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These studies are available for the following degree students:</p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Master's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master's Degree Programme in Mathematics&nbsp;(Subject Teacher)</li><li>Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Doctoral Programme in Mathematics and Statistics</li><li>Doctoral Programme in Mathematics and Science (Specialication in Mathematics)</li><br></ul>","fi":"<p>Tämä opintojakso on tarjolla Matematiikan syventävät opinnot -ristiinopiskeluverkostossa. Verkoston opinnot ovat tarjolla seuraaville opiskelijoille:</p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajien kandidaattiohjelma</li><li>Matematiikan aineenopettajien maisteriohjelma</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan kandidaattiohjelma (matematiikan opintosuunta)</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan maisteriiohjelma (matematiikan opintosuunta)</li><li>Matematiikan ja tilastotieteen tohtoriohjelma</li><li>Matemaattisten tieteiden ja luonnontieteiden tohtoriohjelma (matematiikan opintosuunta)</li><br></ul>"},"cooperationNetwork":{"abbreviation":"matematiikansyventavat","name":{"en":"Cross-institutional studies in advanced courses in mathematics and statistics","fi":"Matematiikan ja tilastotieteen syventävien kurssien ristiinopiskelu","sv":"Korsstudier i fördjupade kurser i matematik och statistik"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"After completing the course, the student will be able to\r\n•\tknow the historic background, basic concepts and the most central theorems of the classical euclidean geometry\r\n•\tknow the basic principles of axiomatic reasoning\r\n•\tproduce exact proofs in the context of classical Euclidean geometry\r\n•\tknow the basic principles of ruler-and-compass constructions, as well as the principles to show the constructions valid.\r\n•\tpresent exact arguments clearly both in a written and oral form, in the context of Euclidean geometry\r\n•\tevaluate sufficiency and validity of geometrical arguments and proofs.","fi":"Opintojakson suoritettuaan opiskelija\r\n•\ttuntee klassisen euklidisen geometrian historiallisen taustan, peruskäsitteet ja keskeisimmät teoreemat\r\n•\ttuntee aksiomaattisen päättelyn perusperiaatteet\r\n•\thallitsee täsmällisen todistamispäättelyn klassisen euklidisen geometrian kontekstissa\r\n•\ttuntee harppi-viivain-konstruktioiden perusperiaatteet ja periaatteet konstruktioiden pätevyyden osoittamiseen\r\n•\thallitsee täsmällisten argumenttien selkeän esittämisen euklidisen geometrian kontekstissa kirjallisesti ja suullisesti\r\n•\tosaa arvioida geometristen argumenttien ja todistusten riittävyyttä ja pätevyyttä."},"tweetText":null,"content":{"en":"Until 31.7.2025:\r\nBasic concepts and classic results of Euclidean plane geometry, axiomatic system and axiomatic reasoning, constructions with a compass and a ruler, congruence and similarity theorems for triangles, isometries and similarities.\r\n\r\nFrom 1.8.2025:\r\n•\tBasic concepts and classic results of Euclidean plane geometry, for example, triangle inequality, inscribed angle theorem and Pythagoras’ theorem\r\n•\tAxiomatic system and axiomatic reasoning\r\n•\tConstructions with a compass and a ruler\r\n•\tCongruence and similarity theorems for triangles\r\n•\tIsometries and similarities\r\n•\tCongruence and similarity of plane geometric figures","fi":"31.7.2025 saakka:\r\nEuklidisen tasogeometrian peruskäsitteet ja klassiset tulokset, aksioomajärjestelmä ja aksiomaattinen päättely, konstruktiot harpilla ja viivaimella, kolmioiden yhtenevyys- ja yhdenmuotoisuuslauseet sekä yhtenevyys- ja yhdenmuotoisuuskuvaukset.\r\n\r\n1.8.2025 alkaen:\r\n\r\n•\tEuklidisen tasogeometrian peruskäsitteet ja klassiset tulokset, kuten kolmioepäyhtälö, kehäkulmalause ja Pythagoraan lause\r\n•\tAksioomajärjestelmä ja aksiomaattinen päättely\r\n•\tKonstruktiot harpilla ja viivaimella\r\n•\tKolmioiden yhtenevyys- ja yhdenmuotoisuuslauseet \r\n•\tYhtenevyys- ja yhdenmuotoisuuskuvaukset.\r\n•\tTasokuvioiden yhtenevyys ja yhdenmuotoisuus"},"additional":{"en":"This course is intended for the following student groups:\r\n•\tMathematics majors\r\n•\tMinor subject students\r\n•\tOpen University students and lifelong learners\r\n\r\nPeriod 2\r\nJoensuu Campus","fi":"Tämä opintojakso on tarkoitettu seuraaville opiskelijaryhmille:\r\n•\tMatematiikan tutkinto-opiskelijat\r\n•\tSivuaineopiskelijat\r\n•\tJatkuvat oppijat ja avoimen yliopiston opiskelijat\r\n\r\nOpetusajankohta Periodi 2\r\nJoensuun kampus"},"prerequisites":{"en":"Basic studies in mathematics.","fi":"Matematiikan perusopinnot"},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Euclidean 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