A look at how calculus has evolved over hundreds of years and why calculus pedagogy needs to change

Calculus Reordered tells the remarkable story of how calculus grew over centuries into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, how it was shaped by Italian philosophers such as Galileo Galilei, and how its current structure sprang from developments in the nineteenth century. Bressoud reveals problems with the standard ordering of its curriculum--limits, differentiation, integration, and series--and he argues that a pedagogy informed by the historical evolution of calculus represents a sounder way for students to learn this fascinating area of mathematics. From calculus's birth in the Hellenistic Eastern Mediterranean, India, and the Islamic Middle East, to its contemporary iteration, Calculus Reordered highlights the ways this essential tool of mathematics came to be.

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