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Full-Text Articles in Algebra
Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg
Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg
George K. Thiruvathukal
This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics.
Randomized Detection Of Extraneous Factors, Manfred Minimair
Randomized Detection Of Extraneous Factors, Manfred Minimair
Manfred Minimair
A projection operator of a system of parametric polynomials is a polynomial in the coefficients of the system that vanishes if the system has a common root. The projection operator is a multiple of the resultant of the system, and the factors of the projection operator that are not contained in the resultant are called extraneous factors. The main contribution of this work is to provide a randomized algorithm to check whether a factor is extraneous, which is an important task in applications. A lower bound for the success probability is determined which can be set arbitrarily close to one. …