Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

I liked this simple calculus exercise

blog.plover.com

Post reply on HN
Print view View original

141–150 of 163 posts

Re: I liked this simple calculus exercise

#141

Post by mrguyorama »

mjd wrote: post #90
kaba0 wrote: post #55

Earlier quoted context omitted.

One of my professors used to say that “even a horse can do derivatives. Integration is the real deal”, another one said that you integrate by “look at it, deeply, deeply, deeply; and then solve it”. The point is, many part of high school math is actually really “algorithmic”. I was one of the few in my class who absolutely loved coordinate geometry over “normal” geometry, because I simply felt really comfortable with…

> “look at it, deeply, deeply, deeply; and then solve it” That's the Feynman method: write down the question, think really hard, then write down the answer. Only three simple steps! Unfortunately, some of us are not Feynman.

I actually hit this personally, because right up UNTIL calculus, math was the Feynman method for me. Everything always just clicked, made perfect sense, and I saw the beauty in it, and it was great fun.

Then for calculus, we learned concepts, like what a derivative is, and I understood that, and understood conceptually (as in, what everything "means" and what it tells you) but I could never take that concept knowledge to the practice problems with me.

I could follow along as the professor walked us through a problem, showing us what heuristics helped and what patterns to follow and how to manipulate the functions to get to something that followed one of the patterns to pull an answer out of your ass, but I could never commute those heuristics and patterns to novel examples. It's weird because I was great at doing the exact same thing for physics: Taking a novel and purposely opaque problem and finding which pattern it corresponds to.

Re: I liked this simple calculus exercise

#142

Post by mrguyorama »

justeleblanc wrote: post #124
privacyking wrote: post #65

That technique won't scale if you're trying to integrate some crazy complex function.

Exam questions have two wonderful property: they have an answer, and the person who wrote it knows that you have the knowledge to find the answer.

Nope, good teachers understand when the question they wrote thinking to test certain concepts falls flat, because of some unforeseen oversight or quirk. Something being clear and intuitive to a math professor is not the same as something being clear and intuitive to the students.

The best professors strike and ignore questions that "failed", ie didn't accurately test what they thought they would.

Re: I liked this simple calculus exercise

#143

Post by whoami_-h »

petschge wrote: post #128
AlecSchueler wrote: post #110

Earlier quoted context omitted.

Sounds like something ChatGPT could do quite quickly though.

Quickly maybe. But to do it well you need a deep understanding of the material which is something that large language models lack.

[dead]

Re: I liked this simple calculus exercise

#144

Post by andrewflnr »

deanCommie wrote: post #131
angry_moose wrote: post #108

Earlier quoted context omitted.

I remember there being a distinct lack of "closing the loop" on concepts in university math. Day 1 of the class: The derivative calculates the slope of a function Day 2: The integral calculates the area under the curve of the function Days 3-89: Rote exercises deriving and integrating increasingly obscure functions Day 90: Final Exam Spending a few days at the end re-exploring the "big picture day-1" to tie together…

It's interesting because I was going to argue with you until I applied the same idea to a subject I couldn't care less about if I tried in school, but now think is deeply fascinating: History. See, I loved math. So all through Calculus I could easily remember the big picture. Every time I practiced an Integral I imagined curves and calculating the areas under them and the visual problem and the relevance of what the…

I think history is potentially even easier. Everyone asks "why?" about things being the way they are, or can be interested in it if you remind them that things could be otherwise. History is the answer to "why?" for a huge number of things with both small and huge life and death consequences. Put another way, "why" is a good framing for a lot of big picture history stuff.

Re: I liked this simple calculus exercise

#145

Post by justeleblanc »

mrguyorama wrote: post #142
justeleblanc wrote: post #124

Earlier quoted context omitted.

Exam questions have two wonderful property: they have an answer, and the person who wrote it knows that you have the knowledge to find the answer.

Nope, good teachers understand when the question they wrote thinking to test certain concepts falls flat, because of some unforeseen oversight or quirk. Something being clear and intuitive to a math professor is not the same as something being clear and intuitive to the students. The best professors strike and ignore questions that "failed", ie didn't accurately test what they thought they would.

I don't quite see how that's relevant to what I said.

Re: I liked this simple calculus exercise

#146

Post by mrguyorama »

justeleblanc wrote: post #145
mrguyorama wrote: post #142

Earlier quoted context omitted.

