[{"extern":"1","publication":"The Journal of Chemical Physics","citation":{"chicago":"Nüske, Feliks, Lorenzo Boninsegna, and Cecilia Clementi. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 2019. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>.","short":"F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).","ieee":"F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems by spectral matching,” <i>The Journal of Chemical Physics</i>, 2019.","apa":"Nüske, F., Boninsegna, L., &#38; Clementi, C. (2019). Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>","bibtex":"@article{Nüske_Boninsegna_Clementi_2019, title={Coarse-graining molecular systems by spectral matching}, DOI={<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>}, number={044116}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2019} }","ama":"Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. 2019. doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>","mla":"Nüske, Feliks, et al. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 044116, 2019, doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>."},"type":"journal_article","department":[{"_id":"101"}],"date_created":"2021-04-30T17:01:13Z","date_updated":"2022-01-06T06:55:20Z","publication_status":"published","title":"Coarse-graining molecular systems by spectral matching","year":"2019","status":"public","author":[{"id":"81513","last_name":"Nüske","first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks"},{"full_name":"Boninsegna, Lorenzo","first_name":"Lorenzo","last_name":"Boninsegna"},{"full_name":"Clementi, Cecilia","last_name":"Clementi","first_name":"Cecilia"}],"publication_identifier":{"issn":["0021-9606","1089-7690"]},"doi":"10.1063/1.5100131","user_id":"81513","article_number":"044116","_id":"21944","language":[{"iso":"eng"}]},{"date_updated":"2022-01-06T07:03:57Z","author":[{"full_name":"Kuklinski, Christiane","first_name":"Christiane","last_name":"Kuklinski"},{"full_name":"Leis, Elena","first_name":"Elena","last_name":"Leis"},{"full_name":"Liebendörfer, Michael","first_name":"Michael","last_name":"Liebendörfer"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"}],"title":"Erklärung von Mathematikleistung im Ingenieursstudium","status":"public","year":"2019","user_id":"30933","_id":"8577","language":[{"iso":"eng"}],"citation":{"bibtex":"@inbook{Kuklinski_Leis_Liebendörfer_Hochmuth_2019, title={Erklärung von Mathematikleistung im Ingenieursstudium}, booktitle={Beiträge zum Mathematikunterricht 2019}, author={Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard}, year={2019} }","ama":"Kuklinski C, Leis E, Liebendörfer M, Hochmuth R. Erklärung von Mathematikleistung im Ingenieursstudium. In: <i>Beiträge Zum Mathematikunterricht 2019</i>. ; 2019.","mla":"Kuklinski, Christiane, et al. “Erklärung von Mathematikleistung Im Ingenieursstudium.” <i>Beiträge Zum Mathematikunterricht 2019</i>, 2019.","short":"C. Kuklinski, E. Leis, M. Liebendörfer, R. Hochmuth, in: Beiträge Zum Mathematikunterricht 2019, 2019.","chicago":"Kuklinski, Christiane, Elena Leis, Michael Liebendörfer, and Reinhard Hochmuth. “Erklärung von Mathematikleistung Im Ingenieursstudium.” In <i>Beiträge Zum Mathematikunterricht 2019</i>, 2019.","ieee":"C. Kuklinski, E. Leis, M. Liebendörfer, and R. Hochmuth, “Erklärung von Mathematikleistung im Ingenieursstudium,” in <i>Beiträge zum Mathematikunterricht 2019</i>, 2019.","apa":"Kuklinski, C., Leis, E., Liebendörfer, M., &#38; Hochmuth, R. (2019). Erklärung von Mathematikleistung im Ingenieursstudium. In <i>Beiträge zum Mathematikunterricht 2019</i>."},"publication":"Beiträge zum Mathematikunterricht 2019","department":[{"_id":"10"}],"type":"book_chapter","date_created":"2019-03-25T15:35:44Z"},{"citation":{"short":"T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).","chicago":"Sahai, Tuhin, Adrian Ziessler, Stefan Klus, and Michael Dellnitz. “Continuous Relaxations for the Traveling Salesman Problem.” <i>Nonlinear Dynamics</i>, 2019. <a href=\"https://doi.org/10.1007/s11071-019-05092-5\">https://doi.org/10.1007/s11071-019-05092-5</a>.","ieee":"T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for the traveling salesman problem,” <i>Nonlinear Dynamics</i>, 2019.","apa":"Sahai, T., Ziessler, A., Klus, S., &#38; Dellnitz, M. (2019). Continuous relaxations for the traveling salesman problem. <i>Nonlinear Dynamics</i>. <a href=\"https://doi.org/10.1007/s11071-019-05092-5\">https://doi.org/10.1007/s11071-019-05092-5</a>","bibtex":"@article{Sahai_Ziessler_Klus_Dellnitz_2019, title={Continuous relaxations for the traveling salesman problem}, DOI={<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>}, journal={Nonlinear Dynamics}, author={Sahai, Tuhin and Ziessler, Adrian and Klus, Stefan and Dellnitz, Michael}, year={2019} }","ama":"Sahai T, Ziessler A, Klus S, Dellnitz M. Continuous relaxations for the traveling salesman problem. <i>Nonlinear Dynamics</i>. 2019. doi:<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>","mla":"Sahai, Tuhin, et al. “Continuous Relaxations for the Traveling Salesman Problem.” <i>Nonlinear Dynamics</i>, 2019, doi:<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>."