---
_id: '34670'
author:
- first_name: Tobias
  full_name: Black, Tobias
  id: '23686'
  last_name: Black
  orcid: 0000-0001-9963-0800
citation:
  ama: Black T. Global generalized solutions to a forager–exploiter model with superlinear
    degradation and their eventual regularity properties. <i>Mathematical Models and
    Methods in Applied Sciences</i>. 2020;30(06):1075-1117. doi:<a href="https://doi.org/10.1142/s0218202520400072">10.1142/s0218202520400072</a>
  apa: Black, T. (2020). Global generalized solutions to a forager–exploiter model
    with superlinear degradation and their eventual regularity properties. <i>Mathematical
    Models and Methods in Applied Sciences</i>, <i>30</i>(06), 1075–1117. <a href="https://doi.org/10.1142/s0218202520400072">https://doi.org/10.1142/s0218202520400072</a>
  bibtex: '@article{Black_2020, title={Global generalized solutions to a forager–exploiter
    model with superlinear degradation and their eventual regularity properties},
    volume={30}, DOI={<a href="https://doi.org/10.1142/s0218202520400072">10.1142/s0218202520400072</a>},
    number={06}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
    Scientific Pub Co Pte Lt}, author={Black, Tobias}, year={2020}, pages={1075–1117}
    }'
  chicago: 'Black, Tobias. “Global Generalized Solutions to a Forager–Exploiter Model
    with Superlinear Degradation and Their Eventual Regularity Properties.” <i>Mathematical
    Models and Methods in Applied Sciences</i> 30, no. 06 (2020): 1075–1117. <a href="https://doi.org/10.1142/s0218202520400072">https://doi.org/10.1142/s0218202520400072</a>.'
  ieee: 'T. Black, “Global generalized solutions to a forager–exploiter model with
    superlinear degradation and their eventual regularity properties,” <i>Mathematical
    Models and Methods in Applied Sciences</i>, vol. 30, no. 06, pp. 1075–1117, 2020,
    doi: <a href="https://doi.org/10.1142/s0218202520400072">10.1142/s0218202520400072</a>.'
  mla: Black, Tobias. “Global Generalized Solutions to a Forager–Exploiter Model with
    Superlinear Degradation and Their Eventual Regularity Properties.” <i>Mathematical
    Models and Methods in Applied Sciences</i>, vol. 30, no. 06, World Scientific
    Pub Co Pte Lt, 2020, pp. 1075–117, doi:<a href="https://doi.org/10.1142/s0218202520400072">10.1142/s0218202520400072</a>.
  short: T. Black, Mathematical Models and Methods in Applied Sciences 30 (2020) 1075–1117.
date_created: 2022-12-21T09:48:11Z
date_updated: 2023-07-10T11:39:59Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1142/s0218202520400072
intvolume: '        30'
issue: '06'
keyword:
- Applied Mathematics
- Modeling and Simulation
language:
- iso: eng
page: 1075-1117
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
  issn:
  - 0218-2025
  - 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Lt
status: public
title: Global generalized solutions to a forager–exploiter model with superlinear
  degradation and their eventual regularity properties
type: journal_article
user_id: '23686'
volume: 30
year: '2020'
...
---
_id: '31376'
article_type: original
author:
- first_name: Max
  full_name: Hoffmann, Max
  id: '32202'
  last_name: Hoffmann
  orcid: 0000-0002-6964-7123
citation:
  ama: 'Hoffmann M. Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver Zugang
    zur hyperbolischen Geometrie. <i>Der Mathematikunterricht</i>. 2020;66 (6):36–47.'
  apa: 'Hoffmann, M. (2020). Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver
    Zugang zur hyperbolischen Geometrie. <i>Der Mathematikunterricht</i>, <i>66 (6)</i>,
    36–47.'
  bibtex: '@article{Hoffmann_2020, title={Zirkel und Lineal ohne Parallelenaxiom:
    Ein konstruktiver Zugang zur hyperbolischen Geometrie.}, volume={66 (6)}, journal={Der
    Mathematikunterricht}, author={Hoffmann, Max}, year={2020}, pages={36–47} }'
  chicago: 'Hoffmann, Max. “Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver
    Zugang zur hyperbolischen Geometrie.” <i>Der Mathematikunterricht</i> 66 (6) (2020):
    36–47.'
  ieee: 'M. Hoffmann, “Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver Zugang
    zur hyperbolischen Geometrie.,” <i>Der Mathematikunterricht</i>, vol. 66 (6),
    pp. 36–47, 2020.'
  mla: 'Hoffmann, Max. “Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver
    Zugang zur hyperbolischen Geometrie.” <i>Der Mathematikunterricht</i>, vol. 66
    (6), 2020, pp. 36–47.'
  short: M. Hoffmann, Der Mathematikunterricht 66 (6) (2020) 36–47.
date_created: 2022-05-22T14:56:06Z
date_updated: 2023-07-19T13:59:16Z
department:
- _id: '97'
language:
- iso: ger
page: 36–47
publication: Der Mathematikunterricht
publication_status: published
quality_controlled: '1'
status: public
title: 'Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver Zugang zur hyperbolischen
  Geometrie.'
type: journal_article
user_id: '32202'
volume: 66 (6)
year: '2020'
...
---
_id: '56244'
author:
- first_name: Bärbel
  full_name: Barzel, Bärbel
  last_name: Barzel
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
citation:
  ama: 'Barzel B, Biehler R. Theory-Based Design of Professional Development for Upper
    Secondary Teachers–Focusing on the Content-Specific Use of Digital Tools. In:
    <i>Professional Development and Knowledge of Mathematics Teachers</i>. Routledge;
    2020:163–192.'
  apa: Barzel, B., &#38; Biehler, R. (2020). Theory-Based Design of Professional Development
    for Upper Secondary Teachers–Focusing on the Content-Specific Use of Digital Tools.
    In <i>Professional development and knowledge of mathematics teachers</i> (pp.
