Published Sep 04, 2026

How do you get first-year students on board when the first maths course of the autumn gets underway? We joined Lars Filipsson, Associate Professor in Mathematics, for the opening lecture of the semester.

Alfvénsalen is filled with the murmur of around 300 students from four Master of Science in Engineering programmes as they gather for their first lecture in single-variable calculus. On stage is Lars Filipsson, Associate Professorin Mathematics and one of KTH’s most experienced mathematics teachers.

After more than 25 years of teaching, he has been named Teacher of the Year and received KTH’s Pedagogical Prize. Even so, he feels a certain nervous excitement ahead of today’s lecture.

“It’s a little nerve-racking, but it always feels good once you get started. This really is the most enjoyable part of the job,” he says during a chat beforehand.

Now he turns to the students.

“Right, shall we get started? Welcome, everyone. It may feel a little formal right now, but it will soon become familiar. Let’s ease into it.”

The tone is set. Mathematics is not something you can avoid.

“Some people say this is a difficult course, but most students pass. There are no shortcuts. You have to be engaged and study 100 per cent from day one.”

But first, it is important to understand why mathematics is needed. It is everywhere – in communications and payment systems, transport and healthcare.

“Our civilisation would not exist without mathematics,” Lars Filipsson points out.

And at its core, single-variable calculus is about something no human being can escape: change. The theory provides tools for describing change at a particular point in time and how changes build up over time.

“These are fundamental concepts for human beings. All life is change.”

The motivation has been delivered. Lars Filipsson is now fully under way, and the pace picks up. So much so that, eventually, the scheduled break comes ten minutes late.

In the foyer outside the lecture hall, classmates Linus Lundberg and Tarik Resulovic take a breather. They are studying Civil Engineering and Urban Management and are happy with the start.

“It’s a bit of a gentle introduction. You probably need these basic concepts to be able to build on them,” says Tarik Resulovic.

He has also watched some of Lars Filipsson’s recorded lectures on YouTube.

“He seems very good at teaching and has a good sense of what’s happening in the room. When he wrote something on the board, he would pause and check the room to see whether people were keeping up.”

Both students enjoy problem-solving and think mathematics is fun. At the same time, they have heard the warnings from students further along in the programme.

“You should be happy if you pass. It’s demanding, and you have to put in the time,” says Linus Lundberg.

After the break, Lars Filipsson is back in front of the blackboard.

“I want to identify a few things that you shouldn’t skip in this course. Together, we’re going to build up an arsenal of concepts so that we can talk about all this over the coming weeks.”

Being able to talk about mathematics is an important part of the teaching. And Lars Filipsson wants the students to be able to do so in Swedish.

Together with his son, who is studying engineering in Lund, he has therefore written the Swedish-language textbook Förändringens matematik (The Mathematics of Change). Each chapter corresponds to a lecture, giving the course a structure of its own. The course also includes seminars with tests and workshops in small groups.

By lunchtime, it is over. As Lars Filipsson steps away from the board, the students break into spontaneous applause.

He himself is fairly exhausted.

“Actually, the lessons should probably be shorter. Two hours is a bit long.”

How did it go?

“It was quite okay. It’s really important to take things slowly at the beginning so that everyone can keep up. Today, there were probably some who thought it was pretty easy and others who found it a bit challenging. But that’s difficult to avoid.”

What happens next?

“I’m going to think a little about tomorrow’s lecture, go through my examples once more and work on making things even more relaxed as we go along.”

Text: Christer Gummeson ( gummeson@kth.se )