Group Theory (original) (raw)
Related papers
Workbooks for Independent Study of Group Theory Proofs
2000
This paper reports on a small project investigating students' experience of a workbook designed to promote in-depth study of proofs. The workbook was one of two used as part of the assessment for an abstract algebra course, and was designed by the course lecturer. In this paper, we first review related research literature. We then provide detail on the setting
On learning fundamental concepts of group theory
The research reported in this paper explores the nature of student knowledge about group theory, and how an individual may develop an understanding of certain topics in this domain. As part of a long-term research and development project in learning and teaching undergraduate mathematics, this report is one of a series of papers on the abstract algebra component of that project.The observations discussed here were collected during a six-week summer workshop where 24 high school teachers took a course in Abstract Algebra as part of their work. By comparing written samples, and student interviews with our own theoretical analysis, we attempt to describe ways in which these individuals seemed to be approaching the concepts of group, subgroup, coset, normality, and quotient group. The general pattern of learning that we infer here illustrates an action-process-object-schema framework for addressing these specific group theory issues. We make here only some quite general observations about learning these specific topics, the complex nature of understanding, and the role of errors and misconceptions in light of an action-process-schema framework. Seen as research questions for further exploration, we expect these observations to inform our continuing investigations and those of other researchers.We end the paper with a brief discussion of some pedagogical suggestions arising out of our considerations. We defer, however, a full consideration of instructional strategies and their effects on learning these topics to some future time when more extensive research can provide a more solid foundation for the design of specific pedagogies.
Developing group theory textbook which connected to the school mathematics' contents
PROCEEDINGS OF THE 6TH NATIONAL CONFERENCE ON MATHEMATICS AND MATHEMATICS EDUCATION
As part of abstract algebra, the group theory is considered as a difficult subject for pre-service mathematics teachers (PMTs) since it seems not related to the future teaching. In line with the Klein's double discontinuity that the learning of group theory at the university did not bring the content from school mathematics and in the school level mathematics' content did not connected to the university mathematics. Therefore, the current study intends to develop the group theory textbook which connected to the school mathematics that provide the PMTs with the mathematical connection. The study involves the educational research and development cycle refers to Borg and Gall's model, which is adjusted to the need of this study. The research procedures consist of three main stages: collecting data, planning, and developing the product. There is a significant need for further studies to be done in this area to implement this group theory textbook to obtain how PMTs aware to the mathematical connection from school mathematics and vice versa. Furthermore, it is essential to conduct the study about the effectiveness of this textbook. Particularly, in overcoming the PMTs' difficulty in the learning process of group theory subject.
Examples of groups in abstract Algebra Course Books
This study has been conducted with the aim to examine the examples of Abelian and non-Abelian groups given in the abstract algebra course books in the university level. The non-examples of Abelian groups serve as examples of non-Abelian groups. Examples with solutions in the course books are trusted by the students and hence miscellaneous of those are required to clarify the subject in enough detail. The results of the current study show that the examples of Abelian groups are about the same among three course books, including number sets only with known operations. The examples of non-Abelian groups are rare in comparison and encapsulate the nonnumeric sets which are novel to students. The current study shows the mentioned examples are not sufficiently examined in the course books. Suggestions for the book writers are given in the study. Mainly it is suggested that more and various examples of Abelian and especially non-Abelian groups should be included in the course books.
EPJ Web of Conferences, 2012
This chapter is a concise mathematical introduction into the algebra of groups. It is build up in the way that definitions are followed by propositions and proofs. The concepts and the terminology introduced here will serve as a basis for the following chapters that deal with group theory in the stricter sense and its application to problems in physics. The mathematical prerequisites are at the bachelor level. 1 This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3.0, which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly cited.
Mathematical tags of group theory
Open Journal of Mathematics and Physics, 2020
I present a collection of mathematical results regarding group theory organized by tags.