    163–192). Routledge.
  bibtex: '@inbook{Barzel_Biehler_2020, title={Theory-Based Design of Professional
    Development for Upper Secondary Teachers–Focusing on the Content-Specific Use
    of Digital Tools}, booktitle={Professional development and knowledge of mathematics
    teachers}, publisher={Routledge}, author={Barzel, Bärbel and Biehler, Rolf}, year={2020},
    pages={163–192} }'
  chicago: Barzel, Bärbel, and Rolf Biehler. “Theory-Based Design of Professional
    Development for Upper Secondary Teachers–Focusing on the Content-Specific Use
    of Digital Tools.” In <i>Professional Development and Knowledge of Mathematics
    Teachers</i>, 163–192. Routledge, 2020.
  ieee: B. Barzel and R. Biehler, “Theory-Based Design of Professional Development
    for Upper Secondary Teachers–Focusing on the Content-Specific Use of Digital Tools,”
    in <i>Professional development and knowledge of mathematics teachers</i>, Routledge,
    2020, pp. 163–192.
  mla: Barzel, Bärbel, and Rolf Biehler. “Theory-Based Design of Professional Development
    for Upper Secondary Teachers–Focusing on the Content-Specific Use of Digital Tools.”
    <i>Professional Development and Knowledge of Mathematics Teachers</i>, Routledge,
    2020, pp. 163–192.
  short: 'B. Barzel, R. Biehler, in: Professional Development and Knowledge of Mathematics
    Teachers, Routledge, 2020, pp. 163–192.'
date_created: 2024-09-25T08:10:17Z
date_updated: 2024-09-25T08:27:23Z
department:
- _id: '363'
language:
- iso: eng
main_file_link:
- url: https://www.taylorfrancis.com/chapters/edit/10.4324/9781003008460-10/theory-based-design-professional-development-upper-secondary-teachers-focusing-content-specific-use-digital-tools-b%C3%A4rbel-barzel-rolf-biehler
page: 163–192
publication: Professional development and knowledge of mathematics teachers
publisher: Routledge
status: public
title: Theory-Based Design of Professional Development for Upper Secondary Teachers–Focusing
  on the Content-Specific Use of Digital Tools
type: book_chapter
user_id: '37888'
year: '2020'
...
---
_id: '16710'
abstract:
- lang: eng
  text: "In this work we present a set-oriented path following method for the computation
    of relative global\r\nattractors of parameter-dependent dynamical systems. We
    start with an initial approximation of the\r\nrelative global attractor for a
    fixed parameter λ0 computed by a set-oriented subdivision method.\r\nBy using
    previously obtained approximations of the parameter-dependent relative global
    attractor\r\nwe can track it with respect to a one-dimensional parameter λ > λ0
    without restarting the whole\r\nsubdivision procedure. We illustrate the feasibility
    of the set-oriented path following method by\r\nexploring the dynamics in low-dimensional
    models for shear flows during the transition to turbulence\r\nand of large-scale
    atmospheric regime changes .\r\n"
author:
- first_name: Raphael
  full_name: Gerlach, Raphael
  id: '32655'
  last_name: Gerlach
- first_name: Adrian
  full_name: Ziessler, Adrian
  last_name: Ziessler
- first_name: Bruno
  full_name: Eckhardt, Bruno
  last_name: Eckhardt
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following
    Method for the Approximation of Parameter Dependent Attractors. <i>SIAM Journal
    on Applied Dynamical Systems</i>. Published online 2020:705-723. doi:<a href="https://doi.org/10.1137/19m1247139">10.1137/19m1247139</a>
  apa: Gerlach, R., Ziessler, A., Eckhardt, B., &#38; Dellnitz, M. (2020). A Set-Oriented
    Path Following Method for the Approximation of Parameter Dependent Attractors.
    <i>SIAM Journal on Applied Dynamical Systems</i>, 705–723. <a href="https://doi.org/10.1137/19m1247139">https://doi.org/10.1137/19m1247139</a>
  bibtex: '@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented
    Path Following Method for the Approximation of Parameter Dependent Attractors},
    DOI={<a href="https://doi.org/10.1137/19m1247139">10.1137/19m1247139</a>}, journal={SIAM
    Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler,
    Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={705–723}
    }'
  chicago: Gerlach, Raphael, Adrian Ziessler, Bruno Eckhardt, and Michael Dellnitz.
    “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent
    Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2020, 705–23. <a
    href="https://doi.org/10.1137/19m1247139">https://doi.org/10.1137/19m1247139</a>.
  ieee: 'R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path
    Following Method for the Approximation of Parameter Dependent Attractors,” <i>SIAM
    Journal on Applied Dynamical Systems</i>, pp. 705–723, 2020, doi: <a href="https://doi.org/10.1137/19m1247139">10.1137/19m1247139</a>.'
  mla: Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation
    of Parameter Dependent Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>,
    2020, pp. 705–23, doi:<a href="https://doi.org/10.1137/19m1247139">10.1137/19m1247139</a>.
  short: R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied
    Dynamical Systems (2020) 705–723.
date_created: 2020-04-16T14:05:41Z
date_updated: 2024-10-01T13:37:43Z
department:
- _id: '101'
doi: 10.1137/19m1247139
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/epdf/10.1137/19M1247139
page: 705-723
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
  issn:
  - 1536-0040
publication_status: published
status: public
title: A Set-Oriented Path Following Method for the Approximation of Parameter Dependent
  Attractors
type: journal_article
user_id: '32655'
year: '2020'
...
---
_id: '35811'
author:
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
- first_name: Viviane
  full_name: Durand-Guerrier, Viviane
  last_name: Durand-Guerrier
citation:
  ama: 'Biehler R, Durand-Guerrier V. University Mathematics Didactic Research on
    Number Theory, Algebra, Discrete Mathematics, Logic. In: Hausberger T, Bosch M,
    Chelloughi F, eds. <i>Proceedings of the Third Conference of the International
    Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September
    2020)</i>. University of Carthage and INDRUM; 2020:283-287.'
  apa: Biehler, R., &#38; Durand-Guerrier, V. (2020). University Mathematics Didactic
    Research on Number Theory, Algebra, Discrete Mathematics, Logic. In T. Hausberger,
    M. Bosch, &#38; F. Chelloughi (Eds.), <i>Proceedings of the Third Conference of
    the International Network for Didactic Research in University Mathematics (INDRUM
    2020, 12-19 September 2020)</i> (pp. 283–287). University of Carthage and INDRUM.
