“All the little bits”
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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!
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 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!
I often find that I find mathematical concepts much easier to understand if they’re presented as Python code rather than math notation. Someone should write a book like that.
Algebraic notation breaks just about every rule programmers are taught about keeping their code human readable. For example:
- Variable and function names should be descriptive
- Don’t cram everything into one line
- Break up large statements
- Consistency is key
- Don’t be fancy for fancy’s sake, don’t over-optimize (this is for learning, remember?)
- Add in-line comments for lines that aren’t easily grasped
- Be explicit where possible (it’s a convention to omit the multiplication operator when multiplying variables because variables are only one letter anyway…)
And then we force kids to cram the whole stdlib (or rather its local bastardization) into their heads or at best give them intentionally bad (uncommented) documentation during exams while wondering why so many just don’t seem to get it, even resent it.
Very well put.
That’s an interesting notion.
For you, is it when it’s presented like:sum = sum([1,2,3]), or when it’s dropping in and explaining how the sum function is implemented?I think there’s definitely something there in either case, but teaching math through “how you would implement it in code” seems really interesting. You could start really basic, and then as you get to more complicated math, you keep using the tools you built before. When you get to those “big idea” moments, you could go back to your old functions and modify them to work in the new use case while still supporting the old. Like showing how
multiplication()needs to change to support complex numbers without making anything else different.I know this is just a simple example but sum() doesn’t teach you about the concept of sums. It would have to be something like:
def sum_up(my_list): result = 0 for item in my_list: result = result + item return resultThen you could run that through a debugger and see how the variables change at every step. That way you can develop an understanding of what’s going on there.
Yeah, thinking about it a bit more, I could have asked it as:
Is it seeing how it’s used with plain, more spelled out names that helps, or is it seeing how it works “under the hood” that makes it more clear?
Your answer clarifies things for me though, and I agree that that would be a really nice book/program/learning thing. :)
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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.
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
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.
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.
The symbols are the most intimidating part of mathematics for me. They are beautiful and mysterious.
