4 ms·

What resources are you using to learn calculus? I am on a similar boat

solardev 3y ago
I'm taking a class at the local community college. It's OK, just some class notes and an e-textbook that I never bother to read. The pedagogy is much as I remember it, the teacher going through the problems on a whiteboard and expecting everyone to rote-memorize things. But mostly, I'm learning from ChatGPT. You can enter (or take a picture of) any problem and ask it to break it down step by step and it does that very well, and explains it better than most resources I've found. There are some OK YouTube or KhanAcademy videos too, but overall I prefer ChatGPT for its higher signal to noise ratio. At home I'll usually ask ChatGPT to explain the first one of a problem type, then try to do it again on my own and double-check it against the posted answers. For subsequent problems, I'll do it myself first (pen and paper or iPad), check it for correctness, and then ask ChatGPT for a breakdown if I screw up. I can usually tell it the mistake I made (i.e. how come I got X in step Y) and it can often correctly guess and explain where I went wrong. Some examples (keep in mind that I'm still working up to calc, so still in pre-calc right now!): * Breaking down the quadratic formula and explaining imaginary numbers: https://chat.openai.com/share/b267e954-fa0b-46ea-8fd6-11f71a346293 https://chat.openai.com/share/b267e954-fa0b-46ea-8fd6-11f71a... * Explaining properties of logs: https://chat.openai.com/share/01d79b4f-81b4-46b3-9767-be93b76a9edf https://chat.openai.com/share/01d79b4f-81b4-46b3-9767-be93b7... * e and natural logs: https://chat.openai.com/share/fbb3f957-ed6f-4c1a-af95-917d0e7be453 https://chat.openai.com/share/fbb3f957-ed6f-4c1a-af95-917d0e... * Word problems: https://chat.openai.com/share/502f7a91-9c2c-4c74-834a-5c791aa209dd https://chat.openai.com/share/502f7a91-9c2c-4c74-834a-5c791a... ----------------- Overall, I find this method of learning math (by rote memorization and parroting) very unsatisfying, and I'm unable to retain most of it in long-term memory. A few days after I learn anything I already forget how to do it. I ended up with an A in the class mostly just cramming the night before + morning of, using ChatGPT and class notes to refresh myself before the tests. But IMO it's a terrible way to learn (at least for me) and part of why I hate math. I never really learn the whys and wherefores of anything, it's just a bunch of magic shortcuts and black-box algorithms that I have to memorize and re-use without any actual understanding. It's the educational equivalent of solving every problem with someone else's function/library :( I have no idea why anything works the way it does, only that I must remember it and re-use it exactly. If anyone has a better approach to learning and retaining this stuff, I'm all ears!
- slekker 3y ago
  I've been considering paying for an LLM to augment my learning, for when I get stuck or can't figure something out. In terms of courses I am looking at Khan Academy but also https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/ https://ocw.mit.edu/courses/18-01sc-single-variable-calculus... (haven't started so I cant speak for quality)
  - solardev 3y ago
    The LLMs completely changed education for me. Whether it's math or music theory or programming, I'd rank ChatGPT amongst the best teachers I've ever known. (There are amazing real-human ones too, but it's really hit and miss!). For $20/mo it's totally worth it, way cheaper than tutoring or buying more textbooks. But for infrequent use, probably the free plan is enough...? I tried MIT OCW but found the videos too long and tedious... it's hard for me to just sit still and listen to videos like that for hours =/ I chose an in-person math class on purpose just to have that real community feel and a live teacher, but YMMV... probably many would prefer the online or async versions instead.
    - velyan 3y ago
      Would be very keen to know more about your learning experience and ideas to make it better. Would you be open to jump on a 15 mins call with me?
      - solardev 3y ago
        Hi! I'm probably not your target audience here, unless you're specifically developing a product that targets math education for midlife washouts, lol. But if you want some rando dude's opinion, sure, I'd be happy to jump into a call with ya. Just let me know and I'll find a slot on your Calendly. But I think you'd get better feedback from someone who's actually in your target audience/user demographic :) I'm just an annoying grumpy gramps who hates math.
  - velyan 3y ago
user5555 3y ago
I highly recommend the online book "Calculus at Moravian University", it does a pretty good job in building a fundamental understanding of calculus from the basics to multiple integration and vector calculus. I also used Joplin to take notes while reading, it's a notebook app where you can also use LateX (admittedly, many people won't like reading and taking notes on the phone, but I like it since it gives me a chance to learn even when you can't easily use books and laptop) https://webwork.moravian.edu/apexcalc/book-1.html https://webwork.moravian.edu/apexcalc/book-1.html

