“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.
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.
When I started algebra in something like 5th grade I had a huge issue with f(x) and the best answer my teacher gave me was that “the equation is a function of x” and couldn’t explain it differently and I couldn’t get over the fact that we are not multiplying whatever f is by X. “If we’re going to set precedent with notation at least be fucking consistent” - 5th grade me probably
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!
“dMonica in my life”
All the little bits by my side…
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.
This was so much me with the concept of generalized Cartesian product. All the class was very confused with that topic, until a bright classmate pointed-out a relationship of that concept with Python list and it started to do so much sense.
Removed by mod
Minor nitpick: the “d” is an operator, not a variable. So it’s “dx”, not “dx”… But there are so many textbooks that don’t get this right, that I’m aware that I’m charging windmills here.
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.
Is the from a book by Sylvanus P. Thompson?
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).
Calculus is just piling stones.
