics courses using the mathematics anxiety scale U.K.
Published in International Journal of Mathematical Education in Science and Technology, 2023
Maria Ryan, Olivia Fitzmaurice, Patrick Johnson
Research into mathematics anxiety has shown that it exists across education sectors and with varying levels (Carey et al., 2017; Dowker et al., 2016). However, there is a dearth of research into the degree of mathematics anxiety among mature students, and particularly in the Irish context. Thus, this study aims to elucidate the existence of mathematics anxiety among mature students in Ireland using the MAS-U.K. to test the levels of mathematics anxiety among this cohort, and thereby endeavours to identify what situations give rise to mathematics anxiety among this cohort through analysis of the MAS-U.K. results. Two sets of hypotheses are proposed for this investigation; first, higher levels of mathematics anxiety are present in older mature students and among female mature students; and second, lower levels of mathematics anxiety are present in mature students of disciplines more associated with mathematics, like engineering. Among this latter group, lower levels of mathematics anxiety is expected in those mature students who have upskilled in mathematics, who are aware of the mathematics modules in the programme, and who are aware of mathematics support facilities in the HEI.
Toward a unified account of definitions in mathematics education research: a systematic literature review
Published in International Journal of Mathematical Education in Science and Technology, 2023
Hermund André Torkildsen, Tore Alexander Forbregd, Eivind Kaspersen, Trygve Solstad
Definitions may therefore support the development of new definitions, both equivalent and non-equivalent. For example, the definition ‘a number of unifix cubes is an even number if we can pair two and two cubes such that no cube is left over’ does not extend to negative numbers, but the definition ‘an even number is a multiple of two’ easily does (the example space is extended). In abstract algebra a vector space is often defined with a (rather long) list of properties. However, we can define a vector space V to be an -module, where is a ring, by simply requiring that is a field (the example space becomes properly smaller, i.e. all vector spaces are modules, but not all modules are vector spaces).
Mathematics teacher education’s missing component: developing pre-service teachers’ appreciation of the utility-value of mathematics
Published in International Journal of Mathematical Education in Science and Technology, 2022
Niamh O’Meara, Olivia Fitzmaurice
This study was conducted in the 2019/2020 academic year and the sample consisted of 23 PSTs who were in the third year of a four-year undergraduate teacher education programme. Upon graduation these PSTs will be recognized by the Teaching Council, the professional regulator of the teaching profession in Ireland, as qualified secondary school mathematics teachers. By the time they entered their mathematics methods module in third year these PSTs had completed seven of the eleven mathematics content modules on their programme with the only outstanding modules still to be completed being Group Theory and Algebraic Structures; History of Mathematics and Differential Equations. At this point in the programme these PSTs had also completed their first mathematics methods module and had spent eight weeks in a post-primary school setting teaching a range of different mathematical concepts to second level students. Due to absenteeism on the days the pre- and post-test were administered only 17 of the 23 PSTs completed the pre- and post-test and hence it was these 17 PSTs who made up the sample for this study. 16 of these PSTs were in attendance for all nine hours of the intervention while one PST missed one hour due to illness.