Hans Niels Jahnke's Books

A History of Analysis

By: Hans Niels Jahnke

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Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.

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Page Count

434

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821826239

ISBN 13

9780821826232

Infinite Series in a History of Analysis

Stages up to the Verge of Summability

By: Hans-Heinrich Körle

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Infinite Series in a History of Analysis

Stages up to the Verge of Summability

By: Hans-Heinrich Körle

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.

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174

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110399164

ISBN 13

9783110399165

A History of the Central Limit Theorem

From Classical to Modern Probability Theory

By: Hans Fischer

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A History of the Central Limit Theorem

From Classical to Modern Probability Theory

By: Hans Fischer

This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.

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415

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387878572

ISBN 13

9780387878577

A History of Analysis

By: Hans Niels Jahnke

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A History of Analysis

By: Hans Niels Jahnke

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434

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American Mathematical Soc.

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ISBN 10

0821826239

ISBN 13

9780821826232

Explanation and Proof in Mathematics

Philosophical and Educational Perspectives

By: Gila Hanna,Hans Niels Jahnke,Helmut Pulte

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Explanation and Proof in Mathematics

Philosophical and Educational Perspectives

By: Gila Hanna,Hans Niels Jahnke,Helmut Pulte

In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.

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289

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441905766

ISBN 13

9781441905765

Explanation and Proof in Mathematics

Philosophical and Educational Perspectives

By: Gila Hanna,Hans Niels Jahnke,Helmut Pulte

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Explanation and Proof in Mathematics

Philosophical and Educational Perspectives

By: Gila Hanna,Hans Niels Jahnke,Helmut Pulte

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294

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Springer

Published Date

ISBN 10

1441905758

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9781441905758

Traditions in German-Speaking Mathematics Education Research

By: Lisa Hefendehl-Hebeker,Hans Niels Jahnke

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Traditions in German-Speaking Mathematics Education Research

By: Lisa Hefendehl-Hebeker,Hans Niels Jahnke

This open access book shares revealing insights into the development of mathematics education research in Germany from 1976 (ICME 3 in Karlsruhe) to 2016 (ICME 13 in Hamburg). How did mathematics education research evolve in the course of these four decades? Which ideas and people were most influential, and how did German research interact with the international community? These questions are answered by scholars from a range of fields and in ten thematic sections: (1) a short survey of the development of educational research on mathematics in German speaking countries (2) subject-matter didactics, (3) design science and design research, (4) modelling, (5) mathematics and Bildung 1810 to 1850, (6) Allgemeinbildung, Mathematical Literacy, and Competence Orientation (7) theory traditions, (8) classroom studies, (9) educational research and (10) large-scale studies. During the time span presented here, profound changes took place in German-speaking mathematics education research. Besides the traditional fields of activity like subject-matter didactics or design science, completely new areas also emerged, which are characterized by various empirical approaches and a closer connection to psychology, sociology, epistemology and general education research. Each chapter presents a respective area of mathematics education in Germany and analyzes its relevance for the development of the research community, not only with regard to research findings and methods but also in terms of interaction with the educational system. One of the central aspects in all chapters concerns the constant efforts to find common ground between mathematics and education. In addition, readers can benefit from this analysis by comparing the development shown here with the mathematical education research situation in their own country. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

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282

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ISBN 10

1013271823

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9781013271823

Book's by Hans Niels Jahnke

A History of Analysis

A History of Analysis

Infinite Series in a History of Analysis

Infinite Series in a History of Analysis

A History of the Central Limit Theorem

A History of the Central Limit Theorem

A History of Analysis

A History of Analysis

Explanation and Proof in Mathematics

Explanation and Proof in Mathematics

Explanation and Proof in Mathematics

Explanation and Proof in Mathematics

Traditions in German-Speaking Mathematics Education Research

Traditions in German-Speaking Mathematics Education Research

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