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Peter Stevenhagen

Mathematisch Instituut, Universiteit Leiden

Advanced Algebra · Nov 16 - Dec 2, 2023

I visited the Syed Babar Ali School of Science and Engineering at LUMS from November 15 to December 2, 2023, in my role of the international teacher in the Advanced Algebra course in the International Mathematics Master. This course uses the Algebra course notes that are part of the mathematics program at my home university in Leiden, the Netherlands. Roughly speaking, it was divided into three parts: group theory, taught by Dr. Imran Anwar, and ring theory, taught by Dr. Spela Spenko, and Galois theory, taught by me. As I already arrived halfway through the last week of Spela’s teaching, the continuity of the course was guaranteed.

They took active part in the ten lectures and tutorials during the two weeks I taught. Before leaving, I gave a final assignment (computation of actual Galois groups over the rationals using reduction modulo primes) which is due on December 13. There will be a final written exam on Galois theory on December 15.

My part of the course was followed for credit by 11 IMM students, and also by a handful of other interested master and PhD students.

My interaction with the IMM students was and still is very pleasant and friendly. With Charlene Kalle, we managed to take them out for dinner, still in the early phase of my lectures. Students were cooperative and hard-working, even though the material in this final part of the course is generally perceived as not so easy. Some, but not all students also asked me many questions outside the course. In addition, some of them came by to discuss their plans for the future. For me, it was very useful to hear firsthand what kind of challenges the students experienced, especially the female students who were thinking about a career in mathematics.

Of a slightly different nature, but in the same direction was the story that a student from Afghanistan, Marjan, told me about her experiences on leaving Kabul.

in 2022, after all, higher education for women had come to a complete standstill. She has more or less been saved by LUMS, and the question of whether some help of a similar nature can be organized for her former classmates is still on my mind.

In my second week of teaching, I was invited to Lahore Women’s College University, where Dr. Rehana Ashraf was an excellent host for me and the seven LUMS students who had come with me. I gave a talk on how it was to be a number theorist, touching upon the education it required, the career possibilities, and the ways in which number theory is applied in real life.

The invitation for lunch in my second week by Syed Babar Ali at his Packages plant was an unexpected high point of my visit. Meeting the visionary behind LUMS was a privilege, and I am pondering ways to forge further ties between LUMS and the Netherlands.

On the last Friday before I left, I spoke in the John Conway Spirited Seminar Series on Escher’s art, and more in particular on the mathematical phenomenon that underlies his 1956 lithograph Print Gallery. This talk, under the title Droste and Escher in Pakistan, featured video clips using the software developed by the Leiden number theory group. It did go into the occurrences of the so-called Droste effect in images taken from all over the world.

During my stay, I could also attend and take part in two meetings of the LUMS Math Circles, which focus on school kids of various ages. It was impressive to see how the enthusiasm of those giving the lectures, coupled with the support of LUMS master students in mathematics, incited interest and inspiration on the side of young people. Such initiatives, which also exist in some other countries, are essential to attract young bright minds to mathematics and change the stereotype of mathematics as being boring or overly complicated. The idea of stressing links with neighboring disciplines such as physics and astronomy, and including cultural and historical aspects of the story, strikes me as an important strategic choice that mathematicians of puzzle-solving inclination sometimes tend to overlook.

A word of thanks and appreciation should finally go to the support staff↵ of the LUMS math department, which made every aspect of my visit a totally smooth and

problem-free experience, and to Dr. Imran Anwar and Dr. Reza Abdolmaleki for being an excellent host.


Applicants are divided into two groups: "International Applicants" who have foreign citizenship and "Pakistani Applicants" who either hold Pakistani citizenship, have dual citizenship, or are Pakistanis residing outside the country.

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