CREACOMP e-Schulung von Kreativität und Problemlösungskompetenz [CreaComp]
Project Lead
Project Duration
01/04/2004 - 31/12/2006Publications
2008
[Windsteiger]
Stimulating Students' Creativity Through Computer-Supported Experiments and Automated Theorem Proving
W. Windsteiger
In: Promoting Creativity for all Students in Mathematics Education, Emiliya Velikova, Agnis Andzans (ed.), pp. 351-357. 2008. 8 Studentska Str., 7017 Rousse, Bulgaria, University of Rousse, Bulgaria, ISBN 978-954-712-420-2. Proceedings of Discussion Group 9, the 11th International Congress on Mathematical Education (ICME 11). [pdf]@inproceedings{RISC3467,
author = {W. Windsteiger},
title = {{Stimulating Students' Creativity Through Computer-Supported Experiments and Automated Theorem Proving}},
booktitle = {{Promoting Creativity for all Students in Mathematics Education}},
language = {english},
pages = {351--357},
address = {8 Studentska Str., 7017 Rousse, Bulgaria},
isbn_issn = {ISBN 978-954-712-420-2},
year = {2008},
note = {Proceedings of Discussion Group 9, the 11th International Congress on Mathematical Education (ICME 11)},
editor = {Emiliya Velikova and Agnis Andzans},
refereed = {yes},
institution = {University of Rousse, Bulgaria},
length = {7}
}
author = {W. Windsteiger},
title = {{Stimulating Students' Creativity Through Computer-Supported Experiments and Automated Theorem Proving}},
booktitle = {{Promoting Creativity for all Students in Mathematics Education}},
language = {english},
pages = {351--357},
address = {8 Studentska Str., 7017 Rousse, Bulgaria},
isbn_issn = {ISBN 978-954-712-420-2},
year = {2008},
note = {Proceedings of Discussion Group 9, the 11th International Congress on Mathematical Education (ICME 11)},
editor = {Emiliya Velikova and Agnis Andzans},
refereed = {yes},
institution = {University of Rousse, Bulgaria},
length = {7}
}
2007
[Mayrhofer]
CreaComp: Computer-Supported Experiments and Automated Proving in Learning and Teaching Mathematics
G. Mayrhofer, S. Saminger, W. Windsteiger
In: Proceedings of ICTMT8, Eva Milkova (ed.), pp. ?-?. 2007. ISBN 978-80-7041-285-5. [pdf]@inproceedings{RISC3066,
author = {G. Mayrhofer and S. Saminger and W. Windsteiger},
title = {{CreaComp: Computer-Supported Experiments and Automated Proving in Learning and Teaching Mathematics}},
booktitle = {{Proceedings of ICTMT8}},
language = {english},
abstract = {We present an environment for learning and teaching mathematics that aims at inspiring the creative potential of students by enabling the learners to perform various kinds of interactive experiments during their learning process. Computer interactions are both of visual and purely formal mathematical nature, where the computer-algebra system Mathematica powers the visualization of mathematical concepts and the tools provided by the theorem proving system Theorema are used for the formal counterparts.},
pages = {?--?},
isbn_issn = {ISBN 978-80-7041-285-5},
year = {2007},
editor = {Eva Milkova},
refereed = {yes},
length = {5}
}
author = {G. Mayrhofer and S. Saminger and W. Windsteiger},
title = {{CreaComp: Computer-Supported Experiments and Automated Proving in Learning and Teaching Mathematics}},
booktitle = {{Proceedings of ICTMT8}},
language = {english},
abstract = {We present an environment for learning and teaching mathematics that aims at inspiring the creative potential of students by enabling the learners to perform various kinds of interactive experiments during their learning process. Computer interactions are both of visual and purely formal mathematical nature, where the computer-algebra system Mathematica powers the visualization of mathematical concepts and the tools provided by the theorem proving system Theorema are used for the formal counterparts.},
pages = {?--?},
isbn_issn = {ISBN 978-80-7041-285-5},
year = {2007},
editor = {Eva Milkova},
