Calculus Reordered: A History of the Big Ideas by David M. Bressoud (PDF)

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 changeCalculus 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Most texts just start with Newton and Leibniz and take off running. This gives very good historical perspective and, in that context, makes the topic much more understandable.

⭐I have used calculus and differential equations for years and “thought” I knew how it worked. Reading this book showed me that I had learned the ideas in “reverse order” from how they were historically discovered or devised. This is NOT just more information. Going through the gradual mathematical developments over the years, in the order that they happened, gave me a much better insight into what calculus was devised to do and what kinds of problems it can now be used for given “recent” improvements.

⭐An excellent overview of the development of mathematical analysis. Serves as an excellent supplement to a real analysis or rigorous calculus book.

⭐This is basically a history book that is very heavy in mathematics. The author shows how some of the concepts of calculus were arrived at from ancient times onwards – thus making the point that calculus did not suddenly sprout in its entirety from the minds of Newton and Leibnitz in the seventeenth century.I found the book to be very well written in a prose that is clear, friendly and authoritative. The book contains many mathematical arguments, derivations, illustrations and proofs. The author has tried to reproduce these as they were first developed through history by the originators. Consequently, I found some of them seem to be rather awkward and different from how we would develop them today. I found some of the mathematics to be clear and easy to follow but some of it to cause me a lot of head scratching. Eventually, I found myself carefully sifting through what I considered to be the most interesting stuff while skimming over what I found to be much less interesting.Overall, I believe that this is really quite a fascinating book that would likely be most appreciated by students of calculus, educators who teach the subject in college and university as well as very serious general readers.

⭐My son loved this as a gift!

⭐This is basically a history book that is very heavy in mathematics. The author shows how some of the concepts of calculus were arrived at from ancient times onwards – thus making the point that calculus did not suddenly sprout in its entirety from the minds of Newton and Leibnitz in the seventeenth century.I found the book to be very well written in a prose that is clear, friendly and authoritative. The book contains many mathematical arguments, derivations, illustrations and proofs. The author has tried to reproduce these as they were first developed through history by the originators. Consequently, I found some of them seem to be rather awkward and different from how we would develop them today. I found some of the mathematics to be clear and easy to follow but some of it to cause me a lot of head scratching. Eventually, I found myself carefully sifting through what I considered to be the most interesting stuff while skimming over what I found to be much less interesting.Overall, I believe that this is really quite a fascinating book that would likely be most appreciated by students of calculus, educators who teach the subject in college and university as well as very serious general readers.

⭐A clear, engaging, and informative history of calculus, analysis, and measure theory. I found the story truly fascinating. I studied these topics in university but I never knew much about how calculus, analysis, and measure theory came to be. Calculus Reordered answers who, how, and why developed these subjects. I would strongly recommend this book to people interested in the history of science. A fair warning, this book assumes that readers have been exposed (maybe long ago :)) to calculus, analysis, and measure theory.

⭐Com sua abordagem sem-par, esse livro tem grande valor como referência para todos aqueles que se interessam pelo Cálculo, especialmente no que tange seu desenvolvimento histórico. Recomendo.

⭐

⭐Muy buen libro, para inspirarse en cálculo.

⭐

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