Applications of Groups and Isomorphic Groups to Topics in the Standard Curriculum, Grades 9-11: Part I

1975 ◽  
Vol 68 (2) ◽  
pp. 99-106
Author(s):  
Zalman Usiskin
Keyword(s):  
Linear Algebra ◽  
Prospective Teachers ◽  
Mathematics Teacher ◽  
Abstract Algebra ◽  
Vector Spaces ◽  
Graduate Level ◽  
The Past ◽  
Standard Curriculum ◽  
Pure Mathematics

The subfield of pure mathematics that has grown most significantly in the past few decades is that of algebra, by which is meant “higher” or “abstract” algebra and linear algebra. Twenty years ago courses in algebra were at the advanced undergraduate and graduate level, and it was easy to become a certified mathematics teacher without having any knowledge of groups, rings, fields, or vector spaces. Today virtually all prospective teachers take a course in which some of these structures are studied.

scholarly journals Address of the President Sir Henry Dale, C.B.E., at the Anniversary Meeting, 1 December 1941

1942 ◽  
Vol 179 (978) ◽  
pp. 233-260 ◽  
Keyword(s):  
Technical College ◽  
High Speed ◽  
Large Scale ◽  
Electrical Engineering ◽  
The United States ◽  
The Past ◽  
Pure Mathematics ◽  
Symbolic Structure ◽  
The Church ◽  
Insight Into

This is the first occasion on which I have had the great honour of addressing the Royal Society on this anniversary of its foundation. According to custom, I begin with brief mention of those whom death has taken from our Fellowship during the past year, and whose memories we honour. Alfred Young (1873-1940), distinguished for his contributions to pure mathematics, was half brother to another of our Fellows, Sydney Young, a chemist of eminence. Alfred Young had an insight into the symbolic structure and manipulation of algebra, which gave him a special place among his mathematical contemporaries. After a successful career at Cambridge he entered the Church, and passed his later years in the country rectory of Birdbrook, Essex. His devotion to mathematics continued, however, throughout his life, and he published a steady stream of work in the branch of algebra which he had invented, and named ‘quantitative substitutional analysis’. He lived to see his methods adopted by Weyl in his quantum mechanics and spectroscopy. He was elected to our Fellowship in 1934. With the death of Miles Walker (1868-1941) the Society loses a pioneer in large-scale electrical engineering. Walker was a man of wide interests. He was trained first for the law, and even followed its practice for a period. Later he studied electrical engineering under Sylvanus Thompson at the Finsbury Technical College and became his assistant for several years. Thereafter, encouraged by Thompson, he entered St John’s College, Cambridge, with a scholarship, and graduated with 1st Class Honours in both the Natural Sciences and the Engineering Tripos. Having entered the service of the British Westinghouse Company, he was sent by them to the United States of America to study electrical engineering with the parent company in Pittsburgh. On his return to England he became their leading designer of high-speed electrical generators

scholarly journals Dreibens Modulo 7: A New Formula for Primality Testing

Elements ◽  
2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Arthur Diep-Nguyen
Keyword(s):  
Number Theory ◽  
Linear Algebra ◽  
Abstract Algebra ◽  
Additional Insight ◽  
Primality Testing ◽  
New Formula ◽  
Insight Into ◽  
Rule Out

In this paper, we discuss strings of 3’s and 7’s, hereby dubbed “dreibens.” As a first step towards determining whether the set of prime dreibens is infinite, we examine the properties of dreibens when divided by 7. by determining the divisibility of a dreiben by 7, we can rule out some composite dreibens in the search for prime dreibens. We are concerned with the number of dreibens of length n that leave a remainder i when divided by 7. By using number theory, linear algebra, and abstract algebra, we arrive at a formula that tells us how many dreibens of length n are divisible by 7. We also find a way to determine the number of dreibens of length n that leave a remainder i when divided by 7. Further investigation from a combinatorial perspective provides additional insight into the properties of dreibens when divided by 7. Overall, this paper helps characterize dreibens, opens up more paths of inquiry into the nature of dreibens, and rules out some composite dreibens from a prime dreiben search.

scholarly journals The Process of Inquiry-Based Teaching Practices from the Perspective of Prospective Mathematics Teachers

2020 ◽  
Vol 10 (3) ◽  
pp. 1-33
Author(s):  
Rabia Sarıca ◽  
Bayram Çetin
Keyword(s):  
Prospective Teachers ◽  
Mathematics Teacher ◽  
Teacher Candidates ◽  
Teaching Practices ◽  
Teaching Method ◽  
Real Life ◽  
Research Process ◽  
Structured Interviews ◽  
Application Process ◽  
3Rd Grade