refereed = {yes},
length = {5}
}
[Mayrhofer]
CreaComp: Experimental Formal Mathematics for the Classroom
G. Mayrhofer, S. Saminger, W. Windsteiger
In: Symbolic Computation and Education, Shangzhi Li, Dongming Wang, and Jing-Zhong Zhang (ed.), pp. 94-114. 2007. World Scientific Publishing Co., Singapore, New Jersey, ISBN 978-981-277-599-3. [url] [pdf]@inproceedings{RISC3067,
author = {G. Mayrhofer and S. Saminger and W. Windsteiger},
title = {{CreaComp: Experimental Formal Mathematics for the Classroom}},
booktitle = {{Symbolic Computation and Education}},
language = {english},
abstract = {CreaComp provides an electronic environment for learning and teaching mathematics that aims at inspiring the creative potential of students. During their learning process, students are encouraged to engage themselves in various kinds of interactive experiments, both of visual and purely formal mathematical nature. The computer-algebra system Mathematica powers the visualization of mathematical concepts and the tools provided by the theorem proving system Theorema are used for the formal counterparts. We present a case study on the concept of equivalence relations and set partitions, in which we demonstrate the entire bandwidth of computer-support that we envision for modern learning environments for mathematics.},
pages = {94--114},
publisher = {World Scientific Publishing Co.},
address = {Singapore, New Jersey},
isbn_issn = {ISBN 978-981-277-599-3},
year = {2007},
editor = {Shangzhi Li and Dongming Wang and and Jing-Zhong Zhang},
refereed = {yes},
length = {20},
url = {http://www.worldscibooks.com/socialsci/6642.html}
}
author = {G. Mayrhofer and S. Saminger and W. Windsteiger},
title = {{CreaComp: Experimental Formal Mathematics for the Classroom}},
booktitle = {{Symbolic Computation and Education}},
language = {english},
abstract = {CreaComp provides an electronic environment for learning and teaching mathematics that aims at inspiring the creative potential of students. During their learning process, students are encouraged to engage themselves in various kinds of interactive experiments, both of visual and purely formal mathematical nature. The computer-algebra system Mathematica powers the visualization of mathematical concepts and the tools provided by the theorem proving system Theorema are used for the formal counterparts. We present a case study on the concept of equivalence relations and set partitions, in which we demonstrate the entire bandwidth of computer-support that we envision for modern learning environments for mathematics.},
pages = {94--114},
publisher = {World Scientific Publishing Co.},
address = {Singapore, New Jersey},
isbn_issn = {ISBN 978-981-277-599-3},
year = {2007},
editor = {Shangzhi Li and Dongming Wang and and Jing-Zhong Zhang},
refereed = {yes},
length = {20},
url = {http://www.worldscibooks.com/socialsci/6642.html}
}
2006
[Buchberger]
Theorema
W. Windsteiger, B. Buchberger, M. Rosenkranz
In: The Seventeen Provers of the World, Freek Wiedijk (ed.), Lecture Notes in Artificial Intelligence (LNAI) 3600, pp. 96-107. 2006. Springer Berlin Heidelberg New York, ISBN 3-540-30704-4. [url] [pdf]@incollection{RISC2737,
author = {W. Windsteiger and B. Buchberger and M. Rosenkranz},
title = {{Theorema}},
booktitle = {{The Seventeen Provers of the World}},
language = {english},
series = {Lecture Notes in Artificial Intelligence (LNAI)},
volume = {3600},
pages = {96--107},
publisher = {Springer Berlin Heidelberg New York},
isbn_issn = {ISBN 3-540-30704-4},
year = {2006},
annote = {2006-03-16-A},
editor = {Freek Wiedijk},
refereed = {yes},
length = {12},
url = {http://link.springer.com/book/10.1007/11542384}
}
author = {W. Windsteiger and B. Buchberger and M. Rosenkranz},
title = {{Theorema}},
booktitle = {{The Seventeen Provers of the World}},
language = {english},
