During my time at CMU, I was able to audit several courses intended for PhD students. The courses where all focused on some optimization aspects, and the topics where closely related to my research. Being able to audit these courses was a real privilege for me, partly because the courses were taught by world leading experts and because some of the content is not taught at my home university, and to my knowledge some parts are not taught at any Finnish university. The courses gave me a deeper insight to some aspects in my field of research and made me familiar with some methods that I have not worked with previously.
At Finnish universities, there are usually not many courses intended for PhD students, and this is one of the main differences I came across. In Finland, a PhD is a much more independent work and you are not considered as students. Whereas at CMU, PhDs are still considered as students and there is a path you should follow, for example there are courses that should be included. I cannot say which system is better, but I think it might be easier to get started if there is a path to follow and clear requirements of what should be achieved.
Two of the courses where focused on integer programming, which covers a specific type of optimization problems. Such optimization problems usually occur in planning or scheduling, and the course was given at Tepper School of Business at CMU. The most famous integer programming problem is perhaps the travelling salesman problem, in which a salesman must visit some specific cities and he wants to find a route that minimizes the total distance to travel. The course was taught by professor Egon Balas, who is one of the early pioneers in integer programming and disjunctive programming. He has been awarded several prestigious awards and he has undoubtedly made a great contribution to the field. He was also a great source of inspiration. He is now 95 years old and he is still able to give interesting lectures twice a week. For me it was inspiring to see that he is still passionate about his research and eager to teach new students.
During my stay at CMU I was also able to give a lecture based on my research. The topic was convex mixed integer nonlinear programming (MINLP) and the lectures was given in a course focused on MINLP. I enjoyed giving the lecture and it resulted in an interesting discussion afterwards, since most of the audience were PhD students working in the field of optimization.