AbstractIntroduction: Inquiry-based teaching is a constructivist-based method that has become popular in recent years. In this method, students work in a systematic way like a scientist during the research process, actively participate in the learning process, solve problems and learn in practice. The aim of this study is to reveal the opinions of prospective teachers about inquiry based teaching practices.Methods: The study was designed in a qualitative research design. The participants of the study are primary mathematics teacher candidates. Data were collected through semi-structured interviews conducted face-to-face with the students. The data were analyzed using content analysis. The findings obtained from the analysis of the prospective teachers’ views were presented with the relevant themes and codes under the titles.Results: Some of the findings of the prospective teachers’ opinions about the process in which inquiry-based teaching method is applied are as follows. It provides permanent learning, is suitable for real life, develops skills such as research, problem solving, leadership, motivates and gives experience to the profession, is learned actively by doing and experiencing in the process, unexpected difficulties are encountered, the traditional method is easier, not suitable for every course, the lecturer should give more feedback and guidance, communication and coordination in group work is required.Discussion: Prospective teachers stated many positive opinions about the process in which the course content was taught using inquiry-based method. It can be said that the application process positively influences the practical knowledge and skills of teacher candidates. However, it is seen that some prospective teachers find the process tiring and time consuming. It is understood that teacher candidates have intense concerns about Public Personnel Selection Examination (KPSS) and this affects the process. KPSS is a test in Turkey for prospective teachers where they should get enough points to be appointed as teachers after graduation. Although the participants of this study are 3rd grade prospective teachers and they take the KPSS exam after graduation; it is understood that KPSS affects them and their motivation.Limitations: This research is limited to the measurement and evaluation course and to the 3rd grade mathematics teacher candidates who are the participants of this study.Conclusions: Prospective teachers mostly have positive opinions about the inquiry-based teaching process. It can be said that it would be beneficial to use this method in teacher education.

A Review On Some Neutrosophic Algebraic Linear Structures

2021 ◽  
Author(s):  
Malath F. Alaswad ◽  
Keyword(s):  
Linear Algebra ◽  
Matrix Theory ◽  
Vector Spaces ◽  
Interested Reader ◽  
Linear Structures ◽  
Basic Concepts

This paper is dedicated to reviewing some of the basic concepts in neutrosophic linear algebra and its generalizations, especially neutrosophic vector spaces, refined neutrosophic, and n-refined neutrosophic vector spaces. Also, this work gives the interested reader a strong background in the study of neutrosophic matrix theory and n-refined neutrosophic matrix theory. We study elementary properties of these concepts such as Kernel, AH-Quotient, and dimension.

Promoting Active Learning in Mathematics Teacher Education

2017 ◽  
pp. 269-284
Author(s):  
Rukiye Didem Taylan
Keyword(s):  
Teacher Education ◽  
Active Learning ◽  
Professional Learning ◽  
Prospective Teachers ◽  
Mathematics Teacher ◽  
Professional Growth ◽  
Flipped Classroom ◽  
Teacher Educators ◽  
Mathematics Teacher Education ◽  
Pedagogical Content

Teacher educators have a responsibility to help prospective teachers in their professional growth. It is important that teacher educators not only teach prospective teachers about benefits of active learning in student learning, but that they also prepare future teachers in using pedagogical methods aligned with active learning principles. This manuscript provides examples of how mathematics teacher educators can promote prospective teachers' active learning and professional growth by bringing together the Flipped Classroom method with video content on teaching and learning as well as workplace learning opportunities in a pedagogy course. The professional learning of prospective teachers is framed according to the components of the Pedagogical Content Knowledge (Park & Olive, 2008; Shulman, 1986). Implications for future trends in teacher education are provided.

Linear Algebra and the Dirac Notation

2006 ◽  
Author(s):  
Phillip Kaye ◽  
Raymond Laflamme ◽  
Michele Mosca
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Linear Algebra ◽  
Hilbert Spaces ◽  
Vector Spaces ◽  
Complex Vector ◽  
Dual Vector ◽  
Finite Dimensional ◽  
Basic Facts

