“All the little bits”
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My intro to calculus came in the form of a battered copy of a 1979 historical calculus textbook by W.M. Priestley, it was significantly easier to understand than any of the usual intro to calculus textbooks that I’ve seen.
https://link.springer.com/book/10.1007/978-1-4684-9349-8
Worth tracking down a copy if you’re planning to learn calculus, mine saw me through undergrad calc handily.
The symbols are the most intimidating part of mathematics for me. They are beautiful and mysterious.
The author of these paragraphs summarizes it very nicely. It takes a lot of talent to break things down like this, I wish more math textbooks were written this way.
I recommend this video as well:
Is the from a book by Sylvanus P. Thompson?
The online version can be found at https://calculusmadeeasy.org/
35 years after graduating from engineering school, this book helped me finally understand why calculus works, instead of just learning how to mechanically apply it.
I’ve always just thought of it as derivatives describe the rate of change and integrals the total of whatever it is that has been done.
Like if we’re talking about an x that describes position in terms of t, time, dx/dt is the rate of change of position over change in time, or speed. Then ddx/dt is change in speed over change in time, or acceleration. And dddx/dt is rate of change in acceleration over change in time (iirc this is called jerk). And going the opposite way, integrating jerk gets acceleration, then speed, then back to position. But you lose information about the initial values for each along the way (eg speed doesn’t care that you started 10m away from the origin, so integrating speed will only tell you about the change in position due to speed).
That’s how I thought of it too. I really liked calculus; being able to measure another part of the graph was interesting to me.
There was a lovely computer science book for kids I can’t remember the name of, and it was all about the evil jargon trying to prevent people from mastering the magical skills of programming and algorithms. I love these approaches. I grew up in an extremely non/anti-academic environment, and I learned to explain things in non-academic ways, and it’s really helped me as an intro lecturer.
Jargon is the mind killer. Shorthands are for the people who have enough expertise to really feel the depths of that shorthand and use it to tickle the old familiar neurons they represent without needing to do the whole dance. It’s easy to forget that to a newcomer, the symbol is just a symbol.
The most annoying thing about learning networking and security are all the acronyms! Sometimes it feels like certification tests are testing acronym memorization more than real concepts.
Definitely are.
In a way it makes sense because the industry loves its acronyms and you’ll be using them.
On the other hand, I have the ability to search. I’m an IT professional, I will have a computer. Let me let the computer do the lookup. Its the old “you won’t have a calculator with you all the time” argument that was dated when my teachers told it to me.
I must not use jargon.
Jargon is the mind-killer.
Jargon is the little-death that brings total confusion. I will face the jargon. I will permit it to pass over me and through me. And when it has gone past I will turn the inner eye to see its path. Where the jargon has gone there will be clarity. Only sense will remain.
Jargon is the little-death
Somewhere in France someone is getting really excited about learning jargon.
I love this. Thanks for sharing.
Good luck with the lecturing. :)
Whenever people talk about evil jargons, or “anti-dummies” wording, the first thing that comes into my mind is lawspeak. You know, how fucking laws are worded, which are anything but obvious to people that only speak “peasant”. It’s worse than academic jargon because it’s something that is likely to be used against you.
Yeah, I may be wrong but I think it usually comes down to a very specific kind of precision needed. It’s not meant to be hostile, I think, but meant to provide a domain-specific explanation clearly to those who need to interpret it in a specific way. In law, specific jargon infers very specific behaviour, so it’s meant to be precise in its own way (not a law major, can’t say for sure), but it can seem completely meaningless if you aren’t prepped for it.
Same thing in other fields. I had a professor who was very pedantic about {braces} vs [brackets] vs (parentheses), and it seemed totally unnecessary to be so corrective in discussions, but when explaining where things went wrong with a student’s work it was vital to be able to quickly differentiate them in their work so they could review the right areas or understand things faster during a lecture later down the line.
But that noise takes longer to teach through, so if it is important, it needs it’s own time to learn, and it will make it inaccessible to anyone who didn’t get that time to learn and digest it.
Calculus is just piling stones.
“dMonica in my life”
All the little bits by my side…
“All the, derivatives. True care. Truth brings.”
I would’ve absolutely paid more attention in maths if the learning material was this utterly contemptuous of “ordinary mathematicians” haha
also full Project Gutenberg text is here https://calculusmadeeasy.org/, thanks for sharing!
Mille mercis !
I’m a chemical engineer and I now better understand calculus slightly better from this post. I did a whole lot of “okkayyy …let’s just stick to the process and wait for this whole thing to blow over”
I know what they were asking me to do but I never really fully understood everything.
I also studied chemical engineering, and throughout high school and university that was exactly it. Calculus was a kind of magic, and you just had to learn all the spells.
With this book I finally understood why the derivative of x^2 is 2x.
Ok I’m no mathematician but I’ll still can’t see why d(x^2) = 2x.
This exact explanation is in the book: https://calculusmadeeasy.org/4.html
I tried to figure it out myself back in high school but the best I came up with is X^2 -->2x because it just fucking does.
okkayyy…let’s just stick to the process and wait for this whole thing to blow over
This is such a classic engineer brain solution to the problem. It just warms my heart.
This reading actually helped me understand calculus a bit better, thanks for sharing!
Honestly, me too! You’re welcome :)
I bought this book when I was taking calc based physics. I never thought I would laugh so much at a math book! Educational and hilarious!
Can an idiot ask what book that is?
calculus made easy?
lol, in my defence I used to be in print publishing and I didn’t catch that. I did say idiot.
That said, that’s ambiguous design and I’ll be briefly uncomfortable on that hill.
I have finally discovered my niche content: math texts that are irreverent and also defiantly uncomplicated.
Read “a mathematicians lament”, by Paul Lockhart. It was originally a short essay (25 pages you can find free online), but expanded into a book that I haven’t read yet.
In a similar vein is Shape, by Jordan Ellenberg.
I read a short paper called “Lockheart’s Lament”, but I didn’t realize he had expanded on it. I might have cried about that one. Thanks for the reccomendations!
Thank you for this beautiful example of using “defiantly” correctly!
He defiantly used it properly, definitely.
Math is never irrelevant
Irreverent not irrelevant
What’s this about the ears on an elephant?
A little confused, but they’ve got the spirit.
Great, now I understand also this
Heck yeah, the standard model.
It’s a Lagrangian, so you can’t approach it directly with Newtonian mechanics.
To be fair, a formula that foreboding should only be approached indirectly, no matter what you’re armed with. I recommend sneaking up behind it.
Now it only rest to include Gravity. Well, tomorrow maybe
This is the nicest I’ve seen this info presented.
They didn’t even need to draw a chart of decreasing deltas and partitions, or talk about tangents and secants.
