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The cybernetic revolution that occured on the eve of twenty-one century effected our life in all demeanors.
The collection, organization, transformation, and interpretation of information are the cornerstones of
science, inductry, business, and goverment. Each of these aspects of information management uses
mathematics as a tool.
Linear algebra is employed in most of computational physics and information technologies. The two main problems that linear algebra studies can be trivially stated as follows:
Solve a linear system of m equations with n unknowns that can be written in concise vector form A x = b.
Determine a spectral decomposition of a matrix A that leads to the matrix eigenvalue problem A x = λx.
Although solutions to these two problems are well-known, entire monographs have been dedicated to their efficient solutions and numerical implementations.
There are many computing resources available that will aid in your exploration and understanding of differential equations. The main software packages that we recommend are
All these packages have the syntax commands closely related to traditional pen-and-paper mathematical language.
According to the National Council of Teachers
of Mathematics, the goal of teaching mathematics is to help all students develop mathematical concepts including the
abilities of students in converting symbolic information into graphical and technology. This can be achieved and constructed using programming that is useful at any stage of mathematical thinking
especially in conjecturing.
In our days, computational thinking should be considered a fundamental
analytic skill in education, along with reading, writing, and arithmetic.
This is a vision for the twenty-first century supported by both, the National
Research Council of the Academy of Science and the National Council of Teachers
The author feels deeply that computing should be an integral part of any
linear algebra course. The graphics capabilities alone warrant its use. Of course. technology is not a substitute for actual
knowledge of material. Technology is a tool to gain insights into complex
problems and it can be a valuable tool to better understand difficult concepts
and learn the scientific methods of inquiry. The author believes that
computing brings additional insight and helps to develop curiosity that theory
alone cannot achieve. As a result, the qualitative aspects of linear algebra could be explored in greater depth.