},"publication":"Nonlinear Dynamics","department":[{"_id":"101"}],"type":"journal_article","date_created":"2020-04-16T14:05:04Z","publication_status":"published","date_updated":"2022-01-06T06:52:55Z","author":[{"full_name":"Sahai, Tuhin","first_name":"Tuhin","last_name":"Sahai"},{"full_name":"Ziessler, Adrian","first_name":"Adrian","last_name":"Ziessler"},{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"publication_identifier":{"issn":["0924-090X","1573-269X"]},"status":"public","title":"Continuous relaxations for the traveling salesman problem","year":"2019","user_id":"47427","doi":"10.1007/s11071-019-05092-5","_id":"16709","language":[{"iso":"eng"}]},{"publication":"Automatica","abstract":[{"text":"We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. Using a recent convergence result for the numerical approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the value of the K-ROM based objective function converges in measure to the value of the full objective function. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier–Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy.","lang":"eng"}],"date_created":"2019-07-10T08:08:16Z","type":"journal_article","department":[{"_id":"101"}],"title":"Koopman operator-based model reduction for switched-system control of PDEs","year":"2019","author":[{"id":"47427","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian"},{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"}],"publication_identifier":{"issn":["0005-1098"]},"publication_status":"published","date_updated":"2022-01-06T06:50:46Z","article_type":"original","intvolume":"       106","language":[{"iso":"eng"}],"doi":"10.1016/j.automatica.2019.05.016","citation":{"bibtex":"@article{Peitz_Klus_2019, title={Koopman operator-based model reduction for switched-system control of PDEs}, volume={106}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>}, journal={Automatica}, author={Peitz, Sebastian and Klus, Stefan}, year={2019}, pages={184–191} }","chicago":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” <i>Automatica</i> 106 (2019): 184–91. <a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">https://doi.org/10.1016/j.automatica.2019.05.016</a>.","short":"S. Peitz, S. Klus, Automatica 106 (2019) 184–191.","ama":"Peitz S, Klus S. Koopman operator-based model reduction for switched-system control of PDEs. <i>Automatica</i>. 2019;106:184-191. doi:<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>","ieee":"S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system control of PDEs,” <i>Automatica</i>, vol. 106, pp. 184–191, 2019.","mla":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” <i>Automatica</i>, vol. 106, 2019, pp. 184–91, doi:<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>.","apa":"Peitz, S., &#38; Klus, S. (2019). Koopman operator-based model reduction for switched-system control of PDEs. <i>Automatica</i>, <i>106</i>, 184–191. <a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">https://doi.org/10.1016/j.automatica.2019.05.016</a>"},"status":"public","page":"184-191","_id":"10593","user_id":"47427","volume":106},{"language":[{"iso":"eng"}],"doi":"10.1007/s10898-019-00737-6","publication_identifier":{"issn":["0925-5001","1573-2916"]},"author":[{"full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet","id":"32643"},{"full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian","id":"47427"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"year":"2019","title":"On the hierarchical structure of Pareto critical sets","intvolume":"        73","article_type":"original","date_updated":"2022-01-06T06:50:46Z","publication_status":"published","date_created":"2019-07-10T08:13:31Z","department":[{"_id":"101"}],"type":"journal_article","publication":"Journal of Global Optimization","issue":"4","abstract":[{"lang":"eng","text":"In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set."}],"_id":"10595","page":"891-913","volume":73,"user_id":"47427","status":"public","citation":{"mla":"Gebken, Bennet, et al. “On the Hierarchical Structure of Pareto Critical Sets.” <i>Journal of Global Optimization</i>, vol. 73, no. 4, 2019, pp. 891–913, doi:<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>.","ama":"Gebken B, Peitz S, Dellnitz M. On the hierarchical structure of Pareto critical sets. <i>Journal of Global Optimization</i>. 