Princeton University Press
Calculus Reordered: A History of the Big Ideas
Key Metrics
- David M Bressoud
- Princeton University Press
- Hardcover
- 9780691181318
- 9.3 X 6.1 X 0.9 inches
- 1.25 pounds
- Mathematics > Calculus
- English
Secure TransactionBook Description
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 calculus's birth in the Hellenistic Eastern Mediterranean--particularly in Syracuse, Sicily and Alexandria, Egypt--as 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 calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order--integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment.
Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
Author Bio
David Bressoud is Director of the Conference Board of the Mathematical Sciences. He is now Dewitt Wallace Professor Emeritus at Macalester College, having served on the faculty from 1994 to 2020.
He is also a former President of the Mathematical Association of America, a Fellow of the American Mathematical Society, and a Fellow of the American Association for the Advancement of Science. He served in the Peace Corps, teaching math and science at the Clare Hall School in Antigua, West Indies before studying with Emil Grosswald at Temple University and then teaching at Penn State for 17 years.
He chaired the Department of Mathematics and Computer Science at Macalester from 1995 until 2001. He has held visiting positions at the Institute for Advanced Study, the University of Wisconsin-Madison, the University of Minnesota, Université Louis Pasteur (Strasbourg, France), and the State College Area High School.
David has received the MAA Gung and Hu Award for Distinguished Service to Mathematics, the MAA Distinguished Teaching Award (Allegheny Mountain Section), the MAA Beckenbach Book Award for Proofs and Confirmations, and has been a Pólya Lecturer and a Leitzel Lecturer for the MAA. He is a recipient of Macalester's Jefferson Award. He has published over sixty research articles in number theory, combinatorics, special functions, and mathematics education. His other books include Factorization and Primality Testing, Second Year Calculus from Celestial Mechanics to Special Relativity, A Radical Approach to Real Analysis (now in 2nd edition), A Radical Approach to Lebesgue's Theory of Integration, Calculus Reordered: A History of the Big Ideas, A Course in Computational Number Theory (with Wagon), and Calculus: Graphical, Numerical, Algebraic (with Demana, Waits, Kennedy, & Boardman).
David has chaired the MAA special interest group, Teaching Advanced High School Mathematics as well as the AP Calculus Development Committee and has served as Director of the FIPSE-sponsored program Quantitative Methods for Public Policy and PI for two NSF-sponsored national studies of Calculus: Characteristics of Successful Programs in College Calculus (NSF #0910240) and Progress through Calculus (NSF #1430540).
A native of Pennsylvania, David lives in Saint Paul, Minnesota with his wife, Jan.
Source: davidbressoud.org
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