Computer Algebra Systems and Dynamic Geometry for Mathematical Thinking

2021 ◽  
pp. 1-27
Author(s):  
Jhony Alexander Villa-Ochoa ◽  
Liliana Suárez-Téllez
Keyword(s):  
Computer Algebra ◽  
Mathematical Thinking ◽  
Dynamic Geometry ◽  
Computer Algebra Systems

WAYS OF USE OF COMPUTER ALGEBRA SYSTEMS IN THE TEACHING OF ADVANCED SECTIONS OF MATHEMATICS

2019 ◽  
pp. 50-55
Author(s):  
I. S. Safuanov ◽  
V. A. Chugunov
Keyword(s):  
Number Theory ◽  
Computer Algebra ◽  
Dynamic Geometry ◽  
Abstract Algebra ◽  
Computer Algebra Systems ◽  
Advanced Mathematics ◽  
Genetic Method ◽  
Computer Technologies ◽  
Modes Of Representation ◽  
Derivatives Of

In this article, possible ways of use of computers for the teaching of advanced sections of mathematics that traditionally belong to undergraduate curricula, namely elements of calculus, number theory and abstract algebra are considered. Use of computer technologies can help also to implement such approaches as genetic method and the use of various modes of representation in education. According to cultural-historical theory of L. S. Vygotsky, computer technologies can be considered as the tool for the construction of concepts in the process of learning. The most appropriate for teaching advanced mathematics are such computer algebra systems as Maple, Mathematica, and various systems of dynamic geometry. We will consider the possibilities of Geogebra for the work with functions at the initial stages of undergraduate calculus courses, namely for the work with concepts of limits and derivatives of functions.

scholarly journals New ideas for handling of loop and angular integrals in D-dimensions in QCD

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Valery E. Lyubovitskij ◽  
Fabian Wunder ◽  
Alexey S. Zhevlakov
Keyword(s):  
Computer Algebra ◽  
Cross Sections ◽  
Orthogonal Basis ◽  
Computer Algebra Systems ◽  
Covariant Formalism ◽  
Linear Combinations ◽  
Recursion Relations ◽  
New Ideas ◽  
Rotational Invariant ◽  
Geometric Picture

Abstract We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

scholarly journals The Interpretative Flexibility, Instrumental Evolution, and Institutional Adoption of Mathematical Software in Educational Practice: The Examples of Computer Algebra and Dynamic Geometry

2008 ◽  
Vol 39 (4) ◽  
pp. 379-394 ◽  
Author(s):  
Kenneth Ruthven
Keyword(s):  
Computer Algebra ◽  
Mathematical Knowledge ◽  
New Technologies ◽  
Early Stage ◽  
Dynamic Geometry ◽  
Educational Practice ◽  
Explicit Recognition ◽  
Mathematical Techniques ◽  
Institutional Adoption ◽  
Interpretative Flexibility

This article examines three important facets of the incorporation of new technologies into educational practice, focusing on emergent usages of the mathematical tools of computer algebra and dynamic geometry. First, it illustrates the interpretative flexibility of these tools, highlighting important differences in ways of conceptualizing and employing them that reflect their appropriation to contrasting practices of mathematics teaching. Second, it examines the cultural process of instrumental evolution in which mathematical frameworks and teaching practices are adapted in response to new possibilities created by these tools, showing that such evolution remains at a relatively early stage. Third, it points to crucial prerequisites, at both classroom and systemic levels, for effective institutional adoption of such tools: explicit recognition of the interplay between the development of instrumental and mathematical knowledge, including the establishment of a recognized repertoire of tool-mediated mathematical techniques supported by appropriate discourses of explanation and justification.

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori
Keyword(s):  
Automorphism Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Computer Algebra ◽  
Character Table ◽  
Computer Algebra Systems ◽  
Split Extension ◽  
Sporadic Group ◽  
Local Subgroup ◽  
Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

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