Frans Keune
Institute for Mathematics, Astrophysics and Particle PhysicsFaculty of Science
Radboud University
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands (postal address)
Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands (visiting address)
e-mail: keune@math.ru.nl
Elements of Higher Mathematics
Learning Mathematics through Numbers
Elements of Higher Mathematics is a translation of the Dutch Getallen. It is based on lectures for first year mathematics students. The construction of the number system all the way from Peano to the complex numbers is the common thread. Contains extra material as well: combinatorics, quadratic reciprocity, primality tests, p-adic numbers, continued fractions, representation by binary quadratic forms. The book is published in 2024 by the Radboud University Press and is freely downloadable.
Number Fields
Number Fields is based on courses Number Theory, Algebraic Number Theory and Class Field Theory. It covers the algebraic number theory up to and including the main theorems of class field theory. The book is published in 2023 by the Radboud University Press and is freely downloadable.
Tuning Educational Structures in Europe
In 1999 in Bologna the ministers of education of 29 European countries agreed a common bachelor-master structure for higher education. In 2001-2002 I participated in the EU-project Tuning Educational Structures in Europe in which for seven subjects/disciplines a framework has been developed for the bachelor-master structure. In the project 101 universities participated. The math group formulated its ideas for a common framework in the document
It is just the common vision of the members of the group and not an official document. On the other hand this project is the only project on this scale and it already had some influence on reforms in higher education in mathematics in several European countries. For more information on the project consult the website of the Tuning Academy.