De Gruyter Textbook- Infinite Series in a History of Analysis

Infinite series are the unifying thread that runs through the history of mathematical analysis. Ever since the 17th century, they have also been inseparably linked to infinitesimal calculus, and form its backbone. This book includes the historical reflections, insights and outlooks that serve to deepen the student's understanding of analysis. "Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had helped it to a first high point when they mastered the infinite. The book traces the history of analysis along the risky route of serial procedures through antiquity. It took quite long for this type of mathematics to revive in our region. When and where it did, infinite series proved the driving force. Not until a good two millennia had gone by, would analysis head towards Greek rigor again. To follow all that trial, error and final accomplishment, is more than studying history: It provides touching, worthwhile access to advanced calculus. Moreover, some steps beyond convergence show infinite series to naturally fit a wider frame.