Infinite series in a history of analysis : stages up to the verge of summability

"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. 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. Foreword Contents 1. The Greek era: Speculation, ideas and the comet of rigor 2. Successful experiments on infinite summation 3. Series of functions: the prototypes 4. Series seriously: the Greek comet reappears 5. On the verge of summability Appendixes (of notes, proofs, exercises) Life Data References Index Hans-heinrich Körle. Includes Bibliographical References And Index.