Happy 4th of July

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crfriend
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Re: Happy 4th of July

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pelmut wrote:I've always felt that calculus is related to mathematics in the same way that astrology is related to astronomy.
In a rare sublimely lucid moment a few years back [0] I actually glimpsed the inner workings of calculus several years ago and was floored by its utility and its value. Unfortunately, I've not had one of those since, so I'm back to doing simple things like trigonometry and basic algebra.

I recall my late partner commenting on my absolute phobia about mathematics. She asserted that I worked it very well in day-to-day activities and had a reasonably established ability with it -- which astonished me. I'd been coasting along for years with the detritus of my Standardised Test Scores knocking about in my head and ignoring reality. My Standard Test Scores (the SATs in the US) unequivocally stated that I should have been an English major; I was Hell-bent on going into computing, which was still regarded as a mathematician's field. I feel I beat the odds on that count, but am still wary of "advanced" math.


[0] "A few years back" in this context refers to the time I was reading one of my late partner's mathematics textbooks which described calculus and its applications whilst I was commuting by rail to Boston. This means that it was likely in the mid-to-late 1990s. In fact I recall the instant when I glimpsed it; we were passing through Natick near a lake and I made some sort of startled noise and sat straight up -- and folks wanted to know what had happened.
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Re: Happy 4th of July

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Definition: Mathematics - the abstract science of number, quantity, and space, either as abstract concepts ( pure mathematics ), or as applied to other disciplines such as physics and engineering ( applied mathematics ).

Definition: Calculus - the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.

So calculus definitely comes within the realms of mathematics. Having used calculus in some very practical situations I can vouch for this.
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Re: Happy 4th of July

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pelmut wrote:I've always felt that calculus is related to mathematics in the same way that astrology is related to astronomy.
Say more. Does the concept of limits seem unscientific?
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Re: Happy 4th of July

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Jim wrote:
pelmut wrote:I've always felt that calculus is related to mathematics in the same way that astrology is related to astronomy.
Say more. Does the concept of limits seem unscientific?
Calculus (the way it was taught to me) seemed to be misusing numbers to do something they weren't really meant to do. I know calculus is a really useful tool, but the way I was introduced to it gave me the same sort of feeling I would get from watching someone breaking up a working machine with a sledge hammer and building a meaningless sculpture from the bits.
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Re: Happy 4th of July

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I was introduced using graphical methods and rates of change of things. Maybe you were just taught in a way that wasn't right for you.
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Re: Happy 4th of July

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pelmut wrote:
Jim wrote:
pelmut wrote:I've always felt that calculus is related to mathematics in the same way that astrology is related to astronomy.
Say more. Does the concept of limits seem unscientific?
Calculus (the way it was taught to me) seemed to be misusing numbers to do something they weren't really meant to do. I know calculus is a really useful tool, but the way I was introduced to it gave me the same sort of feeling I would get from watching someone breaking up a working machine with a sledge hammer and building a meaningless sculpture from the bits.
Calculus made good sense to me, and seemed useful from the beginning. But the most advanced math class I took, Differencial Equations, I never understood. I got an "A", but all I learned was how to choose and apply the right formula.
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Re: Happy 4th of July

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Jim wrote:..Calculus made good sense to me, and seemed useful from the beginning. But the most advanced math class I took, Differencial Equations, I never understood. I got an "A", but all I learned was how to choose and apply the right formula.
That's the crux of the matter, they tried to teach us that way and I just could not do it like that. I could never remember formulæ, but I could work them out from basic principles - if only they had taught the basic principles properly. That ability has served me in good stead in the course of my career as an inventor and design engineer; I'm often dealing with things for which there are no well-known formulæ and I have to make up my own.
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Re: Happy 4th of July

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pelmut wrote:
Jim wrote:..Calculus made good sense to me, and seemed useful from the beginning. But the most advanced math class I took, Differencial Equations, I never understood. I got an "A", but all I learned was how to choose and apply the right formula.
That's the crux of the matter, they tried to teach us that way and I just could not do it like that. I could never remember formulæ, but I could work them out from basic principles - if only they had taught the basic principles properly. That ability has served me in good stead in the course of my career as an inventor and design engineer; I'm often dealing with things for which there are no well-known formulæ and I have to make up my own.
That's the way it was for me as well, constantly working things out from principles rather than remembering by rote. Drove my high school deductive geometry teacher nuts because I'd skip all her classes except the tests, which during that term were all just proving theorems. I didn't open the text book she was "teaching" from because it might spoil the fun. I wanted to see the statement then prove it cold. Once she gave me zero for a proof, and then I realised that she didn't understand the subject matter herself. She was just teaching the textbook, maybe renaming some sides and angles but not much else. I protested and made her review my proof, telling her I knew it was perfect. I wasn't really that precocious but that zero got my back up, especially when she said "that's not the proof in the book, did you really think you could pass my class with no study?" I forced her to admit that there isn't just one proof for any theorem. It took her a few days to get back to me with my new mark of 100%. I think she had to take it to the head of the department, because she couldn't do it herself. I also recall being outraged at being expected to learn to use trig tables but not first how to derive them.

This ability served me well as a technician and designer of circuits and systems that engineers couldn't seem to bring in on a budget at all, and as a troubleshooter of last resort for all kinds of problems in my field or not.
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Re: Happy 4th of July

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Shades of Carl Friedrich Gauss, eh?
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Re: Happy 4th of July

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Caultron wrote:Shades of Carl Friedrich Gauss, eh?
Well, maybe the Trailer Park Boys version. :cyclops:
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