  bibtex: '@inbook{Biehler_Durand-Guerrier_2020, place={Bizerte, Tunisia}, title={University
    Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics,
    Logic}, booktitle={Proceedings of the Third Conference of the International Network
    for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September
    2020)}, publisher={University of Carthage and INDRUM}, author={Biehler, Rolf and
    Durand-Guerrier, Viviane}, editor={Hausberger, T. and Bosch, M. and Chelloughi,
    F.}, year={2020}, pages={283–287} }'
  chicago: 'Biehler, Rolf, and Viviane Durand-Guerrier. “University Mathematics Didactic
    Research on Number Theory, Algebra, Discrete Mathematics, Logic.” In <i>Proceedings
    of the Third Conference of the International Network for Didactic Research in
    University Mathematics (INDRUM 2020, 12-19 September 2020)</i>, edited by T. Hausberger,
    M. Bosch, and F. Chelloughi, 283–87. Bizerte, Tunisia: University of Carthage
    and INDRUM, 2020.'
  ieee: 'R. Biehler and V. Durand-Guerrier, “University Mathematics Didactic Research
    on Number Theory, Algebra, Discrete Mathematics, Logic,” in <i>Proceedings of
    the Third Conference of the International Network for Didactic Research in University
    Mathematics (INDRUM 2020, 12-19 September 2020)</i>, T. Hausberger, M. Bosch,
    and F. Chelloughi, Eds. Bizerte, Tunisia: University of Carthage and INDRUM, 2020,
    pp. 283–287.'
  mla: Biehler, Rolf, and Viviane Durand-Guerrier. “University Mathematics Didactic
    Research on Number Theory, Algebra, Discrete Mathematics, Logic.” <i>Proceedings
    of the Third Conference of the International Network for Didactic Research in
    University Mathematics (INDRUM 2020, 12-19 September 2020)</i>, edited by T. Hausberger
    et al., University of Carthage and INDRUM, 2020, pp. 283–87.
  short: 'R. Biehler, V. Durand-Guerrier, in: T. Hausberger, M. Bosch, F. Chelloughi
    (Eds.), Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020), University
    of Carthage and INDRUM, Bizerte, Tunisia, 2020, pp. 283–287.'
date_created: 2023-01-10T11:14:02Z
date_updated: 2024-11-11T11:59:12Z
ddc:
- '510'
department:
- _id: '363'
editor:
- first_name: T.
  full_name: Hausberger, T.
  last_name: Hausberger
- first_name: M.
  full_name: Bosch, M.
  last_name: Bosch
- first_name: F.
  full_name: Chelloughi, F.
  last_name: Chelloughi
file:
- access_level: closed
  content_type: application/pdf
  creator: krueter
  date_created: 2024-11-11T11:58:37Z
  date_updated: 2024-11-11T11:58:37Z
  file_id: '56978'
  file_name: Biehler_INDRUM2020_283-287.pdf
  file_size: 576039
  relation: main_file
  success: 1
file_date_updated: 2024-11-11T11:58:37Z
has_accepted_license: '1'
keyword:
- Number Theory
- Algebra
- Discrete Mathematics
- Logic
- Research in University Mathematics Edcuation
language:
- iso: eng
main_file_link:
- url: ⟨hal-03114041⟩
page: 283-287
place: Bizerte, Tunisia
publication: Proceedings of the Third Conference of the International Network for
  Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)
publisher: University of Carthage and INDRUM
related_material:
  link:
  - relation: confirmation
    url: https://hal.science/hal-03114041/
status: public
title: University Mathematics Didactic Research on Number Theory, Algebra, Discrete
  Mathematics, Logic
type: book_chapter
user_id: '37888'
year: '2020'
...
---
_id: '35829'
author:
- first_name: Leander
  full_name: Kempen, Leander
  last_name: Kempen
- first_name: Sandra
  full_name: Krämer, Sandra
  last_name: Krämer
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
citation:
  ama: 'Kempen L, Krämer S, Biehler R. Investigating high school graduates’ personal
    meaning of the notion of “mathematical proof.” In: Hausberger T, Bosch M, Chelloughi
    F, eds. <i>Proceedings of the Third Conference of the International Network for
    Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)</i>.
    University of Carthage and INDRUM; 2020:358-367.'
  apa: Kempen, L., Krämer, S., &#38; Biehler, R. (2020). Investigating high school
    graduates’ personal meaning of the notion of “mathematical proof.” In T. Hausberger,
    M. Bosch, &#38; F. Chelloughi (Eds.), <i>Proceedings of the Third Conference of
    the International Network for Didactic Research in University Mathematics (INDRUM
    2020, 12-19 September 2020)</i> (pp. 358–367). University of Carthage and INDRUM.
  bibtex: '@inbook{Kempen_Krämer_Biehler_2020, place={Bizerte, Tunisia}, title={Investigating
    high school graduates’ personal meaning of the notion of “mathematical proof”},
    booktitle={Proceedings of the Third Conference of the International Network for
    Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)},
    publisher={University of Carthage and INDRUM}, author={Kempen, Leander and Krämer,
    Sandra and Biehler, Rolf}, editor={Hausberger, T. and Bosch, M. and Chelloughi,
    F.}, year={2020}, pages={358–367} }'
  chicago: 'Kempen, Leander, Sandra Krämer, and Rolf Biehler. “Investigating High
    School Graduates’ Personal Meaning of the Notion of ‘Mathematical Proof.’” In
    <i>Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020)</i>, edited
    by T. Hausberger, M. Bosch, and F. Chelloughi, 358–67. Bizerte, Tunisia: University
    of Carthage and INDRUM, 2020.'
  ieee: 'L. Kempen, S. Krämer, and R. Biehler, “Investigating high school graduates’
    personal meaning of the notion of ‘mathematical proof,’” in <i>Proceedings of
    the Third Conference of the International Network for Didactic Research in University
    Mathematics (INDRUM 2020, 12-19 September 2020)</i>, T. Hausberger, M. Bosch,
    and F. Chelloughi, Eds. Bizerte, Tunisia: University of Carthage and INDRUM, 2020,
    pp. 358–367.'
  mla: Kempen, Leander, et al. “Investigating High School Graduates’ Personal Meaning
    of the Notion of ‘Mathematical Proof.’” <i>Proceedings of the Third Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2020, 12-19 September 2020)</i>, edited by T. Hausberger et al., University of
    Carthage and INDRUM, 2020, pp. 358–67.
  short: 'L. Kempen, S. Krämer, R. Biehler, in: T. Hausberger, M. Bosch, F. Chelloughi
    (Eds.), Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020), University
    of Carthage and INDRUM, Bizerte, Tunisia, 2020, pp. 358–367.'
date_created: 2023-01-10T11:56:38Z
date_updated: 2024-11-11T12:00:29Z
ddc:
- '510'
department:
- _id: '363'
editor:
- first_name: T.
  full_name: Hausberger, T.