I'm taking a class at the local community college. It's OK, just some class notes and an e-textbook that I never bother to read. The pedagogy is much as I remember it, the teacher going through the problems on a whiteboard and expecting everyone to rote-memorize things. But mostly, I'm learning from ChatGPT. You can enter (or take a picture of) any problem and ask it to break it down step by step and it does that very well, and explains it better than most resources I've found. There are some OK YouTube or KhanAcademy videos too, but overall I prefer ChatGPT for its higher signal to noise ratio. At home I'll usually ask ChatGPT to explain the first one of a problem type, then try to do it again on my own and double-check it against the posted answers. For subsequent problems, I'll do it myself first (pen and paper or iPad), check it for correctness, and then ask ChatGPT for a breakdown if I screw up. I can usually tell it the mistake I made (i.e. how come I got X in step Y) and it can often correctly guess and explain where I went wrong. Some examples (keep in mind that I'm still working up to calc, so still in pre-calc right now!): * Breaking down the quadratic formula and explaining imaginary numbers: https://chat.openai.com/share/b267e954-fa0b-46ea-8fd6-11f71a346293 https://chat.openai.com/share/b267e954-fa0b-46ea-8fd6-11f71a... * Explaining properties of logs: https://chat.openai.com/share/01d79b4f-81b4-46b3-9767-be93b76a9edf https://chat.openai.com/share/01d79b4f-81b4-46b3-9767-be93b7... * e and natural logs: https://chat.openai.com/share/fbb3f957-ed6f-4c1a-af95-917d0e7be453 https://chat.openai.com/share/fbb3f957-ed6f-4c1a-af95-917d0e... * Word problems: https://chat.openai.com/share/502f7a91-9c2c-4c74-834a-5c791aa209dd https://chat.openai.com/share/502f7a91-9c2c-4c74-834a-5c791a... ----------------- Overall, I find this method of learning math (by rote memorization and parroting) very unsatisfying, and I'm unable to retain most of it in long-term memory. A few days after I learn anything I already forget how to do it. I ended up with an A in the class mostly just cramming the night before + morning of, using ChatGPT and class notes to refresh myself before the tests. But IMO it's a terrible way to learn (at least for me) and part of why I hate math. I never really learn the whys and wherefores of anything, it's just a bunch of magic shortcuts and black-box algorithms that I have to memorize and re-use without any actual understanding. It's the educational equivalent of solving every problem with someone else's function/library :( I have no idea why anything works the way it does, only that I must remember it and re-use it exactly. If anyone has a better approach to learning and retaining this stuff, I'm all ears!

slekker 3y ago
I've been considering paying for an LLM to augment my learning, for when I get stuck or can't figure something out. In terms of courses I am looking at Khan Academy but also https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/ https://ocw.mit.edu/courses/18-01sc-single-variable-calculus... (haven't started so I cant speak for quality)
- solardev 3y ago
  The LLMs completely changed education for me. Whether it's math or music theory or programming, I'd rank ChatGPT amongst the best teachers I've ever known. (There are amazing real-human ones too, but it's really hit and miss!). For $20/mo it's totally worth it, way cheaper than tutoring or buying more textbooks. But for infrequent use, probably the free plan is enough...? I tried MIT OCW but found the videos too long and tedious... it's hard for me to just sit still and listen to videos like that for hours =/ I chose an in-person math class on purpose just to have that real community feel and a live teacher, but YMMV... probably many would prefer the online or async versions instead.
  - velyan 3y ago
    Would be very keen to know more about your learning experience and ideas to make it better. Would you be open to jump on a 15 mins call with me?
    - solardev 3y ago
      Hi! I'm probably not your target audience here, unless you're specifically developing a product that targets math education for midlife washouts, lol. But if you want some rando dude's opinion, sure, I'd be happy to jump into a call with ya. Just let me know and I'll find a slot on your Calendly. But I think you'd get better feedback from someone who's actually in your target audience/user demographic :) I'm just an annoying grumpy gramps who hates math.
- velyan 3y ago

user5555 3y ago

I highly recommend the online book "Calculus at Moravian University", it does a pretty good job in building a fundamental understanding of calculus from the basics to multiple integration and vector calculus. I also used Joplin to take notes while reading, it's a notebook app where you can also use LateX (admittedly, many people won't like reading and taking notes on the phone, but I like it since it gives me a chance to learn even when you can't easily use books and laptop) https://webwork.moravian.edu/apexcalc/book-1.html https://webwork.moravian.edu/apexcalc/book-1.html