Session Overview
Session
Curriculum: Curriculum (general topic)
Time:
Monday, 29/Sep/2014:
11:00am - 1:00pm

Session Chair: Csaba Sárvári
Location: VSP 1.03
Von-Seckendorff-Platz 1 Room 1.03

Presentations

Teaching numerical methods using CAS

Ildikó Perjési-Hámori

University of Pécs, Hungary

University of Pécs launched Information Technology (IT) engineer MSc program in 2013. The curriculum involves Numerical Methods as a facultative subject. In my lecture our experience during the teaching of this subject is summarized.

The focus of the subject was solving model problems using Maple, a Computer Algebra System (CAS), sometimes substitute the exact mathematical proofing. During the solutions we have tried to take advantage of opportunities offered by the used Maple computer algebra system. While composing the topics of the course, the rapid development of computer algebra systems was taken into consideration (eg. different methods of solutions of linear equation systems). On the other hand, this way students with limited mathematical skill are also able to understand more complex tasks, such as solution of multivariate interpolations and regressions, or that of partial differential equations. In our lecture we present some real-life examples from the course material.

Perjési-Hámori-CADGME2014-154_b.zip

Extremal Polynomials with Computer Algebra: An Elementary Approach

Robert Vajda

University of Szeged, Hungary

Most math students are familiar with classic Chebyshev polynomials T_n. They are usually introduced as a class of orthogonal polynomials wrt a certain weight function on a closed bounded interval [a,b]. However, it turns out that they can be also introduced as a class of extremal polynomials: namely, the nth (scaled) Chebyshev polynomial is the polynomial which deviates least from the zero constant polynomial on an interval among the monic polynomials with degree at most n. In this talk we investigate the explicit characterization of the generalized Chebyshev polynomials of low degree on some particular subsets of the complex plane: To give the coefficients, roots and norms of these polynomials can be computationally difficult. We consider some approaches to attack the problem by computer algebra and we sketch a pool of possible student projects that can be built around this topic.

The illustrative computational and graphical tools are developed in Mathematica by the author.
Vajda-CADGME2014-137_a.pdf
Vajda-CADGME2014-137_b.zip

Software Support of Functional Line in Precalculus Studies

Vladimir Nodelman

Holon Institute of Technology, Israel

The functional line penetrates and closely interlaces with all areas of mathematics at different levels of studies, often determining their content and methods. Precalculus plays a special role in formation of the corresponding conceptual vocabulary. It is here that students become familiar with different properties, types and operations on functions, master the skills of "reading" graphs of functions, learn to recognize and take advantage of the functional dependencies "hidden" in a problem.

An adequate software, which concentrates students' attention not only and not so much on the demonstration of examples of the concepts being studied, as activates independent creative activity in detection and use of the corresponding properties of the studied material and the connections between them can significantly increase the strength and depth of understanding of the studied matter.

This report presents an approach to development and use of such software and its implementation in the author’s non-profit program VisuMatica. Various examples illustrate the technique of dynamic creation and evolutionary development of generalized models as result of live collaborative analysis of the needs and characteristics of the studied material, and proper activities of the students.