Name: Calculus Reordered
ISBN: 9780691181318

Calculus Reordered

Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, 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 presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in 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 instead that the historical order--which follows first 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.

What Hacker News says

SideQuarkApr 2025

> But should you learn integration before differentiation? I’d never considered this approach until I read David M. Bressoud’s fantastic book Calculus Reordered,

Ha, I learned calculus integration first from Ivan Niven's "CALCULUS An Introductory Approach," copyright 1961, that as a kid I found in the attic in my dads undergrad engineering books. When I got to high school and took calc, I was able to do all the stuff they were teaching, but in weird orders and methods compared to more modern books.

Now, 40+ years later, I still have that book on my bookshelf in the calculus section :)

Till now, it's it only book I've seen that teaches it this way.

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sirsinsalotJan 2024

I'm currently reading "Calculus Reordered: A history of the big ideas" by David M Bressoud, which really helped me contextualise all the peculiarities of calculus.

It really does feel like a hodgepodge of poorly fitting parts that could use some revision in terms of notation and teaching, but I feel like that's part of the charm.

I like that it encodes so much history and culture "up front". It reminds me of PHP. There is no way a good language designer would create PHP intentionally but as ugly as it was, it was brilliant in 1999. Index.php and you're done.

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hackermailmanSep 2023

Logs are linearized exponents so all the laws of exponents are the log laws: log(xy) is logx + logy. Logs are also a way to scale which is what they were originally used for to do large multiplication without electronic assistants. We log scale graph axis/plots all the time today. They also describe the shape of some processes hence come up in compsci like tree algos. If you have a logarithmic process and work increases by a million new inputs then actual work is only 6x increase. So log is also the number of zeros in a number

There's a book called Calculus Reordered by Bressoud that describes Napier logs/natural ln(x) too

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fslothFeb 2022

For "serious" studies - for mathematics there are lot of really good books that go through the evolution of the methodologies over the centuries - I've read David Bressoud's "Calculus Reordered" and John Stillwell's "Mathematics and it's history" and can recommend both.

For physics the field is so wide it's hard to pinpoint where to start. On Quantum Physics Jim Baggot's "The meaning of Quantum Theory" is the best introductory text by any measure for "mediacore academics" like myself. It tries to hand hold the reader through the firs steps of the historical evolution of quantum theory and why quantum theory is so weird as it is - as a physics MSc I wish I had read this book two decades ago :)

For "light" approach the newer "Cosmos" series is pretty damn good in highlighting some of the key scientific work of past centuries. Don't let the cute animation fool you, this is deep, deep stuff and the producers should be regarded among the top science communicators. I've never seen a better "generalist" explanation for Faraday's and Maxwell's work, the discovery Cepheid variable stars and lots of other stuff.

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ABeeSeaApr 2021

They are probably terrible for self-study, but I want to mention them anyway. I am a huge fan of David Bressoud’s Calculus (and analysis!) books. His first one doesn’t have exercises and his second one has a lot of physics.

They are all heavy on written narrative and interlaced with history. I find all four of them absolutely fascinating.

Calculus: https://www.amazon.com/Calculus-Reordered-History-Big-Ideas/...

https://www.amazon.com/Second-Year-Calculus-Undergraduate-Ma...

Analysis:

https://www.amazon.com/Approach-Analysis-Mathematical-Associ...

https://www.amazon.com/Lebesgues-Integration-Mathematical-As...

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pugioOct 2019

I just finished reading this, and thoroughly enjoyed it. It provides a clear description of the fundamental intuition at the heart of calculus (chop stuff up infinitely, then put it back together again), and a mix of the historical background of its development and its ancient and modern applications.

All books of this nature are somewhat idiosyncratic – it's not a history, not a textbook, nor an applied maths book; it's a packet of passion sent by someone who's clearly excited and enthralled with his topic: "Here's a story about something really cool! Maybe you'll think it's cool too!"

I've been investigating recent books with different approaches to calculus (trying to build a free online course that empowers people in maths). Here are some other books I can recommend/mention:

[0] "Burn Math Class: And Reinvent Mathematics for Yourself" Goes from 1+1 all the way to derivatives and integrals. My favorite work of math demystification and pedagogy.

[1] "Calculus Reordered: A History of the Big Ideas" Released this year, exactly as the title says. An accessible history, explaining each idea as it enters the world stage. I've only just started this, but it's a definitely more historically thorough, albeit less engaging, book than Infinite Powers. (Since historical accuracy seems to be TFA's main focus, I wonder what they would think of this book.)

[2] "Change Is the Only Constant: The Wisdom of Calculus in a Madcap World" Another just-published book – this is the year for Calculus! Amazon has lost/delayed my preordered copy, but from the author's other work I expect this to be a LOT of fun.

[3] "Magnificent Principia: Exploring Isaac Newton's Masterpiece" Sort of "the annotated Newton". Outlines Sir Isaac's history, social environment, and development of the Principia Mathematica. The bulk of this book is going through each section of the Principia, translating the language into modern speech/formulations (where needed), and explaining what Newton was getting at. Also not as gripping as Infinite Powers, but a great way of reading and understanding one of the most foundational scientific/mathematical texts of all time.

[4] "Introductory Calculus For Infants" I'm about to have my first child, so am naturally collecting suitable reading material for the budding babe (suggestions welcome!).

[0] https://amzn.to/2pVXJwj [1] https://amzn.to/2pMCZr5 [2] https://amzn.to/31Ny32e [3] https://amzn.to/2BIimyM [4] https://amzn.to/33ZxbJj

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