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Calculus Made Easy by Silvanus P. Thompson (1910)

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Re: Calculus Made Easy by Silvanus P. Thompson (1910)

#11

Post by mlyle »

hotnfresh wrote: post #8
2OEH8eoCRo0 wrote: post #2

My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.

Late 30s here. I keep feeling like I should learn math better, but damn, I just never need it. It’s much easier to learn stuff I need. As it is, I’ve lost everything back to about 8th grade math because I’ve never used any of it, so it’s just as gone as all the French I used to know but never found an excuse to use. [edit] and I’m dreading my kids getting past elementary school math because they’re gonna be like “why…

Quadratics are useful-- finding dimensions of things in the plane; relating area and constrained side lengths, etc. They come up a lot if you want to solve problems.

And good luck taking on calculus without being super solid in the mathematical tools you use against quadratics -- factoring, completing squares, manipulation of binomials, pairing up like terms, etc.

Re: Calculus Made Easy by Silvanus P. Thompson (1910)

#12

Post by dvt »

Qem wrote: post #3

Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus…

I think I'd also prefer the infinitesimal version of calculus, but the idea of limits is applicable to many other areas of math, not just calculus (evaluating infinite series, for example). So learning limits is probably a better pathway to higher mathematics.

Re: Calculus Made Easy by Silvanus P. Thompson (1910)

#14

Post by JadeNB »

dvt wrote: post #12
Qem wrote: post #3

Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus…

I think I'd also prefer the infinitesimal version of calculus, but the idea of limits is applicable to many other areas of math, not just calculus (evaluating infinite series, for example). So learning limits is probably a better pathway to higher mathematics.

> I think I'd also prefer the infinitesimal version of calculus, but the idea of limits is applicable to many other areas of math, not just calculus (evaluating infinite series, for example). So learning limits is probably a better pathway to higher mathematics.

I'd say that limits in the sense that you mean (as opposed to category-theoretic limits) are precisely the domain of calculus or, if one wishes so to call it (because one is proving things!), analysis. For example, many US universities, mine included, regard the computation of infinite series as part of Calculus II.

Re: Calculus Made Easy by Silvanus P. Thompson (1910)

#15

Post by JadeNB »

hotnfresh wrote: post #8
2OEH8eoCRo0 wrote: post #2

My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.

Late 30s here. I keep feeling like I should learn math better, but damn, I just never need it. It’s much easier to learn stuff I need. As it is, I’ve lost everything back to about 8th grade math because I’ve never used any of it, so it’s just as gone as all the French I used to know but never found an excuse to use. [edit] and I’m dreading my kids getting past elementary school math because they’re gonna be like “why…

The quadratic equation is completing the square while inexplicably avoiding all the intuition of completing the square. For example, to solve x^2 + 6x + 5 = 0, you would re-write it as (x^2 + 6x + 9) - 4 = 0, which is (x + 3)^2 - 4 = 0 and hence equivalent to (x + 3)^2 = 4, so that x + 3 = ±2 and hence x = 3 ± 2 is 1 or 5. Euclid thought of things this way, though his language is, of course, very different to modern language; see, for example, Proposition 6 of Book II (http://aleph0.clarku.edu/~djoyce/elements/bookII/propII6.htm...).

That's the same answer as the quadratic formula, but makes a lot more sense to me! Of course I've cooked the numbers so that you don't wind up with surds in the answer, but those are just complications in bookkeeping, not in concept.

Re: Calculus Made Easy by Silvanus P. Thompson (1910)

#16

Post by wallflower »

My calculus teacher tried to talk me out of taking the AP Calculus AB exam because I wasn’t doing that well in his class. “Calculus the Easy Way” which teaches in the setting of a mythical fantasy world where applied problems are solved with calculus unlocked the secret of calculus for me. I ended up scoring a “4” which was a big triumph for me, as it placed me out of taking calculus with all the people who did not want to be taking calculus.

https://www.thriftbooks.com/w/calculus-the-easy-way-easy-way...

Re: Calculus Made Easy by Silvanus P. Thompson (1910)

#17

Post by finite_depth »

btilly wrote: post #7
Qem wrote: post #3

Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus…

I have mixed feelings about this. I've been through nonstandard analysis. My response was, "We shouldn't need the axiom of choice to define the derivative." But I think that it is extremely important to understand that the infinitesimal notation really MEANS something. Here is some Python to demonstrate. # d is a functor. It takes a function and returns a second function. # The second function captures the change in…

Most calculus students don't need the full formal power of rigorous analysis. Calculus, taken alone and with the elementary properties of the real numbers assumed and a few elementary properties of infinitesimals (0 <<< infinitesimal^2 <<< infinitesimal <<< any positive real), can get you a lot of power for very little formal work.

Re: Calculus Made Easy by Silvanus P. Thompson (1910)

#18

Post by del_operator »

I picked this book up when I was learning Algebra to see what the hype was about as a kid. It was dull. I went back to the library stacks after some weeks and found Calculus and Pizza to be even easier to swallow.

Calculus Made Easy is a good book. It made me appreciate even easier books when you need them and have enthusiasm for learning a topic.

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