series = {Lecture Notes in Artificial Intelligence (LNAI)},
volume = {3600},
pages = {96--107},
publisher = {Springer Berlin Heidelberg New York},
isbn_issn = {ISBN 3-540-30704-4},
year = {2006},
annote = {2006-03-16-A},
editor = {Freek Wiedijk},
refereed = {yes},
length = {12},
url = {http://link.springer.com/book/10.1007/11542384}
}
[Buchberger]
CreaComp: e-Schulung von Kreativität und Problemlösekompetenz
B. Buchberger, E.P. Klement, G. Pilz, S. Saminger, W. Windsteiger
Technical report no. 06-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). 2006. [pdf]@techreport{RISC4961,
author = {B. Buchberger and E.P. Klement and G. Pilz and S. Saminger and W. Windsteiger},
title = {{CreaComp: e-Schulung von Kreativität und Problemlösekompetenz}},
language = {english},
number = {06-09},
year = {2006},
length = {154},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
author = {B. Buchberger and E.P. Klement and G. Pilz and S. Saminger and W. Windsteiger},
title = {{CreaComp: e-Schulung von Kreativität und Problemlösekompetenz}},
language = {english},
number = {06-09},
year = {2006},
length = {154},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Craciun]
Theorema: Towards Computer-Aided Mathematical Theory Exploration
B. Buchberger, A. Craciun, T. Jebelean, L. Kovacs, T. Kutsia, K. Nakagawa, F. Piroi, N. Popov, J. Robu, M. Rosenkranz, W. Windsteiger
Journal of Applied Logic 4(4), pp. 470-504. 2006. ISSN 1570-8683. [doi] [pdf]@article{RISC2487,
author = {B. Buchberger and A. Craciun and T. Jebelean and L. Kovacs and T. Kutsia and K. Nakagawa and F. Piroi and N. Popov and J. Robu and M. Rosenkranz and W. Windsteiger},
title = {{Theorema: Towards Computer-Aided Mathematical Theory Exploration}},
language = {english},
journal = {Journal of Applied Logic},
volume = {4},
number = {4},
pages = { 470--504},
isbn_issn = {ISSN 1570-8683},
year = {2006},
annote = {2005-09-09-A},
refereed = {yes},
length = {35},
url = {http://dx.doi.org/10.1016/j.jal.2005.10.006}
}
author = {B. Buchberger and A. Craciun and T. Jebelean and L. Kovacs and T. Kutsia and K. Nakagawa and F. Piroi and N. Popov and J. Robu and M. Rosenkranz and W. Windsteiger},
title = {{Theorema: Towards Computer-Aided Mathematical Theory Exploration}},
language = {english},
journal = {Journal of Applied Logic},
volume = {4},
number = {4},
pages = { 470--504},
isbn_issn = {ISSN 1570-8683},
year = {2006},
annote = {2005-09-09-A},
refereed = {yes},
length = {35},
url = {http://dx.doi.org/10.1016/j.jal.2005.10.006}
}
[Windsteiger]
An Automated Prover for Zermelo-Fraenkel Set Theory in Theorema
W. Windsteiger
JSC 41(3-4), pp. 435-470. 2006. Elsevier, ISSN 0747-7171. [url] [pdf]@article{RISC2788,
author = {W. Windsteiger},
title = {{An Automated Prover for Zermelo-Fraenkel Set Theory in Theorema}},
language = {english},
abstract = {This paper presents some fundamental aspects of the design and theimplementation of an automated prover for Zermelo-Fraenkel set theory withinthe Theorema system. The method applies the``Prove-Compute-Solve''-paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.},
journal = {JSC},
volume = {41},
number = {3-4},
pages = {435--470},
publisher = {Elsevier},
isbn_issn = {ISSN 0747-7171},
year = {2006},
refereed = {yes},
keywords = {Automated theorem proving, Set theory, Theorema},
length = {36},
url = {http://authors.elsevier.com/sd/article/S0747717105001495}
}
author = {W. Windsteiger},
title = {{An Automated Prover for Zermelo-Fraenkel Set Theory in Theorema}},
language = {english},
abstract = {This paper presents some fundamental aspects of the design and theimplementation of an automated prover for Zermelo-Fraenkel set theory withinthe Theorema system. The method applies the``Prove-Compute-Solve''-paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.},
journal = {JSC},
volume = {41},
number = {3-4},
