Calculus Reordered: A History Of The Big Ideas - 9780691181318

How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to change Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculusÆs birth in the Hellenistic Eastern Mediterraneanùparticularly in Syracuse, Sicily and Alexandria, Egyptùas well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculusÆs evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical orderùintegration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalitiesùmakes more sense in the classroom environment. Exploring the motivations behind calculusÆs discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.

• | Author: David M. Bressoud
• | Publisher: Princeton University Press
• | Publication Date: Jul 16, 2019
• | Number of Pages: 242 pages
• | Language: English
• | Binding: Hardcover/Mathematics
• | ISBN-10: 0691181314
• | ISBN-13: 9780691181318