Learning Abstract Algebra with ISETL:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1994
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are preseted in a lecture |
| Beschreibung: | 1 Online-Ressource (XXI, 248 p) |
| ISBN: | 9781461226024 9781461276029 |
| DOI: | 10.1007/978-1-4612-2602-4 |
Internformat
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| 245 | 1 | 0 | |a Learning Abstract Algebra with ISETL |c by Ed Dubinsky, Uri Leron |
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| 300 | |a 1 Online-Ressource (XXI, 248 p) | ||
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| 500 | |a Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are preseted in a lecture | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Group Theory and Generalizations | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Dubinsky, Ed |
| author_facet | Dubinsky, Ed |
| author_role | aut |
| author_sort | Dubinsky, Ed |
| author_variant | e d ed |
| building | Verbundindex |
| bvnumber | BV042420053 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879621734 (DE-599)BVBBV042420053 |
| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2602-4 |
| format | Electronic eBook |
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| id | DE-604.BV042420053 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461226024 9781461276029 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855470 |
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| physical | 1 Online-Ressource (XXI, 248 p) |
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| spelling | Dubinsky, Ed Verfasser aut Learning Abstract Algebra with ISETL by Ed Dubinsky, Uri Leron New York, NY Springer New York 1994 1 Online-Ressource (XXI, 248 p) txt rdacontent c rdamedia cr rdacarrier Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are preseted in a lecture Mathematics Group theory Group Theory and Generalizations Mathematik ISETL (DE-588)4205825-9 gnd rswk-swf MS-DOS (DE-588)4114641-4 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 s ISETL (DE-588)4205825-9 s MS-DOS (DE-588)4114641-4 s 1\p DE-604 Leron, Uri Sonstige oth https://doi.org/10.1007/978-1-4612-2602-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dubinsky, Ed Learning Abstract Algebra with ISETL Mathematics Group theory Group Theory and Generalizations Mathematik ISETL (DE-588)4205825-9 gnd MS-DOS (DE-588)4114641-4 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4205825-9 (DE-588)4114641-4 (DE-588)4061777-4 |
| title | Learning Abstract Algebra with ISETL |
| title_auth | Learning Abstract Algebra with ISETL |
| title_exact_search | Learning Abstract Algebra with ISETL |
| title_full | Learning Abstract Algebra with ISETL by Ed Dubinsky, Uri Leron |
| title_fullStr | Learning Abstract Algebra with ISETL by Ed Dubinsky, Uri Leron |
| title_full_unstemmed | Learning Abstract Algebra with ISETL by Ed Dubinsky, Uri Leron |
| title_short | Learning Abstract Algebra with ISETL |
| title_sort | learning abstract algebra with isetl |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik ISETL (DE-588)4205825-9 gnd MS-DOS (DE-588)4114641-4 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik ISETL MS-DOS Universelle Algebra |
| url | https://doi.org/10.1007/978-1-4612-2602-4 |
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