Teaching Portfolio Daniel Meyer March 19, 2015

Contents 1 Teaching experience

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2 Development of teaching, experience in course and curriculum development 2 3 Teaching and learning materials

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4 Teaching philosophy and approach to teaching

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5 Pedagogical education and studies

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6 Experience in educational leadership

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7 Results in student and peer evaluations. Honors and awards and assessments of pedagogical competence 5 8 Other teaching merits

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Appendix: List of teaching activities

Personal Information Daniel Meyer University of Jyv¨ askyl¨ a PO Box 35 FI-40014 University of Jyv¨ askyl¨a [email protected] Education Ph.D. in Mathematics, University of Washington, Seattle, 2004. Advisor: Professor Steffen Rohde. Diploma in Mathematics, Technische Universit¨at Berlin, Germany, 1998. Advisor: Professor Steffen Rohde.

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Teaching experience

During my academic career, I have had the opportunity to both study as well as teach mathematics in Germany, the U.S.A., Switzerland, and Finland. Each country has a slightly different approach to teaching, and thus I have gained valuable experience of different teaching cultures. At Jacobs University I have been teaching mathematics courses on all levels, including introductory undergraduate math courses, advanced undergraduate math courses, and standard as well as topics graduate math courses. Additionally, I have taught mathematics service courses of various levels here. I have been the organizer of the “dynamics and geometry” seminar, as well as the mathematics colloquium. A joint seminar with the University of Bremen was organized by me, with the aim to exchange ideas between research groups at the two institutions. I currently advise my first Ph.D. student, Mikhail Hlushanka. My first bachelor student, Alexandru Ciolan, just defended his thesis; he will be a graduate student at the University of Bonn. I have been the secondary reader of various Ph.D. theses at Jacobs University. At the University of Michigan, Ann Arbor, I taught various undergraduate courses while I was a postdoc there. I was also running the “Geometric Function Theory Seminar”, as well as the “Study Seminar”. I served as the secondary reader for several Ph.D. theses. At the University of Washington, Seattle, I was teaching several calculus courses on all levels. I was also running the “Current Problems Seminar”. At Helsinki University I had no formal teaching duties, but I did organize a seminar on recent developments in random surfaces. Additionally I was the second reader for a Licentiate Thesis.

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Development of teaching, experience in course and curriculum development

The very first course I taught at Jacobs University was “Perspectives of Mathematics”. It is designed to give second year mathematics students an overview of different areas of mathematics, as opposed to rigorous development of material. I took the opportunity to completely redesign the course. The main aim was to learn aspects of mathematics that are usually somewhat neglected when just solving homework problems. Every student has to give two presentations, i.e., talks. Seminar talks are among the most important ways to exchange mathematical ideas. Students should learn to give talks as early as possible. Conversely, students should learn to ask questions during talks and think critically about the material. This is much facilitated by student presentations, since the presented work comes from a less authoritative source. Students were also supposed to learn writing mathematics. They had to do a write-up of one of their presentations. Here I wanted them to focus on writing something that was very polished. Students got the write-ups of the other students to compare different styles. Another thing I did in this class was to have open ended problems. For example, there is a construction of Peano curves by repeatedly folding a paper and opening each crease to a right angle. I described the construction and students were supposed play around with it (write a computer program, vary the 2

construction, formulate conjectures, try to prove those conjectures, and so on). Often, the most difficult aspect of mathematics is to understand the definitions. When doing research, a lot of time is spent with formulating definitions. I gave students the task of formulating definitions, such as Hausdorff distance (How would you define the distance between sets? What properties does your definition have? For what types of sets does it work?). The course was very successful, the format has since been adopted by other people teaching this course. I very much like to try out new and different things in my teaching. Part of the reason is that new technologies changes how information is available to students. This presents a big challenge for teaching. While I do not believe anybody has found the “magic formula” yet (nor do I believe such a thing exists), it is important to try different approaches. When I was a graduate students at the University of Washington, Seattle, I developed and taught the “Complex Analysis preparation course”. This is a course designed to prepare graduate students to take the preliminary exam after their second year of study. The material has since been used by people who taught this course later. I also developed the “Current Problems” seminar. This was a seminar for beginning graduate students. The aim was to give these students an overview of different areas of mathematics, as well as help them in finding an area and an advisor. Faculty were explicitly excluded, to create an atmosphere where students would not be embarrassed to ask “simple” questions.

