Surprising functions and other features

Irregular functions and functional equations
Prof. Dr. H.-H. Kairies, TU Clausthal

Real functions are discussed, some of which are far from being differentiable.
Examples:
a) Continuous, nowhere differentiable functions, linked to the names Weierstrass, Tagaki, Knopp, Wunderlich,
b) Riemann's famous function, which is differentiable exactly at certain rational points,
c) Singular functions (i.e. (i.e. continuous, monotonically increasing functions that have the derivative zero almost everywhere), associated with the names Cantor, Minkowski, de Rham.
The choice of functions is motivated by two facts:
1) Their irregularity, which is difficult to grasp graphically, has fascinated mathematicians for more than a hundred years and has given rise to many works on the fine structure of real functions.
2) They all satisfy a system of simple functional equations and, on the other hand, can be characterized as a unique solution of this system.

Surprises - from amazement to understanding
Prof. Dr. Wilfried Herget, University of Halle-Wittenberg

Amazement at the unexpected, the surprising, the memorable: this arouses attention, interest, triggers curious questioning and targeted exploration right up to the clarifying resolution of the original tension - an excellent anchor for the joy of questioning and research and for sustainable learning. Numerous examples for the classroom will be presented and actively "lived through".

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