I love to teach. And as a researcher it is my strong belief that the knowledge we accumulate through research is valuable only if it is shared with young minds and driven listeners.
Like a young soccer player, the mathematics student needs to develop technique and also lots of practice. And just like a soccer player, the mathematics student will profit most from a broad and solid education in the early stage. However, as the soccer player trains in order to compete, the mathematician needs technique in order to make mathematics by tackling challenging problems. In this context, the role of the mentor is that of a coach: one provides encouragement, guidance and makes sure that the person being mentored is working on interesting problems and is aware of basic tools that are available.
As a student, I was fortunate enough to profit from the intensive mentoring system in Darmstadt, which ranged from a simple welcome talk before commencement of studies to far into the course of academic study. I also benefited a lot from special small group tutorials, which were offered complementary to the classical exercise sessions in order to deepen our knowledge and to broaden our perspective. Besides that, the open door policy of my teachers always encouraged me to stop by whenever I felt the need to meet and ask questions, discuss suggestions, and address problems. Therefore an open door policy is firmly anchored in my own teaching philosophy, as it serves to foster an environment of collaboration, high performance, and mutual respect between students and teachers.
Many students begin by equating mathematics with computation or dangerous hand-waving, but I want my students to have a deep understanding of mathematics. Therefore, I am always doing my best to prepare my lectures and to motivate their contents. In fact, I think that students need to see perfect and very clear proofs in the lectures so that they strive for perfection themselves. I am likewise doing my best when it comes to creating interesting problem sheets. By combining the textbook’s problems with, multi-part problems, applications, proofs and conceptual questions, I hope to provide questions to attract every student, that is, to reward struggling students with success and challenge successful students to work even harder. From a purely pedagogical point of view the books “How to Teach Mathematics” by Kranty and “Academic Teaching” by Elmgren and Henriksson have always been very appreciated and helpful guides.
On top of all this, and maybe most importantly, I want my students to understand mathematics as a way of communication. And just like well-argued essays and communications skills are expected in humanities, I expect my students to be able to write convincing, clear mathematical arguments at professional standards and to be able to communicate mathematical ideas and problems with other students and colleagues. I try to convey these skills, for instance, by offering complementary learning activities such as weekly exercise sessions that focus on the student’s independent study. In this context I would like to mention “the principle of minimum help” which has been developed by Aebli and has find its way into higher education pedagogy since the work of Görts. Simply put, the principle of minimum help suggests that the intensity and strength of the intervention by the teacher shall increase step by step in relation to the lack of success of the students and that these interventions shall support the students to find a solution on their own, if possible. In recent years this valuable concept has always been central to me and my role as a teacher.
In recent years I worked within several teams in the delivery of numerous University lecture courses. As a student, I started from early on with being a tutor for various math courses. Later, as a Ph.D. student in Darmstadt and Erlangen, I co-organized many courses and seminars for mathematicians, math teachers, physicists and engineers even though I was awarded a research scholarship. During my time at the University of Copenhagen, I co-organized several Master and Ph.D. courses. My career as a lecturer started in Helsinki, where I taught a course on the “Representation Theory of Compact Lie Groups” and a course on “Operator Algebras”. At the University of Hamburg, I taught a course for physics students, in which I provided important tools and tricks for solving mathematical problems related to physics in a rigorous way. This course, with the title “A Tool Kit for Physicists”, was evaluated extremely positive. In the forthcoming spring I will give a PhD course on “Algebraic Geometry” at Linnaeus University in Växjö. Besides all that, I also try to advertise mathematics to interested school children and non-experts. I do this, for example, by visiting local schools and cultural events, where I speak about the beauty and usefulness of mathematics in everyday life. In 2015 I even taught a thought-provoking summer school course on symmetries for academically talented school children. All of these valuable experiences allowed me to develop my ability to communicate concepts and knowledge to students and people from different backgrounds. Furthermore, the administration and organization of lectures, exercise classes, tutorials and exams with up to 1000 participants demanded good structuring and coordination skills.
SUMMARY & OUTLOOK
Teaching is a great pleasure to me and one of my passions, and I am excited to continue to improve my teaching abilities in order to serve my students better. For example, right now I am participating in the högskolepedagogisk introduktionskurs of BTH. During the upcoming spring 2018, I will continue with BTH’s högskolepedagogiska projektkurs and, if possible, also with BTH’s forskarhandledningskurs.
Winter Term 2018 Diskrete Matematik, Lecturer, BTH
Spring Term 2018 Algebraic Geometry, Lecturer, Växjö
Summer Term 2016 Mathematics for Physicists III, Assistant, Hamburg
Summer Term 2016 A Tool Kit for Physicists II, Lecturer, Hamburg
Summer Term 2015 Mathematics for Physicists II, Assistant, Hamburg
Winter Term 2015 A Tool Kit for Physicists I, Lecturer, Hamburg
Winter Term 2015 Mathematics for Physicists I, Assistant, Hamburg
Summer Term 2015 “A-N-N-A, von hinten wie von vorne...”, Lecturer, Meisenheim
Summer Term 2015 Mathematics for Physicists IV, Assistant, Hamburg
Summer Term 2015 Functional Analysis, Assistant, Hamburg
Fall Term 2014 Operator Algebras, Lecturer, Helsinki, Lecture Notes available
Spring Term 2014 Representation Theory of Compact Lie Groups, Lecturer, Helsinki
Summer Term 2013 Advanced Complex Analysis, Assistant, Copenhagen
Fall Term 2012 Representation Theory of Lie Algebras, Assistant, Copenhagen
Summer Term 2012 Introduction to Noncommutative Geometry, Assistant, Copenhagen
Summer Term 2011 Geometry for Teachers, Assistant, Erlangen
Winter Term 2010 Linear Algebra 1, Tutor, Erlangen
Winter Term 2009 Mathematics III for Electrical Engineers, Assistant, Darmstadt
Summer Term 2009 Mathematics I for Mechanical Engineers, Tutor, Darmstadt
Summer Term 2009 Seminar on Lie Algebras, Dozent (with Dr. H. Seppänen), Darmstadt
Winter Term 2008 Geometry for Teachers, Tutor, Darmstadt
Winter Term 2007 Analysis 2, Assistant, Darmstadt
Summer Term 2007 Analysis 1, Assistant, Darmstadt
Winter Term 2006 Functional Analysis, Tutor, Darmstadt
Summer Term 2006 Analysis 1, Tutor, Darmstadt
Winter Term 2005 Manifolds and Transformations Groups, Tutor, Darmstadt
Winter Term 2004 Integration Theory, Tutor, Darmstadt
Summer Term 2004 Complex Analysis, Tutor, Darmstadt