We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum mechanics, remind the reader of some basic facts about complex vector spaces, and introduce some notions that might not have been covered in an elementary linear algebra course. The linear algebra notation used in quantum computing will likely be familiar to the student of physics, but may be alien to a student of mathematics or computer science. It is the Dirac notation, which was invented by Paul Dirac and which is used often in quantum mechanics. In mathematics and physics textbooks, vectors are often distinguished from scalars by writing an arrow over the identifying symbol: e.g a⃗. Sometimes boldface is used for this purpose: e.g. a. In the Dirac notation, the symbol identifying a vector is written inside a ‘ket’, and looks like |a⟩. We denote the dual vector for a (defined later) with a ‘bra’, written as ⟨a|. Then inner products will be written as ‘bra-kets’ (e.g. ⟨a|b⟩). We now carefully review the definitions of the main algebraic objects of interest, using the Dirac notation. The vector spaces we consider will be over the complex numbers, and are finite-dimensional, which significantly simplifies the mathematics we need. Such vector spaces are members of a class of vector spaces called Hilbert spaces. Nothing substantial is gained at this point by defining rigorously what a Hilbert space is, but virtually all the quantum computing literature refers to a finite-dimensional complex vector space by the name ‘Hilbert space’, and so we will follow this convention. We will use H to denote such a space. Since H is finite-dimensional, we can choose a basis and alternatively represent vectors (kets) in this basis as finite column vectors, and represent operators with finite matrices. As you see in Section 3, the Hilbert spaces of interest for quantum computing will typically have dimension 2n, for some positive integer n. This is because, as with classical information, we will construct larger state spaces by concatenating a string of smaller systems, usually of size two.

The Reorganization Report of 1923

1951 ◽  
Vol 44 (2) ◽  
pp. 90-96
Author(s):  
Charles H. Butler
Keyword(s):  
United States ◽  
Secondary Education ◽  
Mathematics Teacher ◽  
Secondary Mathematics ◽  
The United States ◽  
National Committee ◽  
Late Professor ◽  
The Past ◽  
Educational Philosophies

An appreciative understanding of the position and the program of mathematics in the modern American scheme of secondary education can best be had by viewing it against the backdrop of history. Its evolution from the stereotyped arithmetic of colonial days to the comprehensive and varied offering of today represents a continuing effort to make mathematics contribute all it could toward the achievement of the broad aims of prevailing educational philosophies, and many influences have been operative in shaping its course. The story of the evolving program of secondary mathematics has been fully and well recounted in numerous books and articles. It is not the purpose of this paper to tell the whole story again, but merely to indicate something of the contribution of one important committee, and especially of one of its members, to the development of the program in mathematics in the United States in the past quarter of a century. This committee was the National Committee on Mathematical Requirements, and the member of it to whom reference was made was the late Professor Raleigh Schorling, to whose memory this issue of The Mathematics Teacher is dedicated.

An attempt to reduce learning difficulties in Linear Algebra courses

2016 ◽  
Vol 8 (2) ◽  
pp. 156
Author(s):  
Marta Graciela Caligaris ◽  
María Elena Schivo ◽  
María Rosa Romiti
Keyword(s):  
Linear Algebra ◽  
Linear Equations ◽  
Learning Difficulties ◽  
Vector Spaces ◽  
Analytic Geometry ◽  
Teaching Activities ◽  
Interactive Tools ◽  
Systems Of Linear Equations

In engineering careers, the study of Linear Algebra begins in the first course. Some topics included in this subject are systems of linear equations and vector spaces. Linear Algebra is very useful but can be very abstract for teaching and learning.In an attempt to reduce learning difficulties, different approaches of teaching activities supported by interactive tools were analyzed. This paper presents these tools, designed with GeoGebra for the Algebra and Analytic Geometry course at the Facultad Regional San Nicolás (FRSN), Universidad Tecnológica Nacional (UTN), Argentina.

Use of Video Analysis to Support Prospective K-8 Teachers' Noticing of Equitable Practices

2014 ◽  
Vol 2 (2) ◽  
pp. 108-140 ◽  
Author(s):  
Amy Roth McDuffie ◽  
Mary Q. Foote ◽  
Corey Drake ◽  
Erin Turner ◽  
Julia Aguirre ◽  
...  
Keyword(s):  
Instructional Practices ◽  
Video Analysis ◽  
Prospective Teachers ◽  
Mathematics Teacher ◽  
Teaching And Learning ◽  
Teacher Educators ◽  
Mathematics Teacher Educators

Mathematics teacher educators (MTEs) designed and studied a video analysis activity intended to support prospective teachers (PSTs) in learning to notice equitable instructional practices. PSTs from 4 sites (N = 73) engaged in the activity 4 to 5 times during the semester, using a set of 4 “lenses” to analyze teaching and learning as shown in videos. In an earlier analysis of this activity, we found that PSTs increased their depth and expanded their foci in noticing equitable instructional practices (Roth McDuf_ e et al., 2013). In this analysis, we shift the focus to our work as MTEs: We examine our decisions and moves in facilitating the video analysis activity with a focus on equity, and we discuss implications for other MTEs.

Sign in / Sign up

Export Citation Format

Share Document