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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":"Upon completion of the course, the student will be able to:\r\n- use Fourier analytic methods in fractal geometry problems\r\n- is familiar with several main research lines in fractal geometry\r\n- use a great variety of methods used in fractal geometry\r\n\r\nGeneric skills: analytical, critical and creative thinking, well-being and self-development, internationality,  responsibility and ethics and communication and interaction.","fi":"Kurssin onnistuneen suorittamisen jälkeen opiskelija:\r\n- osaa käyttää Fourier analyysin menetelmiä fraktaaligeometrian ongelmissa\r\n- on perehtynyt useaan fraktaaligeometrian keskeiseen ongelmaan\r\n- hallitsee monipuolisesti fraktaaligeometrian tutkimusmetodeja\r\n\r\nGeneeriset taidot: analyyttinen, kriittinen ja luova ajattelu, hyvinvointi ja itsensä kehittäminen, kansainvälisyys, vastuullisuus ja eettisyys sekä viestintä ja vuorovaikutus."},"tweetText":null,"content":{"en":"- Fourier transform\r\n- typical and exceptional projections\r\n- general intersections\r\n- Besicovitch sets\r\n- random covering sets\r\n- visible parts","fi":"- Fourier-muuunnos\r\n- tyypilliset ja poikkeukselliset projektiot\r\n- yleisiä leikkauksia\r\n- Besicovitch-joukot\r\n- satunnaiset peitejoukot\r\n- näkyvä osa"},"additional":{"en":"Language of instruction\r\nFinnish/English (according to the participants)\r\n\r\nTiming\r\n4. or 5. year\r\n\r\nTarget group\r\nMajors in mathematics and graduate students","fi":"Opetuskieli\r\nSuomi/English (tarpeen mukaan)\r\n\r\nAjoitus\r\n4. tai 5. opintovuosi\r\n\r\nKohderyhmä\r\nMatematiikan pääaineopiskelijat ja jatko-opiskelijat"},"prerequisites":{"en":"802651S Measure and integration. Courses 8000AE47 Measure and Integration 2 and 802650S Fractal Geometry are useful but not necessary.","fi":"802651S Mitta ja integraali. Kurssit 8000AE47 Mitta ja integraali 2 sekä 802650S Fraktaaligeometria ovat hyödyllisiä mutta eivät välttämättömiä."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Fractal Geometry 2","id":"otm-95265fcb-a26d-3407-9576-7e065f18e5e9","code":"802674S","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-71fd8cc0-9fb4-38e1-bbb0-d1d63f911ddf"],"organisations":[],"attainmentLanguages":["fi"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}