What Is Calculus About? by W. W. Sawyer (PDF)

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Book by Sawyer, W. W.

User’s Reviews

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

⭐It all began one winter’s night.Forty years ago and one month on the February winter night of the lunar eclipse in North America in 1968 was the day I began to read W.W. Sawyer’s “What is Calculus About?” And my life was forever changed.I had never read a style of writing up to that point on any topic that exuded as much confidence, as much philosophy of learning and conveyed as much mystery, the mystery of how to handle infinity as that deceptively small book.I had known about the concept of infinity but up to that point did not know that you could calculate with it. That is take limits. Take derivatives. Then work backwards. But when Sawyer explained it it was like watching a professional magician. There was it could be said a “fresh rebelliousness” in his attitude toward Mathematics understanding and its teaching. It was as if reading his words got you directly in contact with the minds of Newton and Leibnitz and other mathematicians of that “happy-go-lucky” era that Sawyer talks about in his book.Everyone had warned me at the time that I wouldn’t be able to learn Calculus on my own. That it was this mathematics that was so special that it was for many impossible to learn especially if you studied it by yourself. That is was somehow an unattainable goal. That I would somehow “ruin” my learning. It was amazing the degree of prejudice that at that time prevailed.But they were all wrong. I ended up mastering it. And then the “fur really began to fly”. I wasn’t supposed to have understood it. I was as one science ( later to be my physics teacher) teacher said: “in way over my head…and if I didn’t watch it I’d wind up ruining my career…life..you name it.” It was the sixties, the 1960’s and my parents generation were total reactionaries. My mother got all hysterical and dragged some of my mathematics books ( unbeknownst to me ) down to the school to the principal and was jumping up and down insisting that I might need psychiatric help. The mathematics teacher of the high school went absolutely berserk with much the same tirade as the physics teacher had. It was to say the least embarassing. All over something they reaqlly didn’t understand.And that is exactly what humanity at it’s very best is like. If they don’t understand it, “watch out”. Because it’s like Einstein said:” always the brilliant minds are persecuted by those minds who are of a simple, pedestrian nature.” ( that’s not a perfect quote but it will do)But through it all there was W.W. Sawyer. You might say he helped me “get through” the sixties. ( I had other heroes too ) In a strange way you could compare him to Dylan at that time ( my other big hero).(And it could be rightfully argued that Sawyer was in fact part of that 1960’s “beat generation” of scholars who were trying to tell society and the Education Establishment that maybe as far as learning they the accepted teaching establishment had got it wrong.)Then there was his bibliography and references at the back. That had me spell-bound as well. His fearlessness about mentioning taboo items like Tensor Analysis and General Relativity had me spellbound. ( again the so-called teachers around me assured me that only 12 people in the whole world understood relativity….what kind of scholarly statement does that sound like?). You see if you tried to understand it, Relativity, in their logic that is referring to the teachers and professors in my backwater little community, it meant you were crazy.And then a few years later I would stop doing mathematics and physics for almost forty years. Only to pick it up recently once again.The memories of that time are truly haunting.Truly one of the greatest Mathematics teachers ever.Simply mystic stuff. No less.With Best RegardsSouthern Jameson Westp.s. they hated me for liking Dylan as well.p.p.s. one of the first to learn General Relativity and master it almost as soon as it was published was also a teenager. Wolfgang Pauli.

⭐Well all I can say about Sawyer is that he made me realize what mathematics was about. While one did not ignore whatone learned at school, Sawyer made you realize that there was more to mathematics then the stuff you did at school.The mathematics you did at school was not enough in it self to explain what mathematics was about.This all the more important in this century where people think the calculator and computer are quite sufficient in understanding mathematics. So while one welcomes the advances, one would be very foolish indeed to ignore the genuine side of the discipline. We owe Sawyer a great deal, a lot more than we realize.

⭐This is a small book on reviewing the essential points in calculus. It is not to be used as a sole book for the study of calculus but could be used as a helper along with textbooks. It has a clear explanation and sufficient amount of exercise problems

⭐My 1st semester calculus prof said that I would either get calculus, or not. I didn’t feel anything. Eventually I moved on to Geology, where I have; made sort of a living for 40 years, had some great times, met some great people, and generally developed a negative attitude towards engineers.Finally, I bought this book which led me through a brilliant demonstration of the derivation of a limit. If you are beginning in calculus and feeling lost, buy this book. Once you grasp the basics of calculus, you can try something more honorable than engineering; maybe even geology.

⭐He lived in the 1800’s and quickly became a legendary teacher with the ability to break down complex math concepts into information that made sense. W.W. Sawyer wrote several math books and this is one of his popular ones still sought after and very valuable today.A friend of mine who recommended this book to me and has retires from career teaching math in public schools and was the head of the math department said, “I had taken calculus in college but this little book finally made it all make sense for me!”

⭐A very good book. Plenty with examples presented in a simple form that makes a very difficult subject possible to understand. I can recomend this book to any one who whish to learn what calculus is all about.

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