Practice with Computer Algebra Systems in Mathematics Education and Teacher Training Courses

2014 ◽  
pp. 594-600
Author(s):  
Hideyo Makishita
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Computer Algebra ◽  
Computer Algebra Systems ◽  
Training Courses

Wherefore “plug-and-chug”?: computer algebra versus A-level mathematics

1991 ◽  
Vol 75 (471) ◽  
pp. 40-48
Author(s):  
Neil Bibby
Keyword(s):  
Mathematics Education ◽  
Computer Algebra ◽  
Current Practice ◽  
Software Systems ◽  
Computer Algebra Systems ◽  
Assessment Tasks ◽  
Algebra Versus ◽  
Huge Challenge

The development in recent years of software systems (“computer algebra” systems, or “symbolic manipulators”) which, in effect, automate large areas of mathematics presents an immediate and huge challenge to mathematics education, especially at A-level. For many students current practice in A-level mathematics seems largely to consist of the assimilation, rehearsal and implementation in stereotyped contexts of a more-or-less well-defined set of standard algorithms in short, “plug-and-chug” mathematics, as Philip Davis has described it. With the aid of computer algebra systems demonstrations of “A-level papers in ten minutes” have recently been possible, and this clearly illustrates the essentially “plug-and-chug” nature of the assessment tasks.

Soundoff: A Case against Computer Symbolic Manipulation in School Mathematics Today

1992 ◽  
Vol 85 (3) ◽  
pp. 180-183
Author(s):  
Bert K. Waits ◽  
Franklin Demana
Keyword(s):  
Mathematics Education ◽  
Computer Algebra ◽  
Graphing Calculators ◽  
School Mathematics ◽  
Computer Algebra Systems ◽  
National Council ◽  
Symbolic Manipulation ◽  
Symbol Manipulation ◽  
Evaluation Standards ◽  
Exploration Tool

The National Council of Teachers of Mathematics and leaders in mathematics education must move vigorously to build a consensus for acceptance of the Curriculum and Evaluation Standards (NCTM 1989). One important assumption of the Curriculum and Evaluation Standards is that all students should use computers and graphing calculators on a regular basis in school mathematics. The symbol-manipulating ability of such computer algebra systems (CAS) as the IBM Math Exploration Tool Kit, Mathematics™, and Derive™ can be used today in school mathematics to do algebra. However, we take exception to the use of computer symbol manipulation in school mathematics today for two important reasons.

Speed and Data Structures in Computer Algebra Systems

1987 ◽  
Author(s):  
Richard J. Fateman ◽  
Carl G. Ponder
Keyword(s):  
Data Structures ◽  
Computer Algebra ◽  
Computer Algebra Systems

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.

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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