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[{"key": "dc.contributor.advisor", "value": "Laukkarinen, Eija", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Tilli, Noora", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-06-07T07:12:40Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-06-07T07:12:40Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2024", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/95630", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4 matematiikan pro gradu\u2013tutkielma keskittyy lineaarialgebraan ja sen opetukseen lukiomatematiikassa. Tarkoituksena on tarjota ehe\u00e4 kattaus lineaarialgebran viidest\u00e4 keskeisest\u00e4 aihealueesta; matriiseista, lineaarisista yht\u00e4l\u00f6ryhmist\u00e4, vektoriavaruuksista, lineaarikuvauksista, sek\u00e4 ominaisarvoista ja -vektoreista. Tutkielma pyrkii my\u00f6s tarjoamaan ymm\u00e4rryst\u00e4 lineaarialgebran k\u00e4sitteist\u00e4 ja niiden keskin\u00e4isist\u00e4 suhteista sek\u00e4 tarjoamaan konkreettista opetusmateriaalia. \n\nJokaisesta aihealueesta keskityt\u00e4\u00e4n k\u00e4sittelem\u00e4\u00e4n kyseisen aihealueen perusteet, keskeiset k\u00e4sitteet ja joitakin sovelluksia. Konkreettisia esimerkkej\u00e4 tarjotaan k\u00e4sitteiden omaksumisen ja k\u00e4yt\u00e4nn\u00f6n ymm\u00e4rt\u00e4misen tueksi. N\u00e4in lukija saa kattavan k\u00e4sityksen kunkin aihealueen merkityksest\u00e4. Lis\u00e4ksi esitell\u00e4\u00e4n viimeaikaisia tuloksia matriisien k\u00e4\u00e4nteisominaisuudesta ja (3 \u00d7 3)- matriisien determinantin ratkaisemisesta alkioiden kopioinnilla.\n\nTutkielmassa k\u00e4sitell\u00e4\u00e4n kompleksilukuja ja niiden k\u00e4ytt\u00f6\u00e4 lineaarialgebrassa. Kompleksiluvut tarjoavat syvemm\u00e4n ymm\u00e4rryksen lineaarialgebrasta sek\u00e4 ty\u00f6kalun monien lineaarialgebran ongelmien ratkaisemiseen. Tutkielmassa k\u00e4sitell\u00e4\u00e4n lineaarialgebran opetusta k\u00e4yt\u00e4nn\u00f6ss\u00e4 konkreettisten opetusvinkkien, teht\u00e4vien ja tietoteknisten apuv\u00e4lineiden avulla opetuksen ja oppimisen tueksi.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-06-07T07:12:40Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-06-07T07:12:40Z (GMT). No. of bitstreams: 0\n Previous issue date: 2024", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "125", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.title", "value": "Lineaarialgebra lukiomatematiikassa", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202406074392", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "lineaarialgebra", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matriisit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matriisilaskenta", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "algebra", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "yht\u00e4l\u00f6t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "polynomit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kompleksiluvut", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "opetus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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