Mathematical Stories II - Recursion, Divisibility and Proofs / essentials (PDF)

With the help of tried and tested, carefully elaborated learning units, the authors convey fundamental mathematical techniques in this essential, which are important far beyond primary school. In the present Volume II, the Gaussian summation formula and a recursion formula are derived and applied. Tasks on divisibility, prime factors and divisors follow. For calculating with remainders, the modulo calculation is introduced and applied. Students learn to perform proofs in a variety of contexts. As in Volume I, "Graphs, Games and Proofs", the tasks encourage mathematical thinking, imagination, and creativity. The detailed sample solutions are designed for non-mathematicians.

This book is a translation of the original German 1st edition Mathematische Geschichten II - Rekursion, Teilbarkeit und Beweise by Susanne Schindler-Tschirner and Werner Schindler, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

The Content

. Mathematical techniques and tasks

. Detailed sample solutions

The Target Groups

. Leaders of study groups as well as support courses for mathematically gifted students in grades 3 and 4, teachers who practice differentiated mathematics lessons.

. Committed parents for extracurricular support

The Authors

Susanne Schindler-Tschirner is a philologist and after studying to become a teacher, she was a project manager at a science publisher. She works in the field of student development and is the author of didactics-oriented publications.

Werner Schindler has a PhD in mathematics. He is head of section at the Federal Office for Information Security (BSI) and adjunct professor in the mathematics department at TU Darmstadt.