Calculus Reordered
by David M. Bressoud · first published 2019
100% recommend
Why HN recommends it
Historical account of how calculus's core ideas developed, including the logic behind its peculiarities. It provides useful context for working through calculus and suits readers who want the story behind it.
Summarised by Claude from recommending comments
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--especiall
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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…
on “Ask HN: Any recommendation for a good History of Science book?” ↗…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...
on “The matrix calculus you need for deep learning (2018)” ↗…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 described Napier logs/natural ln(x) too
on “An Intuition for Logarithms” ↗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…
on “On Leibniz Notation” ↗> 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…
on “A balanced review of Math Academy” ↗…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…
on “Calculus for the Curious” ↗