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.

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.

The writings and example of Isaac Newton transformed understandings of the practice and meaning of the sciences across Europe in the centuries following the publication of the Principia in 1687. The essays in these volumes consider the impact of Newton's ideas from three distinct but interlocking perspectives: their reception in particular geographical areas and language communities; their importance for particular fields of intellectual and practical endeavour, and their influence on other thinkers who, in turn, shaped Newton's intellectual legacy. They provide, for the first time, a picture of the fate of Newton's work across mainland Europe, giving an account of Newton's influence in the humanities, arts and social sciences, as well as in mathematics, physics and the natural sciences in general.

Carl Gustav Jakob Jacobi (1804 - 1851) gilt heute nach C. F. Gauss und neben P. G. Lejeune Dirichlet als der wichtigste deutsche Mathematiker der ersten Halfte des 19. Jahrhunderts. Als Vertreter der "reinen" Mathematik machte er sich v. a. durch seine Beitrage zur Zahlentheorie und Theorie der elliptischen Funktionen einen Namen. Jacobi leistete jedoch auch wesentliche Beitrage zur Analytischen Mechanik, die er in der Tradition Eulers, Lagranges und Hamiltons v. a. als einen Zweig der hoheren Analysis betrachtete.Den umfassendsten und authentischsten Einblick in seine Anschauungen zu dieser Disziplin geben seine "Vorlesungen uber analytische Mechanik", Jacobi las diese Vorlesung im Wintersemester 1847/ 48 in Berlin; es handelt sich um seine letzte Veranstaltung zur Mechanik uberhaupt. Jacobis Schuler Wilhelm Scheibner (1826 - 1907) fertigte eine vollstandige und sorgfaltige Mitschrift dieser Vorlesung an. Der Text wurde von Helmut Pulte editiert und mit Einleitung und Kommentar versehen.