2019;73(4):891-913. doi:<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>","bibtex":"@article{Gebken_Peitz_Dellnitz_2019, title={On the hierarchical structure of Pareto critical sets}, volume={73}, DOI={<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>}, number={4}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2019}, pages={891–913} }","apa":"Gebken, B., Peitz, S., &#38; Dellnitz, M. (2019). On the hierarchical structure of Pareto critical sets. <i>Journal of Global Optimization</i>, <i>73</i>(4), 891–913. <a href=\"https://doi.org/10.1007/s10898-019-00737-6\">https://doi.org/10.1007/s10898-019-00737-6</a>","ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “On the hierarchical structure of Pareto critical sets,” <i>Journal of Global Optimization</i>, vol. 73, no. 4, pp. 891–913, 2019.","short":"B. Gebken, S. Peitz, M. Dellnitz, Journal of Global Optimization 73 (2019) 891–913.","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “On the Hierarchical Structure of Pareto Critical Sets.” <i>Journal of Global Optimization</i> 73, no. 4 (2019): 891–913. <a href=\"https://doi.org/10.1007/s10898-019-00737-6\">https://doi.org/10.1007/s10898-019-00737-6</a>."}},{"abstract":[{"lang":"eng","text":"In comparison to classical control approaches in the field of electrical drives like the field-oriented control (FOC), model predictive control (MPC) approaches are able to provide a higher control performance. This refers to shorter settling times, lower overshoots, and a better decoupling of control variables in case of multi-variable controls. However, this can only be achieved if the used prediction model covers the actual behavior of the plant sufficiently well. In case of model deviations, the performance utilizing MPC remains below its potential. This results in effects like increased current ripple or steady state setpoint deviations. In order to achieve a high control performance, it is therefore necessary to adapt the model to the real plant behavior. When using an online system identification, a less accurate model is sufficient for commissioning of the drive system. In this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system identification is proposed. The method does not require high-frequency signal injection, but uses the measured values already required for the FCS-MPC. An evaluation of the least squares-based identification on a laboratory test bench showed that the model accuracy and thus the control performance could be improved by an online update of the prediction models."}],"citation":{"ama":"Hanke S, Peitz S, Wallscheid O, Böcker J, Dellnitz M. Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In: <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>. ; 2019. doi:<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>","bibtex":"@inproceedings{Hanke_Peitz_Wallscheid_Böcker_Dellnitz_2019, title={Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification}, DOI={<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>}, booktitle={2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)}, author={Hanke, Soren and Peitz, Sebastian and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}, year={2019} }","mla":"Hanke, Soren, et al. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019, doi:<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>.","chicago":"Hanke, Soren, Sebastian Peitz, Oliver Wallscheid, Joachim Böcker, and Michael Dellnitz. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” In <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019. <a href=\"https://doi.org/10.1109/precede.2019.8753313\">https://doi.org/10.1109/precede.2019.8753313</a>.","short":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, M. Dellnitz, in: 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019.","apa":"Hanke, S., Peitz, S., Wallscheid, O., Böcker, J., &#38; Dellnitz, M. (2019). Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>. <a href=\"https://doi.org/10.1109/precede.2019.8753313\">https://doi.org/10.1109/precede.2019.8753313</a>","ieee":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, and M. Dellnitz, “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification,” in <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019."},"publication":"2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)","department":[{"_id":"101"}],"type":"conference","date_created":"2019-07-10T08:15:23Z","date_updated":"2022-01-06T06:50:46Z","publication_status":"published","publication_identifier":{"isbn":["9781538694145"]},"author":[{"full_name":"Hanke, Soren","last_name":"Hanke","first_name":"Soren"},{"id":"47427","last_name":"Peitz","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"full_name":"Wallscheid, Oliver","first_name":"Oliver","last_name":"Wallscheid"},{"last_name":"Böcker","first_name":"Joachim","full_name":"Böcker, Joachim"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"status":"public","title":"Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification","year":"2019","doi":"10.1109/precede.2019.8753313","user_id":"47427","_id":"10597","language":[{"iso":"eng"}]},{"date_updated":"2022-01-06T06:51:28Z","publication_status":"inpress","conference":{"location":"Regensburg","name":"53. Jahrestagung der Gesellschaft für Didaktik der Mathematik"},"author":[{"full_name":"Schumacher, Jan","first_name":"Jan","orcid":"0000-0002-6676-9774","last_name":"Schumacher","id":"26809"}],"status":"public","title":"Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen","year":"2019","user_id":"26809","language":[{"iso":"ger"}],"_id":"13106","citation":{"mla":"Schumacher, Jan. “Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen.” <i>Beiträge zum Mathematikunterricht 2019</i>.","bibtex":"@inproceedings{Schumacher, title={Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen}, booktitle={Beiträge zum Mathematikunterricht 2019}, author={Schumacher, Jan} }","ama":"Schumacher J. Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen. In: <i>Beiträge zum Mathematikunterricht 2019</i>.","ieee":"J. Schumacher, “Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen,” in <i>Beiträge zum Mathematikunterricht 2019</i>, Regensburg.","apa":"Schumacher, J. (n.d.). Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen. In <i>Beiträge zum Mathematikunterricht 2019</i>. Regensburg.","short":"J. Schumacher, in: Beiträge zum Mathematikunterricht 2019, n.d.","chicago":"Schumacher, Jan. “Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen.” In <i>Beiträge zum Mathematikunterricht 2019</i>, n.d."},"publication":"Beiträge zum Mathematikunterricht 2019","department":[{"_id":"360"},{"_id":"98"}],"type":"conference","date_created":"2019-08-30T11:58:37Z"},{"language":[{"iso":"eng"}],"publication_status":"accepted","date_updated":"2022-01-06T06:51:28Z","author":[{"id":"26809","orcid":"0000-0002-6676-9774","first_name":"Jan","last_name":"Schumacher","full_name":"Schumacher, Jan"},{"first_name":"Sebastian","last_name":"Rezat","full_name":"Rezat, Sebastian"}],"title":"A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers","year":"2019","department":[{"_id":"360"},{"_id":"98"}],"type":"conference","keyword":["diagrammatic reasoning","hypothetical learning trajectory","induction extrapolatory method","integers","negative numbers","permanence principle","semiotics"],"date_created":"2019-08-30T12:00:50Z","abstract":[{"lang":"eng","text":"In this paper, we first outline a Hypothetical Learning Trajectory (HLT), which aims at a formal understanding of the rules for manipulating integers. The HLT is based on task formats, which promote algebraic thinking in terms of generalizing rules from the analysis of patterns and should be familiar to students from their mathematics education experiences in elementary school. Second, we analyze two students' actual learning process based on Peircean semiotics. The analysis shows that the actual learning process diverges from the hypothesized learning process in that the students do not relate the different levels of the diagrams in a way that allows them to extrapolate the rule for the subtraction of negative numbers. Based on this finding, we point out consequences for the design of the tasks."}],"publication":"Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)","editor":[{"last_name":"Jankvist","first_name":"Uffe Thomas","full_name":"Jankvist, Uffe Thomas"},{"full_name":"Van den Heuvel-Panhuizen, Marja","last_name":"Van den Heuvel-Panhuizen","first_name":"Marja"},{"full_name":"Veldhuis, Michiel","first_name":"Michiel","last_name":"Veldhuis"}],"user_id":"26809","_id":"13107","publisher":"Freudenthal Group & Freudenthal Institute, Utrecht University and ERME","conference":{"end_date":"2019-02-10","start_date":"2019-02-06","name":"CERME 11","location":"Utrecht"},"status":"public","place":"Utrecht, the Netherlands","quality_controlled":"1","citation":{"chicago":"Schumacher, Jan, and Sebastian Rezat. “A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers.” In <i>Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)</i>, edited by Uffe Thomas Jankvist, Marja Van den Heuvel-Panhuizen, and Michiel Veldhuis. Utrecht, the Netherlands: Freudenthal Group &#38; Freudenthal Institute, Utrecht University and ERME, n.d.","short":"J. Schumacher, S. Rezat, in: U.T. Jankvist, M. Van den Heuvel-Panhuizen, M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019), Freudenthal Group &#38; Freudenthal Institute, Utrecht University and ERME, Utrecht, the Netherlands, n.d.","ieee":"J. Schumacher and S. Rezat, “A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers,” in <i>Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)</i>, Utrecht.","apa":"Schumacher, J., &#38; Rezat, S. (n.d.). A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, &#38; M. Veldhuis (Eds.), <i>Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)</i>. Utrecht, the Netherlands: Freudenthal Group &#38; Freudenthal Institute, Utrecht University and ERME.","bibtex":"@inproceedings{Schumacher_Rezat, place={Utrecht, the Netherlands}, title={A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers}, booktitle={Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)}, publisher={Freudenthal Group &#38; Freudenthal Institute, Utrecht University and ERME}, author={Schumacher, Jan and Rezat, Sebastian}, editor={Jankvist, Uffe Thomas and Van den Heuvel-Panhuizen, Marja and Veldhuis, MichielEditors} }","ama":"Schumacher J, Rezat S. A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers. In: Jankvist UT, Van den Heuvel-Panhuizen M, Veldhuis M, eds. <i>Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)</i>. 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