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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":"The student becomes familiar with the basic examples of finitely-generated infinite groups, and the basic concepts, constructions and tools in geometric group theory, in particular from a large-scale perspective.","fi":"The student becomes familiar with the basic examples of finitely-generated infinite groups, and the basic concepts, constructions and tools in geometric group theory, in particular from a large-scale perspective."},"tweetText":null,"content":{"en":"Geometric group theory is an approach to group theory, where geometric ideas are used to provide tools for solving algebraic problems and as a source of interesting properties and questions. Some of these methods are of a topological nature (fundamental groups and covering spaces), and some are more in the direction of large-scale / coarse geometry (Cayley graphs and growth rates of groups). Our emphasis is on the latter, and we concentrate on finitely-generated infinite groups.\r\n\r\nWe cover basic notions, such as Cayley graphs, growth rates of groups, quasi-isometry, the Svarc-Milnor theorem, free products with amalgamations, HNN extensions, presentations, and word-hyperbolic groups. Examples play a major role in geometric group theory, and we cover the main &#34;nice&#34; constructions (abelian, free groups, wreath products). We also overview more special constructions in the literature, such as the Grigorchuk group.","fi":"Geometric group theory is an approach to group theory, where geometric ideas are used to provide tools for solving algebraic problems and as a source of interesting properties and questions. Some of these methods are of a topological nature (fundamental groups and covering spaces), and some are more in the direction of large-scale / coarse geometry (Cayley graphs and growth rates of groups). Our emphasis is on the latter, and we concentrate on finitely-generated infinite groups.\r\n\r\nWe cover basic notions, such as Cayley graphs, growth rates of groups, quasi-isometry, the Svarc-Milnor theorem, free products with amalgamations, HNN extensions, presentations, and word-hyperbolic groups. Examples play a major role in geometric group theory, and we cover the main &#34;nice&#34; constructions (abelian, free groups, wreath products). We also overview more special constructions in the literature, such as the Grigorchuk group."},"additional":{"en":"Course will be given on campus in autumn 2026.","fi":"Course will be given on campus in autumn 2026."},"prerequisites":{"en":"Basics of Algebra II (Algebran peruskurssi II) strongly recommended, Group Theory (Ryhmäteoria) recommended","fi":"Algebran peruskurssi II (Basics of Algebra II) strongly recommended, Ryhmäteoria (Group Theory) recommended"},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Geometric Group Theory","id":"otm-588e0fa4-0d31-3624-9d93-4aac95f056b8","code":"MATE6036","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-69f8ea31-de0c-3050-ab2a-e571fbab1f95"],"organisations":[],"attainmentLanguages":[],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}