Infinite series in a history of analysis : stages up to the verge of summability /
Körle, Hans-Heinrich.
Infinite series in a history of analysis : stages up to the verge of summability / Hans-Heinrich Körle. - 1 online resource (150 pages) - De Gruyter Studium . - De Gruyter textbook. .
Includes bibliographical references and index.
Frontmatter -- 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.
"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.
English.
3110359839 (electronic bk.) 9783110359831 (electronic bk.) 9783110399165 (electronic bk.) 3110399164 (electronic bk.)
838149 MIL
Series, Infinite.
Mathematics--Philosophy--History.
Séries infinies.
Mathématiques--Philosophie--Histoire.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Mathematics--Philosophy.
Series, Infinite.
Electronic books.
History.
QA295 / .K75 2015eb
515/.243
Infinite series in a history of analysis : stages up to the verge of summability / Hans-Heinrich Körle. - 1 online resource (150 pages) - De Gruyter Studium . - De Gruyter textbook. .
Includes bibliographical references and index.
Frontmatter -- 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.
"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.
English.
3110359839 (electronic bk.) 9783110359831 (electronic bk.) 9783110399165 (electronic bk.) 3110399164 (electronic bk.)
838149 MIL
Series, Infinite.
Mathematics--Philosophy--History.
Séries infinies.
Mathématiques--Philosophie--Histoire.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Mathematics--Philosophy.
Series, Infinite.
Electronic books.
History.
QA295 / .K75 2015eb
515/.243