Let G be a finite directed graph, (G) the minimum size of a subset X of edges such that the graph G = (V, E X) is directed acyclic and (G) the number of pairs of nonadjacent vertices in the undirected graph obtained from G by replacing each directed edge with an undirected edge. Chudnovsky, Seymour and Sullivan proved that if G is triangle-free, then (G) (G). They conjectured a sharper bound (so called the "CSS conjecture") that (G) (G)/2. Nathanson and Sullivan verified this conjecture for the directed Cayley graph Cay(Z/NZ, E A ) whose vertex set is the additive group Z/NZ and whose edge set E A is determined by E A = {(x, x + a) : x Z/NZ, a A} when N is prime and |A| (N -1)/4 by introducing "height". In this work, we extend the definition of height and apply to answer the CSS conjecture for Cay(Z/NZ, E A ) to any positive integer N and |A| (N -1)/4.

This paper focuses on the Southern African Association for Research in Mathematics, Science and Technology Education’s (SAARMSTE’s) role as a platform supporting research dissemination and connecting researchers in early grades mathematics (EGM) in the Southern African region. A review of the Long Papers in SAARMSTE over the last 20 years supports the finding of the other review papers in this Special Issue: that there has been substantial growth of attention to EGM since 2013. However, two distinctions are marked when looking at conference papers rather than journal papers. Firstly, there is a particularly large expansion of work in the last 5 years, with a broadening base of participation in this work. Second, looking across all the formats of conference presentations indicates SAARMSTE’s role in supporting and building EGM as a key focus of research attention, and bringing together regional and international groups with interests in this area. Given that conference proceedings usually offer a broader picture of emerging interests than journal papers, we reflect on the range of foci of attention within EGM in the SAARMSTE Proceedings, and trends within this. These trends also help us to point to areas that are likely to be of key interest in the next decade.

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 46, Issue 5 p. 334-334 Buchbesprechung Asymptotic Solutions of Differential Equations and Their Applications. (Publication No. 13 of the Mathematics Research Center, US Army, The University of Wisconsin) × + 249 S. mit Fig. New York/London/Sydney 1964. John Wiley & Sons, Inc. Preis geb. 38 $ H. Mühlig, H. Mühlig DresdenSearch for more papers by this author H. Mühlig, H. Mühlig DresdenSearch for more papers by this author First published: 1966 https://doi.org/10.1002/zamm.19660460545AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume46, Issue51966Pages 334-334 RelatedInformation

This work shows the results of a research carried out in secondary school and university developing a co-disciplinary Research and Study Course (RSC) on questions connected to Physics and Mathematics in different groups. We present preliminary results of the RSC developed in three different groups: science education researchers, N=25 Mathematics teacher students (training teachers of Mathematics) at University, and N= 68 secondary school students. The development and scope of the RSC in each group is described by using the RSC components as defined by Chevallard’s Anthropological Theory of Didactics (ATD). Furthermore, a short description of the Praxeological Model of Reference is presented. This model was built by the researchers group in order to reply to the generative question, unknown in the beginning, and to anticipate and to conceive the evolution of the possible SRC in each institution. Some general results in each group are discussed and some conclusions concerning the ecology of the pedagogy of research and questioning the world at university and secondary schools are drawn.

This article is about research done on the ways of using visuals in teaching introductory mathematics. Research showed that the use of visuals improves the learning of mathematics. However, more research is needed to explore which math concepts need to be addressed, how to choose visuals for that purpose, and how to incorporate them in teaching mathematics. The analysis shows that the effective use of correctly chosen visuals in teaching introductory mathematics positively impacts students’ attitudes toward mathematics, and enhances their learning, engagement, and motivation. Keywords: analytical thinking skills, instructional strategies with visuals, introductory mathematics, student engagement, and motivation

We use data from papers posted to the Mathematics section of the arXiv to explore the representation of women in mathematics research. We show that women are under-represented as authors of mathematics papers on the arXiv, even in comparison to the proportion of women who hold full-time positions in mathematics departments. However, some subfields have much greater participation than others.

To achieve a successful mathematics education through the implementation of the school mathematics curriculum, the teacher’s beliefs emanating from their experiences (including learning theories) with their environment should be a considerable factor. This is to ensure that all learning situation in mathematics classroom generate understanding among the individuals involve for it to be meaningful. In this paper my goal is to highlight on some issues which are of great importance to mathematics education as a field of study. The issues in focus are; theory and practice, the role of theory in mathematics education research, some widely used learning theories in mathematics education, theories of models and modelling and their impact on mathematics research, teaching and learning, the aims of teaching and learning mathematics, and the status of mathematics education as knowledge field.

In this paper I will outline the process I have developed for conducting applied mathematics research with undergraduates and give some examples of the projects we have worked on. Several of these projects have led to refereed publications that could be used to illustrate topics taught in the undergraduate curriculum.

In this study, in order to provide a developmental discussion on general mathematics in universities and the direction for follow-up research, research trends were examined for papers published in Korean domestic academic journals over the past 10 years. The results of the research are as follows: First, among studies related to mathematics education and general education, research on general mathematics in universities is severely lacking. Considering that nearly all universities offer courses related to general mathematics, professors and researchers responsible for general mathematics should dedicate more attention to research on general college mathematics. Second, concerning the subjects and content areas of mathematics, research on general mathematics shows a bias towards basic general mathematics for science and engineering students. Therefore, there is a need for research on basic general mathematics for students in the humanities and social sciences, as well as research on pure general mathematics applicable to all students. Third, there is a lack of research on evaluation and educational technology in the field of general mathematics. Evaluation plays a crucial role in education, and it is important to conduct research on the evaluation of general mathematics and the utilization of educational technology, especially considering the increasing emphasis on the use of various technological tools in mathematics education. Fourth, in terms of research methods, the majority of studies focus on quantitative research. Therefore, it is necessary to employ diverse research methods that are suitable for the teaching and learning environment of general mathematics. Fifth, concerning the research topic on teaching and learning, while there have been numerous studies targeting science and engineering students, there is a need for a variety of studies on teaching and learning that encompass all students, including those in the humanities and social sciences, as well as the professors themselves.