scholarly journals SMIS: A Stepwise Multiple Integration Solver Using a CAS

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2866
Author(s):  
José Luis Galán-García ◽  
Pedro Rodríguez-Cielos ◽  
Yolanda Padilla-Domínguez ◽  
María Ángeles Galán-García ◽  
Iván Atencia ◽  
...  
Keyword(s):  
Exact Solution ◽  
Computer Algebra ◽  
Teaching And Learning ◽  
Math Education ◽  
Computer Algebra Systems ◽  
Final Solution ◽  
Algebraic Form ◽  
Multiple Integration ◽  
Numerical Software ◽  
Normal Procedure

Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algebra Systems (CAS) are needed for this last approach. In this paper, we introduce SMIS, a new stepwise solver for multiple integration developed in a CAS. The two main objectives of SMIS are: (1) to increase the capabilities of CAS to help the user to deal with this topic and (2) to be used in Math Education providing an important tool for helping with the teaching and learning process of this topic. SMIS can provide just the final solution or an optional stepwise solution (even including some theoretical comments). The optional stepwise solutions provided by SMIS are of great help for (2). Although SMIS has been developed in the specific CAS Derive, since the code is provided, it can be easily migrated to any CAS which deals with integrals and text management that allow us to display comments for intermediate steps.

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sciences, traditional “learning on supply” (i.e., defining the learning goal as the accumulation of knowledge) is no longer applicable; instead, adequate learning and teaching methods have to be established to guide learners towards efficient self-controlled learning.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.

Taking the Work out of Homework

2011 ◽  
Vol 104 (7) ◽  
pp. 514-519
Author(s):  
Teodora B. Cox ◽  
Stacy L. Singer
Keyword(s):  
Computer Algebra ◽  
Teaching And Learning ◽  
Learning Experiences ◽  
Computer Algebra Systems ◽  
Mathematics Students ◽  
Web Based ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Computer Based

Technology daily impacts students' learning experiences. The increased use of calculators, computer algebra systems, and computer–based and Web–based assessments opens up new opportunities and challenges for teaching and learning mathematics. Students' lives are becoming busier, and they have less time to dedicate to homework outside the classroom. Also, many students admit that they do not enjoy completing homework assignments.

PENERAPAN STRATEGI PEMBELAJARAN INQUIRY DENGAN PENDEKATAN CTL (CONTEXTUAL TEACHING AND LEARNING) UNTUK MENINGKATKAN HASIL BELAJAR MATEMATIKA SISWA KELAS VIII-D SMPN 4 TAMBANG

2018 ◽  
Vol 2 (2) ◽  
pp. 156
Author(s):  
Zulkifli Zulkifli
Keyword(s):  
Learning Outcomes ◽  
Teaching And Learning ◽  
Student Learning Outcomes ◽  
Average Score ◽  
Mathematics Students ◽  
Algebraic Form ◽  
Student Activity ◽  
Average Value ◽  
The Subject ◽  
Improve Student Learning

This research is based on the low learning outcome of mathematics students of grade VIII SMPN 4 Tambang.The purpose of this research is to improve the learning outcomes of mathematics through the application ofinquiry learning with CTL approach. This research was conducted in SMPN 4 Tambang with subject of classVIII-D students with 29 students. This classroom action research was started in early January 2017. Theresearch instrument consists of a teacher and student activity sheet instrument and a test of learning outcomes.Based on the results of research and discussion can be concluded that the strategy of inquiry learning with CTLapproach can improve student learning outcomes of mathematics on the subject matter of algebraic form inclass VIII-D SMPN 4 Tambang. On the basic score the number of students who reached the KKM as many as 14people (48.28%) with an average score of 58.79. In cycle I the number of students who reach the KKM of 19people (65.52%) with an average value of 65.69%. In cycle II the number reaching KKM is 25 people (86.21%).

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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