  last_name: Hausberger
- first_name: M.
  full_name: Bosch, M.
  last_name: Bosch
- first_name: F.
  full_name: Chelloughi, F.
  last_name: Chelloughi
file:
- access_level: closed
  content_type: application/pdf
  creator: krueter
  date_created: 2024-11-11T11:59:58Z
  date_updated: 2024-11-11T11:59:58Z
  file_id: '56979'
  file_name: Kempen_INDRUM2020_358-367.pdf
  file_size: 911728
  relation: main_file
  success: 1
file_date_updated: 2024-11-11T11:59:58Z
has_accepted_license: '1'
language:
- iso: eng
page: 358-367
place: Bizerte, Tunisia
publication: Proceedings of the Third Conference of the International Network for
  Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)
publisher: University of Carthage and INDRUM
related_material:
  link:
  - relation: confirmation
    url: https://hal.science/hal-03113983/
status: public
title: Investigating high school graduates’ personal meaning of the notion of “mathematical
  proof”
type: book_chapter
user_id: '37888'
year: '2020'
...
---
_id: '33594'
author:
- first_name: Sebastian
  full_name: Rezat, Sebastian
  id: '31132'
  last_name: Rezat
- first_name: Sara
  full_name: Rezat, Sara
  id: '58338'
  last_name: Rezat
citation:
  ama: Rezat S, Rezat S. Schulbücher. Werkzeuge zum Üben in den Fächern Deutsch und
    Mathematik. <i>Die Grundschulzeitschrift 320</i>. 2020;320:10-13.
  apa: Rezat, S., &#38; Rezat, S. (2020). Schulbücher. Werkzeuge zum Üben in den Fächern
    Deutsch und Mathematik. <i>Die Grundschulzeitschrift 320</i>, <i>320</i>, 10–13.
  bibtex: '@article{Rezat_Rezat_2020, title={Schulbücher. Werkzeuge zum Üben in den
    Fächern Deutsch und Mathematik}, volume={320}, journal={Die Grundschulzeitschrift
    320}, author={Rezat, Sebastian and Rezat, Sara}, year={2020}, pages={10–13} }'
  chicago: 'Rezat, Sebastian, and Sara Rezat. “Schulbücher. Werkzeuge zum Üben in
    den Fächern Deutsch und Mathematik.” <i>Die Grundschulzeitschrift 320</i> 320
    (2020): 10–13.'
  ieee: S. Rezat and S. Rezat, “Schulbücher. Werkzeuge zum Üben in den Fächern Deutsch
    und Mathematik,” <i>Die Grundschulzeitschrift 320</i>, vol. 320, pp. 10–13, 2020.
  mla: Rezat, Sebastian, and Sara Rezat. “Schulbücher. Werkzeuge zum Üben in den Fächern
    Deutsch und Mathematik.” <i>Die Grundschulzeitschrift 320</i>, vol. 320, 2020,
    pp. 10–13.
  short: S. Rezat, S. Rezat, Die Grundschulzeitschrift 320 320 (2020) 10–13.
date_created: 2022-10-09T21:19:45Z
date_updated: 2024-11-11T16:31:11Z
department:
- _id: '463'
- _id: '360'
intvolume: '       320'
language:
- iso: ger
page: 10-13
publication: Die Grundschulzeitschrift 320
status: public
title: Schulbücher. Werkzeuge zum Üben in den Fächern Deutsch und Mathematik
type: journal_article
user_id: '31132'
volume: 320
year: '2020'
...
---
_id: '35821'
author:
- first_name: Lea
  full_name: Budde, Lea
  last_name: Budde
- first_name: Daniel
  full_name: Frischemeier, Daniel
  last_name: Frischemeier
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
- first_name: Franz Yannik
  full_name: Fleischer, Franz Yannik
  id: '42660'
  last_name: Fleischer
  orcid: https://orcid.org/0000-0003-0318-0329
- first_name: Dietrich
  full_name: Gerstenberger, Dietrich
  last_name: Gerstenberger
- first_name: Susanne
  full_name: Podworny, Susanne
  id: '30619'
  last_name: Podworny
  orcid: 0000-0002-6313-5987
- first_name: Carsten
  full_name: Schulte, Carsten
  id: '60311'
  last_name: Schulte
citation:
  ama: 'Budde L, Frischemeier D, Biehler R, et al. Data Science Education in Secondary
    School: How to Develop Statistical Reasoning When Exploring Data Using CODAP.
    In: Arnold P, ed. <i>New Skills in the Changing World of Statistics Education:
    Proceedings of the Roundtable Conference of the International Association for
    Statistical Education (IASE), July 2020</i>. ISI/IASE; 2020.'
  apa: 'Budde, L., Frischemeier, D., Biehler, R., Fleischer, F. Y., Gerstenberger,
    D., Podworny, S., &#38; Schulte, C. (2020). Data Science Education in Secondary
    School: How to Develop Statistical Reasoning When Exploring Data Using CODAP.
    In P. Arnold (Ed.), <i>New Skills in the Changing World of Statistics Education:
    Proceedings of the Roundtable conference of the International Association for
    Statistical Education (IASE), July 2020</i>. ISI/IASE.'
  bibtex: '@inbook{Budde_Frischemeier_Biehler_Fleischer_Gerstenberger_Podworny_Schulte_2020,
    place={Voorborg, The Netherlands}, title={Data Science Education in Secondary
    School: How to Develop Statistical Reasoning When Exploring Data Using CODAP},
    booktitle={New Skills in the Changing World of Statistics Education: Proceedings
    of the Roundtable conference of the International Association for Statistical
    Education (IASE), July 2020}, publisher={ISI/IASE}, author={Budde, Lea and Frischemeier,
    Daniel and Biehler, Rolf and Fleischer, Franz Yannik and Gerstenberger, Dietrich
    and Podworny, Susanne and Schulte, Carsten}, editor={Arnold, P.}, year={2020}
    }'
  chicago: 'Budde, Lea, Daniel Frischemeier, Rolf Biehler, Franz Yannik Fleischer,
    Dietrich Gerstenberger, Susanne Podworny, and Carsten Schulte. “Data Science Education
    in Secondary School: How to Develop Statistical Reasoning When Exploring Data
    Using CODAP.” In <i>New Skills in the Changing World of Statistics Education:
    Proceedings of the Roundtable Conference of the International Association for
    Statistical Education (IASE), July 2020</i>, edited by P. Arnold. Voorborg, The
    Netherlands: ISI/IASE, 2020.'