pages = {435--470},
publisher = {Elsevier},
isbn_issn = {ISSN 0747-7171},
year = {2006},
refereed = {yes},
keywords = {Automated theorem proving, Set theory, Theorema},
length = {36},
url = {http://authors.elsevier.com/sd/article/S0747717105001495}
}
[Windsteiger]
Analytica V: Towards the Mordell-Weil Theorem
E. M. Clarke, A. S. Gavlovski, K. Sutner, W. Windsteiger
In: Proceedings of Calculemus'06, A. Bigatti, S. Ranise (ed.), Proceedings of Calculemus'06, pp. ?-?. 2006. [pdf]@inproceedings{RISC2912,
author = {E. M. Clarke and A. S. Gavlovski and K. Sutner and W. Windsteiger},
title = {{Analytica V: Towards the Mordell-Weil Theorem}},
booktitle = {{Proceedings of Calculemus'06}},
language = {english},
abstract = {Analytica V is a theorem proving system that is built on top of the symbolic computation system Mathematica. It was originally designed by E. Clarke and X. Zhao in the early 1990's. We describe here a redesign of the system that extends its abilities to reasoning about some aspects of number theory.},
pages = {?--?},
isbn_issn = {?},
year = {2006},
editor = {A. Bigatti and S. Ranise},
refereed = {yes},
length = {16},
conferencename = {Calculemus'06}
}
author = {E. M. Clarke and A. S. Gavlovski and K. Sutner and W. Windsteiger},
title = {{Analytica V: Towards the Mordell-Weil Theorem}},
booktitle = {{Proceedings of Calculemus'06}},
language = {english},
abstract = {Analytica V is a theorem proving system that is built on top of the symbolic computation system Mathematica. It was originally designed by E. Clarke and X. Zhao in the early 1990's. We describe here a redesign of the system that extends its abilities to reasoning about some aspects of number theory.},
pages = {?--?},
isbn_issn = {?},
year = {2006},
editor = {A. Bigatti and S. Ranise},
refereed = {yes},
length = {16},
conferencename = {Calculemus'06}
}
2005
[Windsteiger]
Wie erfinde ich mathematische Algorithmen? Wie beweise ich mathematische Algorithmen?
W. Windsteiger
Technical report no. 05-18 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). December 2005. Presentation slides for a presentation given at Schwerpunktfach Mathematik, Europagymnasium Auhof, December 15, 2005. [nb] [pdf]@techreport{RISC2789,
author = {W. Windsteiger},
title = {{Wie erfinde ich mathematische Algorithmen? Wie beweise ich mathematische Algorithmen?}},
language = {deutsch},
abstract = {In dieser Präsentation werden interessierten Schülern Methoden nähergebracht, wie mathematische Algorithmen erfunden werden können. Es wird gezeigt, wie mit Hilfe von Algorithmen-Schemata Algorithmen gefunden bzw. die Korrektheit von Algorithmen bewiesen werden kann. Als Beispiele werden der Horner-Algorithmus zum Evaluieren von Polynomen bzw. der Neville-Algorithmus zur Polynom-Interpolation herangezogen.},
number = {05-18},
year = {2005},
month = {December},
note = {Presentation slides for a presentation given at Schwerpunktfach Mathematik, Europagymnasium Auhof, December 15, 2005},
length = {15},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
author = {W. Windsteiger},
title = {{Wie erfinde ich mathematische Algorithmen? Wie beweise ich mathematische Algorithmen?}},
language = {deutsch},
abstract = {In dieser Präsentation werden interessierten Schülern Methoden nähergebracht, wie mathematische Algorithmen erfunden werden können. Es wird gezeigt, wie mit Hilfe von Algorithmen-Schemata Algorithmen gefunden bzw. die Korrektheit von Algorithmen bewiesen werden kann. Als Beispiele werden der Horner-Algorithmus zum Evaluieren von Polynomen bzw. der Neville-Algorithmus zur Polynom-Interpolation herangezogen.},
number = {05-18},
year = {2005},
month = {December},
note = {Presentation slides for a presentation given at Schwerpunktfach Mathematik, Europagymnasium Auhof, December 15, 2005},
length = {15},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