Nope, good teachers understand when the question they wrote thinking to test certain concepts falls flat, because of some unforeseen oversight or quirk. Something being clear and intuitive to a math professor is not the same as something being clear and intuitive to the students. The best professors strike and ignore questions that "failed", ie didn't accurately test what they thought they would.

I don't quite see how that's relevant to what I said.

>the person who wrote it knows that you have the knowledge to find the answer.

This isn't always true. The person who wrote it only knows what they taught, not what you have learned. The point of the test is to find what you have learned.

This is just a nitpick I think.

Re: I liked this simple calculus exercise

#147

Post by sizzle »

sizzle wrote: post #137
angry_moose wrote: post #108

Earlier quoted context omitted.

I remember there being a distinct lack of "closing the loop" on concepts in university math. Day 1 of the class: The derivative calculates the slope of a function Day 2: The integral calculates the area under the curve of the function Days 3-89: Rote exercises deriving and integrating increasingly obscure functions Day 90: Final Exam Spending a few days at the end re-exploring the "big picture day-1" to tie together…

I wish I could give this comment hold, straight up put me off math because of this lack of real world application in lower level calc and adhd brain craving meaning and substance.

*Gold

Re: I liked this simple calculus exercise

#148

Post by BeFlatXIII »

postsantum wrote: post #138
deanCommie wrote: post #131

Earlier quoted context omitted.

It's interesting because I was going to argue with you until I applied the same idea to a subject I couldn't care less about if I tried in school, but now think is deeply fascinating: History. See, I loved math. So all through Calculus I could easily remember the big picture. Every time I practiced an Integral I imagined curves and calculating the areas under them and the visual problem and the relevance of what the…

Funny enough, I ended up with the opposing view - history doesn't matter, narratives do. During the last year I learned about propaganda, psy ops and myths much more than I knew before. And at the risk of sounding as an edgy teenager, I can vouch for the phrase "History is written by victors" which stopped being a platitude for me and became a part of my worldview

I prefer the existentialist "history is written by those who write history." Often, the victors give themselves a better justification for their conquest than admitting that someone bigger and badder may eventually dethrone them. However, some losers write histories praising their new overlords and their incredible military might, not out to gain favor with the new king but to preserve the dignity of the old king. The defeat was inevitable because of the invader's futuristic military powers aided by the Gods (instead of admitting the old king had no strategy).

Re: I liked this simple calculus exercise

#149

Post by deanCommie »

postsantum wrote: post #138
deanCommie wrote: post #131

Earlier quoted context omitted.

It's interesting because I was going to argue with you until I applied the same idea to a subject I couldn't care less about if I tried in school, but now think is deeply fascinating: History. See, I loved math. So all through Calculus I could easily remember the big picture. Every time I practiced an Integral I imagined curves and calculating the areas under them and the visual problem and the relevance of what the…

Funny enough, I ended up with the opposing view - history doesn't matter, narratives do. During the last year I learned about propaganda, psy ops and myths much more than I knew before. And at the risk of sounding as an edgy teenager, I can vouch for the phrase "History is written by victors" which stopped being a platitude for me and became a part of my worldview

You're not wrong but what's the difference between history and narratives?

"History" is the study of different narratives to TRY to come to a semblance of truth, but even for recent events this is almost impossible.

Pick an example like "Did the US dropping the nuclear bomb on Japan ultimately save lives, or was it unnecessary" and it's impossible to find the truth between 2 conflicting narratives, each fairly justifiable.

Another one is, most Soviet Anti-American Propaganda was true.

Re: I liked this simple calculus exercise

#150

Post by sn9 »

kaba0 wrote: post #96
wholinator2 wrote: post #75

Earlier quoted context omitted.

I think this experience is typical of self teaching from a math textbook. It's extremely difficult to find a good book that leaves no gaps while simultaneously explaining everything that might be difficult to understand. The key thing when encountering this for me is to expand my horizons and begin looking for videos or other supplementary materials. A teacher would show you the proof, or at least help you along the…

Thanks! My only gripe is that I just don’t know a logical order to follow through with math.. this is somehow less of a problem in other subjects. That said, I have been long thinking about a dependency graph for knowledge, where the nodes are great books on the topic.

You just have to look at the university curricula for a few universities' math programs.

Then find the syllabus for each course and look at the recommended textbooks.

You should be able to find the best ones that way.

Post reply on HN