Arithmetic, Algebra, Analysis

Více o knize

These three volumes represent the first complete English translation of Felix Klein's influential series, Elementarmathematik vom hoheren Standpunkte aus. This translation is significant for two reasons: it includes the previously untranslated volume III and offers a complete revised version of volumes I and II, which had previously omitted several parts of the original text. Published between 1902 and 1908, these volumes are based on lecture notes from courses Klein taught to future mathematics teachers, introducing a new approach to teacher training that remains relevant today. Klein guides students toward a comprehensive and methodological understanding of school mathematics, illustrating his concept of "elementarisation" from a higher standpoint. Volume I focuses on what Klein refers to as the three big A's: arithmetic, algebra, and analysis, always integrating geometric interpretation and visualization, reflecting his belief in mathematics as rooted in spatial intuition. A notable example of elementarisation is his discussion on the transcendence of "e" and π, where he provides concise and accessible proofs. In this volume, Klein famously addresses the gap between mathematics education in schools and universities, emphasizing his goal to bridge this discontinuity.