Learn more about mathematics

​The Department of Mathematical Sciences wants to provide more exploration courses. To begin with there are two courses given together with the Physics Department: “The History of the Art of Navigation” and “A Mathematical Guide to Ganymede”.

Photo Elin GötmarkSo-called exploration courses are evening courses that only require general entry requirements and are therefore accessible to more people than the usual range of courses offered. The course The History of the Art of Navigation was given last spring with eight three-hour lectures, where Elin Götmark at Mathematical Sciences and Maria Sundin at Physics alternated as teachers. The course was available before as well but was reworked with more mathematics and less history of shipping. The students of the course were mixed – someone had worked at sea, someone was a history student, and there were also those who had studied at the mathematics programme. Pretty many were retirees.

– The lectures were real fun to hold and it was also fun to immerse myself in the area. One must be aware of the differing mathematical background of the students, and for example not assume that they know any trigonometry. That, we must do from scratch. I also have a course in nautical mathematics for those who study to become sea captains at Campus Lindholmen and the courses have cross-fertilized each other. I would like to teach it again!

Mathematics from ancient times

The basic question of the course is how we can know where on Earth we are. When we know this, we might ask in which direction to move to get to another place. This will of course be more important at sea where there are no landmarks in nature. By measuring the height of the sun above the horizon with a sextant, we can figure out at which latitude we are. The mathematics that is used goes back to ancient times, for example the circumference of the Earth was accurately calculated already before the birth of Christ. Maria’s lectures have been given in a historical order, while Elin’s have been in a more mathematical order, beginning with the simpler concepts and reaching the most advanced, such as spherical trigonometry.

The courses have guaranteed admission and last autumn there were about 50 students, but there is room for more. There was no course book but tips were given about books and links. The students received a solid list of study questions from the lectures and the mathematical questions were more about explaining methods than actually doing the calculations.

Colonisation of Ganymede

Photo Torbjörn LundhThe course given this spring is A Mathematical Guide to Ganymede and it is given for the second time. From Mathematical Sciences Torbjörn Lundh has now taken over after Ulf Persson, who has retired, and here as well it is Maria Sundin who gives the other half of the lectures. Ganymede is the biggest moon of the solar system and it orbits around the planet Jupiter. The course deals with how a trip from Earth to Ganymede and a colonisation of this moon could happen. In a popular scientific way mathematics, physics and astronomy are combined and used when investigating appropriate trajectories, how the planets move, how the sky changes during the journey and the physical conditions of Ganymede. What could the future colonisers experience?

– It is fascinating to see with what frenzy and interest many of the participants are following the course. The majority have working life behind them and they choose to struggle with the questions like anything. In addition, one gets so clever questions, and not only at the lectures. Last Saturday afternoon, in the pause at the Concert Hall, a gentleman stepped forward to me, gave me one of the firmer handshakes that I ever have received and said emphatically: You must post the solution of problem number two now! I have really been stuck and have asked all my acquaintances!

Why exploration courses?

It has been rewarding to cooperate with the Physics Department, which already has established and well-marketed exploration courses, but now our department also wants to develop courses of its own. The idea is to have a total of four courses where each is given every two years, and the first newly developed course will be about statistics and be given in the autumn of 2019. There will be statistical applications of different societal problems and insights in how a statistician thinks. The fourth course is still at the idea stage, but may be about the history of mathematics. But why give scientific training courses at all?

Elin: It is of advantage to society, maybe especially the statistics, which many people have poor knowledge of, while statistics is often used to back up various statements. We reach out to other students than we usually do and can give them a different picture of mathematics than what they might have, that it does not have to be a heavy subject but can be fun as well. Hopefully they will be more interested in mathematics and science. For us teachers it is also good, we can immerse ourselves in new areas and meet other types of students.

Torbjörn: Ultimately, it is a matter of democracy and transparency. We need to be visible to gain the confidence of the public to continue working with mathematics, also with areas of mathematics which are not always easy to explain. The difficult part so far with this exploration course is to find the balance between the difficult and the simple, the serious and the showy, the new and the familiar and between lecture and discussion. About future courses, I would very much like to see an exploration course on unsolved mathematical problems. I am sure it would be titillating enough to become popular! 

Text: Setta Aspström
Photo: Elin Götmark and sextant, Setta Aspström
Torbjörn Lundh, private

Page manager Published: Mon 16 Apr 2018.