  ieee: 'L. Budde <i>et al.</i>, “Data Science Education in Secondary School: How
    to Develop Statistical Reasoning When Exploring Data Using CODAP,” in <i>New Skills
    in the Changing World of Statistics Education: Proceedings of the Roundtable conference
    of the International Association for Statistical Education (IASE), July 2020</i>,
    P. Arnold, Ed. Voorborg, The Netherlands: ISI/IASE, 2020.'
  mla: 'Budde, Lea, et al. “Data Science Education in Secondary School: How to Develop
    Statistical Reasoning When Exploring Data Using CODAP.” <i>New Skills in the Changing
    World of Statistics Education: Proceedings of the Roundtable Conference of the
    International Association for Statistical Education (IASE), July 2020</i>, edited
    by P. Arnold, ISI/IASE, 2020.'
  short: 'L. Budde, D. Frischemeier, R. Biehler, F.Y. Fleischer, D. Gerstenberger,
    S. Podworny, C. Schulte, in: P. Arnold (Ed.), New Skills in the Changing World
    of Statistics Education: Proceedings of the Roundtable Conference of the International
    Association for Statistical Education (IASE), July 2020, ISI/IASE, Voorborg, The
    Netherlands, 2020.'
date_created: 2023-01-10T11:41:21Z
date_updated: 2024-11-12T11:03:59Z
ddc:
- '510'
department:
- _id: '363'
- _id: '67'
editor:
- first_name: P.
  full_name: Arnold, P.
  last_name: Arnold
file:
- access_level: closed
  content_type: application/pdf
  creator: krueter
  date_created: 2024-11-12T11:03:44Z
  date_updated: 2024-11-12T11:03:44Z
  file_id: '56999'
  file_name: IASE2020_Roundtable_24_Frischem.pdf
  file_size: 340591
  relation: main_file
  success: 1
file_date_updated: 2024-11-12T11:03:44Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- url: https://fddm.uni-paderborn.de/fileadmin/mathematik/Didaktik_der_Mathematik/BiehlerRolf/Publikationen/IASE2020_Roundtable_24_Frischem.pdf
place: Voorborg, The Netherlands
publication: 'New Skills in the Changing World of Statistics Education: Proceedings
  of the Roundtable conference of the International Association for Statistical Education
  (IASE), July 2020'
publisher: ISI/IASE
status: public
title: 'Data Science Education in Secondary School: How to Develop Statistical Reasoning
  When Exploring Data Using CODAP'
type: book_chapter
user_id: '37888'
year: '2020'
...
---
_id: '35913'
author:
- first_name: Michael
  full_name: Liebendörfer, Michael
  id: '30933'
  last_name: Liebendörfer
  orcid: 0000-0001-9887-2074
- first_name: Robin
  full_name: Göller, Robin
  last_name: Göller
- first_name: Lara
  full_name: Gildehaus, Lara
  last_name: Gildehaus
- first_name: Jörg
  full_name: Kortemeyer, Jörg
  last_name: Kortemeyer
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
- first_name: Reinhard
  full_name: Hochmuth, Reinhard
  last_name: Hochmuth
- first_name: Laura
  full_name: Ostsieker, Laura
  last_name: Ostsieker
- first_name: Jana
  full_name: Rode, Jana
  last_name: Rode
- first_name: Niclas
  full_name: Schaper, Niclas
  last_name: Schaper
citation:
  ama: 'Liebendörfer M, Göller R, Gildehaus L, et al. The role of learning strategies
    for performance in mathematics courses for engineers. In: Hausberger T, Bosch
    M, Chelloughi F, eds. <i>Proceedings of the Third Conference of the International
    Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September
    2020)</i>. University of Carthage and INDRUM; 2020.'
  apa: Liebendörfer, M., Göller, R., Gildehaus, L., Kortemeyer, J., Biehler, R., Hochmuth,
    R., Ostsieker, L., Rode, J., &#38; Schaper, N. (2020). The role of learning strategies
    for performance in mathematics courses for engineers. In T. Hausberger, M. Bosch,
    &#38; F. Chelloughi (Eds.), <i>Proceedings of the Third Conference of the International
    Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September
    2020)</i>. University of Carthage and INDRUM.
  bibtex: '@inbook{Liebendörfer_Göller_Gildehaus_Kortemeyer_Biehler_Hochmuth_Ostsieker_Rode_Schaper_2020,
    place={Bizerte, Tunisia}, title={The role of learning strategies for performance
    in mathematics courses for engineers}, booktitle={Proceedings of the Third Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2020, 12-19 September 2020)}, publisher={University of Carthage and INDRUM}, author={Liebendörfer,
    Michael and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler,
    Rolf and Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas},
    editor={Hausberger, T. and Bosch, M. and Chelloughi, F.}, year={2020} }'
  chicago: 'Liebendörfer, Michael, Robin Göller, Lara Gildehaus, Jörg Kortemeyer,
    Rolf Biehler, Reinhard Hochmuth, Laura Ostsieker, Jana Rode, and Niclas Schaper.
    “The Role of Learning Strategies for Performance in Mathematics Courses for Engineers.”
    In <i>Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020)</i>, edited
    by T. Hausberger, M. Bosch, and F. Chelloughi. Bizerte, Tunisia: University of
    Carthage and INDRUM, 2020.'
  ieee: 'M. Liebendörfer <i>et al.</i>, “The role of learning strategies for performance
    in mathematics courses for engineers,” in <i>Proceedings of the Third Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2020, 12-19 September 2020)</i>, T. Hausberger, M. Bosch, and F. Chelloughi, Eds.
    Bizerte, Tunisia: University of Carthage and INDRUM, 2020.'
  mla: Liebendörfer, Michael, et al. “The Role of Learning Strategies for Performance
    in Mathematics Courses for Engineers.” <i>Proceedings of the Third Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2020, 12-19 September 2020)</i>, edited by T. Hausberger et al., University of
    Carthage and INDRUM, 2020.
  short: 'M. Liebendörfer, R. Göller, L. Gildehaus, J. Kortemeyer, R. Biehler, R.
