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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":"Students master the first and the second main theorems of Nevanlinna Theory, Clunie’s lemma, and the central estimating techniques of logarithmic derivatives. They can apply these results in analyzing value distribution of meromorphic solutions of differential equations.","fi":"Opiskelija hallitsee Nevanlinnan teorian ensimmäisen ja toisen päälauseen, Clunien lemman, sekä logaritmisen derivaatan keskeiset arviointimenetelmät. Hän osaa soveltaa näitä tuloksia differentiaaliyhtälöiden meromorfisten ratkaisujen arvojenjakautumisen analysoinnissa."},"tweetText":null,"content":{"en":"Nevanlinna’s theory of value distribution is a deep generalization of Picard’s Theorem for meromorphic functions. In this course we will cover the most central contents of Nevanlinna Theory of one complex variable starting from the Poisson-Jensen formula, including the first and the second main theorem of Nevanlinna Theory, the lemma on the logarithmic derivatives, Clunie’s lemma and the defect relations. In addition, some applications of Nevanlinna theory in the theory of differential equations are included in the course.","fi":"Nevanlinnan arvojenjakautumisteoria on Picardin lauseen syvällinen laajennus meromorfifunktioiden teoriaan. Kurssilla käsitellään Nevanlinnan teorian keskeinen sisältö yhden kompleksimuuttujan tapauksessa lähtien Poisson-Jensenin kaavasta. Tärkeimmät kurssiin sisältyvät asiat ovat Nevanlinnan ensimmäinen ja toinen päälause, logaritmisen derivaatan lemma, Clunien lemma ja defektirelaatiot. Lisäksi käsitellään Nevanlinnan teorian sovelluksia differentiaaliyhtälöiden teoriaan."},"additional":{"en":"This course is open for everyone.\r\n\r\nThe course is held every other year during the spring semester.","fi":"Tämä opintojakso on avoin kaikille.\r\n\r\nKurssi järjestetään kevätlukukaudella joka toinen vuosi."},"prerequisites":{"en":"Basic understanding of complex analysis up to the Cauchy integral formula.","fi":"Perustiedot kompleksianalyysistä Cauchyn integraalilauseeseen asti."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Nevanlinna Theory","id":"otm-0b0f219d-4404-3e6c-b243-2f7eeffe78f1","code":"LF00DE25","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-42edd1ec-1dc5-35c1-b11f-d74a959e96c9"],"organisations":[],"attainmentLanguages":["en","fi"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}