What Is Or What Might Be the Benefit of Using Computer Algebra Systems in the Learning and Teaching of Calculus?

2017 ◽  
pp. 161-193 ◽  
Author(s):  
Hans-Georg Weigand
Keyword(s):  
Computer Algebra ◽  
Computer Algebra Systems ◽  
Learning And Teaching

Mathematics in Virtual Knowledge Spaces

2008 ◽  
pp. 1582-1604
Author(s):  
Sabina Jeschke ◽  
Thomas Richter
Keyword(s):  
Computer Algebra ◽  
Rapid Growth ◽  
Traditional Learning ◽  
Computer Algebra Systems ◽  
Learning And Teaching ◽  
Knowledge Spaces ◽  
New Concepts ◽  
Numerical Software ◽  
Growth Of Knowledge ◽  
Scientists And Engineers

The workplace of scientists and engineers is about to change: even though numerical software and computer algebra systems remove the burden of routine calculation, it becomes more important than ever to get familiar with new concepts and methods quickly. Given the rapid growth of knowledge in today’s sciences, traditional “learning on supply” (i.e., defining the learning goal as the accumulation of knowledge) is no longer applicable; instead, adequate learning and teaching methods have to be established to guide learners towards efficient self-controlled learning.

Mathematics in Virtual Knowledge Spaces

2007 ◽  
pp. 232-263 ◽  
Author(s):  
Sabina Jeschke ◽  
Thomas Richter
Keyword(s):  
Computer Algebra ◽  
Rapid Growth ◽  
Traditional Learning ◽  
Computer Algebra Systems ◽  
Learning And Teaching ◽  
Knowledge Spaces ◽  
New Concepts ◽  
Numerical Software ◽  
Growth Of Knowledge ◽  
Scientists And Engineers

The workplace of scientists and engineers is about to change: even though numerical software and computer algebra systems remove the burden of routine calculation, it becomes more important than ever to get familiar with new concepts and methods quickly. Given the rapid growth of knowledge in today’s sciences, traditional “learning on supply” (i.e., defining the learning goal as the accumulation of knowledge) is no longer applicable; instead, adequate learning and teaching methods have to be established to guide learners towards efficient self-controlled learning.

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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