    Hochmuth, L. Ostsieker, J. Rode, N. Schaper, in: T. Hausberger, M. Bosch, F. Chelloughi
    (Eds.), Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020), University
    of Carthage and INDRUM, Bizerte, Tunisia, 2020.'
date_created: 2023-01-11T07:49:41Z
date_updated: 2024-11-12T11:01:58Z
ddc:
- '510'
department:
- _id: '363'
- _id: '625'
editor:
- first_name: T.
  full_name: Hausberger, T.
  last_name: Hausberger
- first_name: M.
  full_name: Bosch, M.
  last_name: Bosch
- first_name: F.
  full_name: Chelloughi, F.
  last_name: Chelloughi
file:
- access_level: closed
  content_type: application/pdf
  creator: krueter
  date_created: 2024-11-12T11:01:45Z
  date_updated: 2024-11-12T11:01:45Z
  file_id: '56997'
  file_name: Liebendoerfer_INDRUM2020_238-247.pdf
  file_size: 1072799
  relation: main_file
  success: 1
file_date_updated: 2024-11-12T11:01:45Z
has_accepted_license: '1'
language:
- iso: eng
place: Bizerte, Tunisia
publication: Proceedings of the Third Conference of the International Network for
  Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)
publisher: University of Carthage and INDRUM
status: public
title: The role of learning strategies for performance in mathematics courses for
  engineers
type: book_chapter
user_id: '37888'
year: '2020'
...
---
_id: '35912'
author:
- first_name: Elisa
  full_name: Lankeit, Elisa
  last_name: Lankeit
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
citation:
  ama: 'Lankeit E, Biehler R. “I only know the absolute value function”–About students’
    concept images and example spaces concerning continuity and differentiability.
    In: Hausberger T, Bosch M, Chelloughi F, eds. <i>Proceedings of the Third Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2020, 12-19 September 2020)</i>. University of Carthage and INDRUM; 2020.'
  apa: Lankeit, E., &#38; Biehler, R. (2020). “I only know the absolute value function”–About
    students’ concept images and example spaces concerning continuity and differentiability.
    In T. Hausberger, M. Bosch, &#38; F. Chelloughi (Eds.), <i>Proceedings of the
    Third Conference of the International Network for Didactic Research in University
    Mathematics (INDRUM 2020, 12-19 September 2020)</i>. University of Carthage and
    INDRUM.
  bibtex: '@inbook{Lankeit_Biehler_2020, place={Bizerte, Tunisia}, title={“I only
    know the absolute value function”–About students’ concept images and example spaces
    concerning continuity and differentiability}, booktitle={Proceedings of the Third
    Conference of the International Network for Didactic Research in University Mathematics
    (INDRUM 2020, 12-19 September 2020)}, publisher={University of Carthage and INDRUM},
    author={Lankeit, Elisa and Biehler, Rolf}, editor={Hausberger, T. and Bosch, M.
    and Chelloughi, F.}, year={2020} }'
  chicago: 'Lankeit, Elisa, and Rolf Biehler. “‘I Only Know the Absolute Value Function’–About
    Students’ Concept Images and Example Spaces Concerning Continuity and Differentiability.”
    In <i>Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020)</i>, edited
    by T. Hausberger, M. Bosch, and F. Chelloughi. Bizerte, Tunisia: University of
    Carthage and INDRUM, 2020.'
  ieee: 'E. Lankeit and R. Biehler, “‘I only know the absolute value function’–About
    students’ concept images and example spaces concerning continuity and differentiability,”
    in <i>Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020)</i>, T.
    Hausberger, M. Bosch, and F. Chelloughi, Eds. Bizerte, Tunisia: University of
    Carthage and INDRUM, 2020.'
  mla: Lankeit, Elisa, and Rolf Biehler. “‘I Only Know the Absolute Value Function’–About
    Students’ Concept Images and Example Spaces Concerning Continuity and Differentiability.”
    <i>Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020)</i>, edited
    by T. Hausberger et al., University of Carthage and INDRUM, 2020.
  short: 'E. Lankeit, R. Biehler, in: T. Hausberger, M. Bosch, F. Chelloughi (Eds.),
    Proceedings of the Third Conference of the International Network for Didactic
    Research in University Mathematics (INDRUM 2020, 12-19 September 2020), University
    of Carthage and INDRUM, Bizerte, Tunisia, 2020.'
date_created: 2023-01-11T07:46:36Z
date_updated: 2024-11-12T11:02:47Z
ddc:
- '510'
department:
- _id: '363'
editor:
- first_name: T.
  full_name: Hausberger, T.
  last_name: Hausberger
- first_name: M.
  full_name: Bosch, M.
  last_name: Bosch
- first_name: F.
  full_name: Chelloughi, F.
  last_name: Chelloughi
file:
- access_level: closed
  content_type: application/pdf
  creator: krueter
  date_created: 2024-11-12T11:02:33Z
  date_updated: 2024-11-12T11:02:33Z
  file_id: '56998'
  file_name: Lankeit_INDRUM2020_133-142.pdf
  file_size: 1087391
  relation: main_file
  success: 1
file_date_updated: 2024-11-12T11:02:33Z
has_accepted_license: '1'
language:
- iso: eng
place: Bizerte, Tunisia
publication: Proceedings of the Third Conference of the International Network for
  Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)
publisher: University of Carthage and INDRUM
status: public
title: “I only know the absolute value function”–About students’ concept images and
  example spaces concerning continuity and differentiability
type: book_chapter
user_id: '37888'
year: '2020'
...
---
_id: '34841'
abstract:
- lang: eng
  text: "We give an exact formula for the number of G-extensions of local function
    fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application
    we give a lower bound for the corresponding counting problem by discriminant.\r\n"
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Raphael
  full_name: Müller, Raphael
  last_name: Müller
citation:
  ama: Klüners J, Müller R. The conductor density of local function fields with abelian
    Galois group. <i>Journal of Number Theory</i>. 2020;212:311-322. doi:<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>
  apa: Klüners, J., &#38; Müller, R. (2020). The conductor density of local function
    fields with abelian Galois group. <i>Journal of Number Theory</i>, <i>212</i>,
    311–322. <a href="https://doi.org/10.1016/j.jnt.2019.11.007">https://doi.org/10.1016/j.jnt.2019.11.007</a>
  bibtex: '@article{Klüners_Müller_2020, title={The conductor density of local function
    fields with abelian Galois group}, volume={212}, DOI={<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>},
    journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners,
    Jürgen and Müller, Raphael}, year={2020}, pages={311–322} }'
  chicago: 'Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i> 212 (2020):
    311–22. <a href="https://doi.org/10.1016/j.jnt.2019.11.007">https://doi.org/10.1016/j.jnt.2019.11.007</a>.'
  ieee: 'J. Klüners and R. Müller, “The conductor density of local function fields
    with abelian Galois group,” <i>Journal of Number Theory</i>, vol. 212, pp. 311–322,
    2020, doi: <a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>.'
  mla: Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i>, vol. 212,
    Elsevier BV, 2020, pp. 311–22, doi:<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>.
  short: J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322.
date_created: 2022-12-22T10:50:03Z
date_updated: 2025-06-13T08:18:30Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2019.11.007
external_id:
  arxiv:
  - '1904.02573 '
intvolume: '       212'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 311-322
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: The conductor density of local function fields with abelian Galois group
type: journal_article
user_id: '82981'
volume: 212
year: '2020'
...
