156,273 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
Computer algebra based assessment of mathematics online
In this paper, we investigate computer algebra based assessment of mathematics online, with a focus on undergraduate students. Introducing a computer algebra system to assist in marking allows a paradigm shift from teacher-provided answers to student-provided answers. The Computer Algebra Based Learning and Evaluation (CABLE) system is presented as an open source infrastructure for mathematical learning objects. Features of the CABLE system, including the modular design, database structure, learning object specification and learning object contextualisation are described and areas for future work are identified
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
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
Toward an Algebraic Theory of Systems
We propose the concept of a system algebra with a parallel composition
operation and an interface connection operation, and formalize
composition-order invariance, which postulates that the order of composing and
connecting systems is irrelevant, a generalized form of associativity.
Composition-order invariance explicitly captures a common property that is
implicit in any context where one can draw a figure (hiding the drawing order)
of several connected systems, which appears in many scientific contexts. This
abstract algebra captures settings where one is interested in the behavior of a
composed system in an environment and wants to abstract away anything internal
not relevant for the behavior. This may include physical systems, electronic
circuits, or interacting distributed systems.
One specific such setting, of special interest in computer science, are
functional system algebras, which capture, in the most general sense, any type
of system that takes inputs and produces outputs depending on the inputs, and
where the output of a system can be the input to another system. The behavior
of such a system is uniquely determined by the function mapping inputs to
outputs. We consider several instantiations of this very general concept. In
particular, we show that Kahn networks form a functional system algebra and
prove their composition-order invariance.
Moreover, we define a functional system algebra of causal systems,
characterized by the property that inputs can only influence future outputs,
where an abstract partial order relation captures the notion of "later". This
system algebra is also shown to be composition-order invariant and appropriate
instantiations thereof allow to model and analyze systems that depend on time
The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads
Lawvere theories and monads have been the two main category theoretic formulations of universal algebra, Lawvere theories arising in 1963 and the connection with monads being established a few years later. Monads, although mathematically the less direct and less malleable formulation, rapidly gained precedence. A generation later, the definition of monad began to appear extensively in theoretical computer science in order to model computational effects, without reference to universal algebra. But since then, the relevance of universal algebra to computational effects has been recognised, leading to renewed prominence of the notion of Lawvere theory, now in a computational setting. This development has formed a major part of Gordon Plotkin’s mature work, and we study its history here, in particular asking why Lawvere theories were eclipsed by monads in the 1960’s, and how the renewed interest in them in a computer science setting might develop in future
Формування предметних компетентностей майбутніх учителів інформатики на практичних заняттях з лінійної алгебри
Armash T. S. Formation of subject specific competences of future teachers of computer science in practical classes on linear algebra.
The tasks of different levels are considered: basic, high-level and creative for the subject of «Linear Algebra», which contribute to the formation and development of subject specific competences of future teachers of computer science on a practical training of linear algebra. Examples are given on specific topics. The content of the practical training on linear algebra for future teachers of computer science.Армаш Т. С. Формування предметних компетентностей майбутніх учителів інформатики на практичних заняттях з лінійної алгебри.
Розглянуто різнорівневі задачі базового, підвищеного та творчого рівня з дисципліни «Лінійна алгебра», які сприяють формуванню та розвитку предметних компетентностей майбутніх учителів інформатики на практичних заняттях з лінійної алгебри. Наведено приклади з окремих тем. Розкрито зміст тем практичних занять з лінійної алгебри для майбутніх учителів інформатики
Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach
OpenDreamKit --- "Open Digital Research Environment Toolkit for the
Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project
that aims at supporting, over the period 2015--2019, the ecosystem of
open-source mathematical software systems. From that, OpenDreamKit will deliver
a flexible toolkit enabling research groups to set up Virtual Research
Environments, customised to meet the varied needs of research projects in pure
mathematics and applications.
An important step in the OpenDreamKit endeavor is to foster the
interoperability between a variety of systems, ranging from computer algebra
systems over mathematical databases to front-ends. This is the mission of the
integration work package (WP6). We report on experiments and future plans with
the \emph{Math-in-the-Middle} approach. This information architecture consists
in a central mathematical ontology that documents the domain and fixes a joint
vocabulary, combined with specifications of the functionalities of the various
systems. Interaction between systems can then be enriched by pivoting off this
information architecture.Comment: 15 pages, 7 figure
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