Robert Vajda, PhD

Position: assistant professor
Phone (office): +36 62 544647
Phone (home): +36 62 493964
Fax: +36 62 544548

Research Interests:

Symbolic Computation, Real Quantifier Elimination, Polynomial Optimization, Mathematics Education

List of Publications:

[1] R. Vajda and Z. Kovács: Interactive Web Portals in Mathematics. In: Teaching Mathematics and Computer Science 1(2), pp. 347-361, 2003. Debrecen, Hungary

[2] M. K. Németh and R. Vajda: Computer-Assisted Assessment of Mathematical Knowledge. In: Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching. Proceedings of the Sprout-Selecting Conference, 2004, pp. 113-127, Pécs, Hungary

[3] B. Moore and R. Vajda: Some Experiments Using Quantifier Elimination to Prove the Non-existence of Dynamically Balanced Spherical Linkages. Bericht-Nr. SFB-Report No. 2008-10, pp. 1-8.

[4] R. Vajda, T. Jebelean and B. Buchberger: Combining Logical and Algebraic Techniques for Natural Style Proving in Elementary Analysis. Mathematics and Computers in Simulation 79(8), pp. 2310-2316. April 2009. Elsevier, Special Issue on Nonstandard Applications of Computer Algebra.

[5] R. Vajda: An e-Learning Environment for Elementary Analysis: Combining Computer Algebra, Graphics and Automated Reasoning. Teaching Mathematics and Computer Science 7(1), pp. 13-34. 2009. Debrecen, Hungary

[6] A. Máder, R. Vajda: Elementary Approaches to the Teaching of the Combinatorial Problem of Rectangular Islands, International Journal of Computers for Mathematical Learning, Vol. 15(3), pp. 267-281, 2010, Springer.

[7] R. Vajda: Effective Real Quantifier Elimination, In: J. Karsai, R. Vajda (eds.), Interesting Mathematical Problems in Sciences and Everyday Life - 2011, University of Szeged, ISBN:978-963-306-109-1, pp. 1-18.

[8] L.L. Stachó, R. Vajda: Hermite Interpolation Sequences over Fields, Linear Algebra and its Applications, Vol. 439(1), 2013, pp. 66-77, Elsevier.

[9] H.-J. Rack, R. Vajda: On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation, Serdica Journal of Computing, Vol. 8(1), 2014, pp. 71-96.

[10] H.-J. Rack, R. Vajda: Optimal Cubic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant, Stud. Univ. Babes-Bolyai Math. 60(2015), No. 2, pp. 151-171.

[11] R. Vajda: Chebyshev Polynomials as Extremal Polynomials with Computer Algebra, The Electronic Journal of Mathematics & Technology, 9(3), 2015, pp. 248-258.

[12] M. Dormán, G. Makay, M. Maróti, R. Vajda: Monoidal Intervals on Three- and Four-Element Sets, Acta Sci. Math. (Szeged) 81:3-4(2015), pp. 399-424.

[13] R. Vajda: Exploring Hermite Interpolation Polynomials Using Recursion, Annales Mathematicae et Informaticae, 45(2015), pp. 151-160.

[14] R. Vajda: Maximal Radius for Stability Regions for Explicit Runge Kutta Methods by Real Quantifier Elimination, 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, (SYNASC 2017), pp. 49-54.

[15] H.-J. Rack, R. Vajda: An Explicit Univariate and Radical Parametrization of the Sextic Proper Zolotarev Polynomials in Power Form, Dolomites Research Notes on Approximation Padova University Press, 12(1), pp. 43-50, 2019.

[16] H.-J. Rack, R. Vajda: Explicit Algebraic Solution of Zolotarev's First Problem for Low-degree Polynomials, J. Numer. Anal. Approx. Theory, 48(2), pp. 175-201, 2020.

[17] R. Vajda: Computational Exploration of the Degree Sequence of the Malyshev Polynomials, CEUR Workshop Proceedings Vol. 2650, 11th ICAI Conf., Eger, Hungary, pp. 420-428, 2020.

[18] H.-J. Rack, R. Vajda: Explicit Solution, for n=6, to a Markov-type Extremal Problem Initiated by Schur, Constructive Theory of Functions, pp. 195-219, Prof. M. Drinov Acad. Publ. House, Sofia, 2020.

[19] R. Vajda, Z. Kovács: GeoGebra and the realgeom Reasoning Tool, CEUR Workshop Proceedings Vol. 2752, PAAR+SC-Square 2020 Workshop, Paris, France, pp. 204-219, 2020.


Applying real quantifier elimination (RQE) to solve nonlinear optimization problems

Here are some Mathematica games and demos. File format: Mathematica Notebook Player. This means that you can play them with the freely available Mathematica Player!

Islands Demos
Sorry, this page is still under construction, I'm going to add detailed information about my current activities soon.