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Teaching and learning materials

I very rarely use a single textbook when I teach a course. This makes it sometimes hard for students, since it is difficult for them to look at many different books with possibly different notation/terminology. On occasion I will prepare handouts, when I’m not satisfied with available presentations of a topic. I do however usually not prepare full lecture notes, since I think it is important that students learn to read mathematics books. Also, they should learn to prepare notes. Comparing notes with other students is very valuable and should be encouraged. I do however let student prepare write-ups in advanced classes of a topic of their choosing. These write-ups are shared between students. This serves as a motivation for students. Furthermore they can compare their writing with those of others, which further helps them in their writing skills.

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Teaching philosophy and approach to teaching

First of all, I like to vary the courses that I teach. The difficulties that I have in preparing a class help to remind me of the difficulties that students might have. I believe it is much easier to teach difficult material if one acknowledges that the material is in fact difficult. Teaching a beginners class presents its own challenges. Richard Feynman said that we do not understand things, if we cannot explain it to a freshman student. I enjoy very much to develop intuitive ways to explain difficult concepts. Limits I explained by starting out with a quite silly poker variant (everybody

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thinks of a number, the highest number wins), for vector calculus my favorite example was the bathtub full with rubber duckies (how do they move/spin, and of course: where do the rubber duckies come from). I’m not afraid to act somewhat silly at times. Often, I pretend to hike or fly around a mountain-range. Additionally to loosen the atmosphere, this also serves the important purpose that abstract mathematical descriptions are in fact used to describe real world phenomena. Understanding a mathematical concept also means not only to know the definitions, but an intuitive understanding what type of phenomenon it describes. For classes on the other end of the spectrum, the “dirty secret” is of course that often one teaches material to really understand it. I only feel comfortable to teach something I have a deep understanding of. Often, when preparing for lectures on advanced material I have dug quite deep, since I wanted to make sure that there is in fact no gap somewhere hidden. I do think that I am quite a demanding teacher. Mathematics is partially learned by “slowly, steadily lowering the resistance”. This means that there are difficult concepts that I do not expect students to understand when first encountered. I do however introduce these concepts early on. When they encounter such concepts the second time, it will be much easier for them to understand those. Also, I have often found that students are as smart as you expect them to be. Put differently, I was often surprised at the quality of student work when I gave them non-standard assignments. As an extra credit project, students had to built an actual physical model of some mathematical object, including a description. I gave a list, but students could choose anything with my approval. I was very impressed with the models that I got. Klein bottles proved to be most popular. One student built a “catastrophe machine”, which appropriately enough kept breaking all the time. Another built models of several Riemann surfaces. These were students in their second year, none of them math majors. Every class of students is different. It is fair to say that I always need some time to adjust. The same is true for the students. It usually takes some time before they become comfortable with asking questions. I do think however that I am quite successful at creating an atmosphere where students ask a lot of questions. It has become somewhat of a custom that some students stay for half an hour or so after each class to ask more questions, often about things that are quite a bit above the level of the class.

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Pedagogical education and studies

Even though I had already taught tutorials while in Germany, it is probably fair to say that my main education as a teacher was in the United States. I first taught my own lectures at the University of Washington, Seattle. As a graduate student, I received proper teaching training. Our lectures were videotaped and later evaluated. Somebody from the teaching office was assigned to me. She would regularly come to my classes, and we would then go over my teaching together. While this made me admittedly nervous at first, she was truly great with her advice. I learned a lot from her, and she really helped me to become a better teacher. More than anything, it made me more aware of my teaching style, as well as how students perceive me. Similar teaching education I received

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at the University of Michigan, Ann Arbor. In the U.S., as well as at Jacobs University, there are quite detailed teaching evaluations, which both involve numerical grades as well as written comments. It is my strong belief, that having such evaluations in place is very important. The additional incentive, as well as the feedback, helps to improve the quality of teaching in general. At the University of Michigan I was involved in the development of “inquiry based learning” courses under the supervision of Michael Artin. During the time I was invited by Stas Smirnov to Geneva. This stopped my involvement in these courses.