---
_id: '19945'
abstract:
- lang: eng
  text: Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,
    …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian
    systems on manifolds equipped with Poisson brackets. The Poisson structure is
    connected to conservation properties and other geometric features of solutions
    to the PDE and, therefore, of great interest for numerical integration. For the
    example of Burgers' equations and related PDEs we use Clebsch variables to lift
    the original system to a collective Hamiltonian system on a symplectic manifold
    whose structure is related to the original Lie-Poisson structure. On the collective
    Hamiltonian system a symplectic integrator can be applied. Our numerical examples
    show excellent conservation properties and indicate that the disadvantage of an
    increased phase-space dimension can be outweighed by the advantage of symplectic
    integration.
article_type: original
author:
- first_name: Robert I
  full_name: McLachlan, Robert I
  last_name: McLachlan
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: https://orcid.org/0000-0002-5940-8057
- first_name: Benjamin K
  full_name: Tapley, Benjamin K
  last_name: Tapley
citation:
  ama: McLachlan RI, Offen C, Tapley BK. Symplectic integration of PDEs using Clebsch
    variables. <i>Journal of Computational Dynamics</i>. 2019;6(1):111-130. doi:<a
    href="https://doi.org/10.3934/jcd.2019005">10.3934/jcd.2019005</a>
  apa: McLachlan, R. I., Offen, C., &#38; Tapley, B. K. (2019). Symplectic integration
    of PDEs using Clebsch variables. <i>Journal of Computational Dynamics</i>, <i>6</i>(1),
    111–130. <a href="https://doi.org/10.3934/jcd.2019005">https://doi.org/10.3934/jcd.2019005</a>
  bibtex: '@article{McLachlan_Offen_Tapley_2019, title={Symplectic integration of
    PDEs using Clebsch variables}, volume={6}, DOI={<a href="https://doi.org/10.3934/jcd.2019005">10.3934/jcd.2019005</a>},
    number={1}, journal={Journal of Computational Dynamics}, publisher={American Institute
    of Mathematical Sciences (AIMS)}, author={McLachlan, Robert I and Offen, Christian
    and Tapley, Benjamin K}, year={2019}, pages={111–130} }'
  chicago: 'McLachlan, Robert I, Christian Offen, and Benjamin K Tapley. “Symplectic
    Integration of PDEs Using Clebsch Variables.” <i>Journal of Computational Dynamics</i>
    6, no. 1 (2019): 111–30. <a href="https://doi.org/10.3934/jcd.2019005">https://doi.org/10.3934/jcd.2019005</a>.'
  ieee: R. I. McLachlan, C. Offen, and B. K. Tapley, “Symplectic integration of PDEs
    using Clebsch variables,” <i>Journal of Computational Dynamics</i>, vol. 6, no.
    1, pp. 111–130, 2019.
  mla: McLachlan, Robert I., et al. “Symplectic Integration of PDEs Using Clebsch
    Variables.” <i>Journal of Computational Dynamics</i>, vol. 6, no. 1, American
    Institute of Mathematical Sciences (AIMS), 2019, pp. 111–30, doi:<a href="https://doi.org/10.3934/jcd.2019005">10.3934/jcd.2019005</a>.
  short: R.I. McLachlan, C. Offen, B.K. Tapley, Journal of Computational Dynamics
    6 (2019) 111–130.
date_created: 2020-10-06T16:44:07Z
date_updated: 2022-01-06T06:54:15Z
department:
- _id: '636'
doi: 10.3934/jcd.2019005
extern: '1'
intvolume: '         6'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://www.aimsciences.org/article/doi/10.3934/jcd.2019005
oa: '1'
page: 111-130
publication: Journal of Computational Dynamics
publication_identifier:
  issn:
  - 2158-2505
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Symplectic integration of PDEs using Clebsch variables
type: journal_article
user_id: '85279'
volume: 6
year: '2019'
...
---
_id: '21944'
article_number: '044116'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Lorenzo
  full_name: Boninsegna, Lorenzo
  last_name: Boninsegna
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
citation:
  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>
  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} }'
  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>.
  ieee: F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems
    by spectral matching,” <i>The Journal of Chemical Physics</i>, 2019.
  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>.
  short: F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).
date_created: 2021-04-30T17:01:13Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5100131
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
  issn:
  - 0021-9606
  - 1089-7690
publication_status: published
status: public
title: Coarse-graining molecular systems by spectral matching
type: journal_article
user_id: '81513'
year: '2019'
...
---
_id: '8577'
author:
- first_name: Christiane
  full_name: Kuklinski, Christiane
  last_name: Kuklinski
- first_name: Elena
  full_name: Leis, Elena
  last_name: Leis
- first_name: Michael
  full_name: Liebendörfer, Michael
  last_name: Liebendörfer
- first_name: Reinhard
  full_name: Hochmuth, Reinhard
  last_name: Hochmuth
citation:
  ama: 'Kuklinski C, Leis E, Liebendörfer M, Hochmuth R. 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>.
  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} }'
  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.
  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.'
date_created: 2019-03-25T15:35:44Z
date_updated: 2022-01-06T07:03:57Z
department:
- _id: '10'
language:
- iso: eng
publication: Beiträge zum Mathematikunterricht 2019
status: public
title: Erklärung von Mathematikleistung im Ingenieursstudium
type: book_chapter
user_id: '30933'
year: '2019'
...
---
_id: '16709'
author:
- first_name: Tuhin
  full_name: Sahai, Tuhin
  last_name: Sahai
- first_name: Adrian
  full_name: Ziessler, Adrian
  last_name: Ziessler
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  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>
  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} }'
  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.
