64,763 research outputs found
A double-edged sword: Use of computer algebra systems in first-year Engineering Mathematics and Mechanics courses
Many secondary-level mathematics students have experience with graphical calculators from high school. For the purposes of this paper we define graphical calculators as those able to perform rudimentary symbolic manipulation and solve complicated equations requiring very modest user knowledge. The use of more advanced computer algebra systems e.g. Maple, Mathematica, Mathcad, Matlab/MuPad is becoming more prevalent in tertiary-level courses.
This paper explores our students’ experience using one such system (MuPad) in first-year tertiary Engineering Mathematics and Mechanics courses.
The effectiveness of graphical calculators and computer algebra systems in mathematical pedagogy has been investigated by a multitude of educational researchers (e.g. Ravaglia et al. 1998). Most of these studies found very small or no correlation between student use of
graphical calculators or exposure to computer algebra systems with future achievement in mathematics courses (Buteau et al. 2010).
In this paper we focus instead on students’ attitude towards a more advanced standalone computer algebra system (MuPad), and whether students’ inclination to use the system is indicative of their mathematical understanding.
Paper describing some preliminary research into use of computer algebra systems for teaching engineering mathematics
Feynman-diagram evaluation in the electroweak theory with computer algebra
The evaluation of quantum corrections in the theory of the electroweak and
strong interactions via higher-order Feynman diagrams requires complicated and
laborious calculations, which however can be structured in a strictly
algorithmic way. These calculations are ideally suited for the application of
computer algebra systems, and computer algebra has proven to be a very valuable
tool in this field already over several decades. It is sketched how computer
algebra is presently applied in evaluating the predictions of the electroweak
theory with high precision, and some recent results obtained in this way are
summarized.Comment: 7 pages, updated version of proceedings contribution to ACAT 2000,
Fermilab, October 200
Gravity, torsion, Dirac field and computer algebra using MAPLE and REDUCE
The article presents computer algebra procedures and routines applied to the
study of the Dirac field on curved spacetimes. The main part of the procedures
is devoted to the construction of Pauli and Dirac matrices algebra on an
anholonomic orthonormal reference frame. Then these procedures are used to
compute the Dirac equation on curved spacetimes in a sequence of special
dedicated routines. A comparative review of such procedures obtained for two
computer algebra platforms (REDUCE + EXCALC and MAPLE + GRTensorII) is carried
out. Applications for the calculus of Dirac equation on specific examples of
spacetimes with or without torsion are pointed out.Comment: 20 pages, Late
Towards topological quantum computer
One of the principal obstacles on the way to quantum computers is the lack of
distinguished basis in the space of unitary evolutions and thus the lack of the
commonly accepted set of basic operations (universal gates). A natural choice,
however, is at hand: it is provided by the quantum R-matrices, the entangling
deformations of non-entangling (classical) permutations, distinguished from the
points of view of group theory, integrable systems and modern theory of
non-perturbative calculations in quantum field and string theory. Observables
in this case are (square modules of) the knot polynomials, and their pronounced
integrality properties could provide a key to error correction. We suggest to
use R-matrices acting in the space of irreducible representations, which are
unitary for the real-valued couplings in Chern-Simons theory, to build a
topological version of quantum computing.Comment: 14 page
Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems
Digital mathematical libraries assemble the knowledge of years of
mathematical research. Numerous disciplines (e.g., physics, engineering, pure
and applied mathematics) rely heavily on compendia gathered findings. Likewise,
modern research applications rely more and more on computational solutions,
which are often calculated and verified by computer algebra systems. Hence, the
correctness, accuracy, and reliability of both digital mathematical libraries
and computer algebra systems is a crucial attribute for modern research.
In this paper, we present a novel approach to verify a digital mathematical
library and two computer algebra systems with one another by converting
mathematical expressions from one system to the other. We use our previously
eveloped conversion tool (referred to as LaCASt) to translate formulae from the
NIST Digital Library of Mathematical Functions to the computer algebra systems
Maple and Mathematica. The contributions of our presented work are as follows:
(1) we present the most comprehensive verification of computer algebra systems
and digital mathematical libraries with one another; (2) we significantly
enhance the performance of the underlying translator in terms of coverage and
accuracy; and (3) we provide open access to translations for Maple and
Mathematica of the formulae in the NIST Digital Library of Mathematical
Functions
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