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This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.
The Invention of the Mathematical Formula.- Numbers, Distances, Points, but No Crooked Lines.- Lines and Variables.- Individual: An Old Term, or What Does the Continuum Consist of?.- Are There Infinite Numbers? - An Unresolved Argument Between Leibniz and Johann Bernoulli.- Johann Bernoulli's Rules of Differential.- What Does "Equal" Mean?.- Euler Absolutizes Formal Arithmetic.- Accents in Algebraic Analysis, According to Euler.- Bolzano: The Republican Revolutionary of Analysis.- Cauchy: The Bourgeois Revolutionary as a Restorer.- The Interregnum: Analysis on Swampy Ground.- Weierstrass: The Last Attempt at a Substantial Analysis.- The Detachment of Analysis from Reality, and the Introduction of Actual Infinity into the Fundamentals of Mathematics.- Analysis With or Without Paradoxes.
Description
This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.