  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>.
  short: T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).
date_created: 2020-04-16T14:05:04Z
date_updated: 2022-01-06T06:52:55Z
department:
- _id: '101'
doi: 10.1007/s11071-019-05092-5
language:
- iso: eng
publication: Nonlinear Dynamics
publication_identifier:
  issn:
  - 0924-090X
  - 1573-269X
publication_status: published
status: public
title: Continuous relaxations for the traveling salesman problem
type: journal_article
user_id: '47427'
year: '2019'
...
---
_id: '10593'
abstract:
- lang: eng
  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.
article_type: original
author:
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
citation:
  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>
  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>
  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>.'
  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>.
  short: S. Peitz, S. Klus, Automatica 106 (2019) 184–191.
date_created: 2019-07-10T08:08:16Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1016/j.automatica.2019.05.016
intvolume: '       106'
language:
- iso: eng
page: 184-191
publication: Automatica
publication_identifier:
  issn:
  - 0005-1098
publication_status: published
status: public
title: Koopman operator-based model reduction for switched-system control of PDEs
type: journal_article
user_id: '47427'
volume: 106
year: '2019'
...
---
_id: '10595'
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.
article_type: original
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  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>
  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>
  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} }'
  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>.'
  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.
  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>.
  short: B. Gebken, S. Peitz, M. Dellnitz, Journal of Global Optimization 73 (2019)
    891–913.
date_created: 2019-07-10T08:13:31Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1007/s10898-019-00737-6
intvolume: '        73'
issue: '4'
language:
- iso: eng
page: 891-913
publication: Journal of Global Optimization
publication_identifier:
  issn:
  - 0925-5001
  - 1573-2916
publication_status: published
status: public
title: On the hierarchical structure of Pareto critical sets
type: journal_article
user_id: '47427'
volume: 73
year: '2019'
...
---
_id: '10597'
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.
author:
- first_name: Soren
  full_name: Hanke, Soren
  last_name: Hanke
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Oliver
  full_name: Wallscheid, Oliver
  last_name: Wallscheid
- first_name: Joachim
  full_name: Böcker, Joachim
  last_name: Böcker
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
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>'
  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>
  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}
    }'
  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>.
  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.
  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>.
  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.'
date_created: 2019-07-10T08:15:23Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1109/precede.2019.8753313
language:
- iso: eng
publication: 2019 IEEE International Symposium on Predictive Control of Electrical
  Drives and Power Electronics (PRECEDE)
publication_identifier:
  isbn:
  - '9781538694145'
publication_status: published
status: public
title: Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous
  Motor Application with Online Least Squares System Identification
type: conference
user_id: '47427'
year: '2019'
...
---
_id: '13106'
author:
- first_name: Jan
  full_name: Schumacher, Jan
  id: '26809'
  last_name: Schumacher
  orcid: 0000-0002-6676-9774
citation:
  ama: 'Schumacher J. Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion
    negativer Zahlen. In: <i>Beiträge zum Mathematikunterricht 2019</i>.'
  apa: Schumacher, J. (n.d.). Rekonstruktion diagrammatischen Schließens am Beispiel
    der Subtraktion negativer Zahlen. In <i>Beiträge zum Mathematikunterricht 2019</i>.
    Regensburg.
  bibtex: '@inproceedings{Schumacher, title={Rekonstruktion diagrammatischen Schließens
    am Beispiel der Subtraktion negativer Zahlen}, booktitle={Beiträge zum Mathematikunterricht
    2019}, author={Schumacher, Jan} }'
  chicago: Schumacher, Jan. “Rekonstruktion diagrammatischen Schließens am Beispiel
    der Subtraktion negativer Zahlen.” In <i>Beiträge zum Mathematikunterricht 2019</i>,
    n.d.
  ieee: J. Schumacher, “Rekonstruktion diagrammatischen Schließens am Beispiel der
    Subtraktion negativer Zahlen,” in <i>Beiträge zum Mathematikunterricht 2019</i>,
    Regensburg.
  mla: Schumacher, Jan. “Rekonstruktion diagrammatischen Schließens am Beispiel der
    Subtraktion negativer Zahlen.” <i>Beiträge zum Mathematikunterricht 2019</i>.
  short: 'J. Schumacher, in: Beiträge zum Mathematikunterricht 2019, n.d.'
conference:
  location: Regensburg
  name: 53. Jahrestagung der Gesellschaft für Didaktik der Mathematik
date_created: 2019-08-30T11:58:37Z
date_updated: 2022-01-06T06:51:28Z
department:
- _id: '360'
- _id: '98'
language:
- iso: ger
publication: Beiträge zum Mathematikunterricht 2019
publication_status: inpress
status: public
title: Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer
  Zahlen
type: conference
user_id: '26809'
year: '2019'
...
---
_id: '13107'
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.
author:
- first_name: Jan
  full_name: Schumacher, Jan
  id: '26809'
  last_name: Schumacher
  orcid: 0000-0002-6676-9774
- first_name: Sebastian
  full_name: Rezat, Sebastian
  last_name: Rezat
citation:
  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>. Utrecht,
    the Netherlands: Freudenthal Group &#38; Freudenthal Institute, Utrecht University
    and ERME.'
  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} }'
  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.'
  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.
  mla: Schumacher, Jan, and Sebastian Rezat. “A Hypothetical Learning Trajectory for
    the Learning of the Rules for Manipulating Integers.” <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 et al., Freudenthal
    Group &#38; Freudenthal Institute, Utrecht University and ERME.
  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.'
conference:
  end_date: 2019-02-10
  location: Utrecht
  name: CERME 11
  start_date: 2019-02-06
date_created: 2019-08-30T12:00:50Z
date_updated: 2022-01-06T06:51:28Z
department:
- _id: '360'
- _id: '98'
editor:
- first_name: Uffe Thomas
  full_name: Jankvist, Uffe Thomas
  last_name: Jankvist
- first_name: Marja
  full_name: Van den Heuvel-Panhuizen, Marja
  last_name: Van den Heuvel-Panhuizen
- first_name: Michiel
  full_name: Veldhuis, Michiel
  last_name: Veldhuis
keyword:
- diagrammatic reasoning
- hypothetical learning trajectory
- induction extrapolatory method
- integers
- negative numbers
- permanence principle
- semiotics
language:
- iso: eng
place: Utrecht, the Netherlands
publication: Proceedings of the Eleventh Congress of the European Society for Research
  in Mathematics Education (CERME11, February 6 – 10, 2019)
publication_status: accepted
publisher: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME
quality_controlled: '1'
status: public
title: A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating
  Integers
type: conference
user_id: '26809'
year: '2019'
...