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Experience in educational leadership

After I have been for one year at Jacobs University, I rewrote the handbook for the mathematics major. This included all course descriptions of all math courses, as well as all formal requirements for graduation. The main tasks involved were to make sure that descriptions would be uniform, and that formal requirements are met (including the ones of other majors needing math service). I felt it was actually an advantage to be relatively new, since it allowed me to ask a lot of questions. For two years, I have been a member of the “Graduate Education Committee”. This sets the university-wide guidelines for all graduate education. Since Jacobs University is quite a young university (about 13 years), some policies were not yet completely fleshed out and had to be rewritten.

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Results in student and peer evaluations. Honors and awards and assessments of pedagogical competence

At Jacobs University, I was chosen “teacher of the year” by the students. Three awards are given out each year, mine was for the “School of Engineering and Science” (which comprises about 60% of the university). These are the evaluations of the most recent courses that I taught. Analysis II How do you rate the course in general? Very good: 100%. The course was well-structured. Strongly agree: 100%. How do you rate the instructor’s performance in general? Very good: 100%. Introduction Complex Analysis How do you rate the course in general? Very good: 80%, good 20%. The course was well-structured. Strongly agree: 100%. How do you rate the instructor’s performance in general? Very good: 80%, good 20%. Multivariable Calculus, ODE How do you rate the course in general? Very good: 71%, good 29%. The course was well-structured. Strongly agree: 24%, agree: 65%, neutral: 12%.

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How do you rate the instructor’s performance in general? Very good: 82%, good 18%. Quotes from evaluations Analysis II: “It was my favourite course in Pure Maths. I really appreciate Mr. Meyer’s teaching style, the subject was interesting, homework problems were demanding, hard, but beautiful, exams were comprehensive. I like that Mr. Meyer gives a deep insight on the matter, shows what lies behind a problem, and makes you understand. From the easier level we continuously increased up to a very high level, but without skipping any step.” Multivariable calculus: “After doing this course, I do not think that there is anything that this course needs to improve, for a science major this is just the right amount of mathematics for the first semester.” “It should last longer.” “I loved that the professor has a great sense of humor, which makes coming and sitting in class very nice.” “The way the things were explained were simply amazing.” “This is the most interesting course I have had so far. Everything is very intuitive and we saw links between geometry, algebra and analysis. The professor was also very good, giving background ideas for the proofs and also introducing applications in different fields.” “Prof. Daniel Meyer is an amazing teacher and he should teach ESM 2B also.” “The professor is very good at communicating ideas and concepts to the class. He wants not only to show some mathematical concepts but to make the students understand them, thus he uses many examples to clarify misunderstandings. He is not the usual boring and bored math professor.” Intro Complex Analysis: “I really learnt something new and interesting, and I can say that this course was my favourite this semester. I liked the content, the structure, the homework problems which made me study more than what we did in class, and problems were in accordance with our progress throughout the course. The course covered beautiful topics that made me eager to consider this field as a possible reasearch direction in future. The theorems were all carefully stated and proved, followed by examples and generalizations.” “I would like to congratulate Prof. Meyer for the way he does his job here. He loves what he is doing and is a true teacher. Nevertheless, I appreciate his way of being in general as a person, both inside and outside classes. He is a very funny and open person who makes a pleasant atmosphere around him and enjoys discussions of all sort, mathematical or not.” Topics Complex Analysis: “I think the course was perfectly planned and teached.” “I congratulate prof. Meyer for his teaching performance and for his personal traits. Once again, he proved a mastering of the subject, he encouraged questions, and in fact raised my interest for futher research into this area. He showed patience and demonstrated perfect teaching skills. I really feel that I

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learned a lot and improved my math knowledge. Nevertheless, he is a friendly, funny and open person, who creates a pleasant atmosphere around.” I am happy to provide the full data sets of the evaluations, they are however quite long (22 pages per course), which is the reason I did not attach them here.

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Other teaching merits

I was very much involved in the organization of the International Mathematical Summer School for Students, which took place at Jacobs University in 2011. This was for students in their last two years of high school, as well as students in their first two years of university. About 90 students from all over the world were selected. Speakers included John Conway, Wendelin Werner, Don Zagier, Etienne Ghys, and John Hubbard among many others. Videos can be found at http://math.jacobs-university.de/summerschool/2011/videos/index.php. This event was successfully repeated in 2013, I was only a little involved this time, since I was visiting UCLA for three months then. This years, I was involved in the organization Bremen Winter School on Kleinian Groups and Transcendental Dynamics, 2014. At Jacobs University I was in charge of the “Math Club”. At this club students meet at the weekend to talk about mathematics.

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