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Kalid from BetterExplained here, glad you like it! I had similar confusions; despite years of engineering classes, I didn't build an intuition for Calculus unt

by kalid 10y ago

Kalid from BetterExplained here, glad you like it! I had similar confusions; despite years of engineering classes, I didn't build an intuition for Calculus until a decade later. It felt like such a waste. (Yes, I could memorize rules; but could I visualize the product and quotient rule?) I decided to Elon Musk It™ and reason from first principles (http://betterexplained.com/articles/honest-learning/ http://betterexplained.com/articles/honest-learning/). What would a learning plan look like, assuming limited motivation, a need for genuine understanding, and goal of starting with appreciation and moving to proficiency? Just like learning music, I'd listen to the song, then clap along to it, then play a few chords along with the band, then learn a bit of music notation, and then practice playing it. I wouldn't start with scales (er... limits) for weeks on end. Not if I was honest about my motivations. Ultimately, we have to acknowledge the approach that helps us. For me, investing a few hours of exploration before the formalities is well worth it.

petra 10y ago
Kalid, thanks for your amazing content! Reading this from the link you provided:"In my ideal world, every Wikipedia topic would have a guide that took you from the 1-minute version to a full technical understanding. Go as far as you wish, make meaningful progress at each step, and have fun along the way.". Have you though how to build/scale it ? Because it would seem like an amazing site, and maybe a good startup.
- defen 10y ago
  > "In my ideal world, every Wikipedia topic would have a guide that took you from the 1-minute version to a full technical understanding. Go as far as you wish, make meaningful progress at each step, and have fun along the way." This is my biggest gripe with Wikipedia for mathematical topics - as it stands, it's only useful if you already know the material, in which case you probably shouldn't be using wikipedia as a reference / refresher except as a last resort.
  - kalid 10y ago
    Exactly. Wikipedia helps me remember things I've forgotten, but it's slow going when trying to learn a new topic. The first paragraph includes a set of links that you recursively follow.
- kalid 10y ago
  Thanks Petra! I've been kicking around ideas for an "intuitive wikipedia", guides explicitly (and realistically) designed to get you from curiosity to mastery. Wikipedia has a few problems: * Too much detail for beginners (to be fair, it's a reference, not a tutorial) * Too difficult to contribute. Even excellent contributors have to fight to get changes in. * Generic, boring, academic "tone of voice" (kills the fun for me) Previously I'd tried to make apps, forums, etc. to help aggregate this, but it was over-engineering. My idea: 1) Have a topic like the Fourier Transform 2) Write a tutorial (http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/ http://betterexplained.com/articles/an-interactive-guide-to-...) 3) Collect feedback [see comments on article], examples, diagrams, etc. Make it easy to contribute an insight. 4) Weave the final result into an honest, realistic guide from curiosity to mastery. (I don't have one built yet for the Fourier Transform.) I'd prefer to organically grow the guide out of our shared experience vs. "imagining" what a hypothetical student needs. (The hypothetical student should study limits for weeks, then derivatives, then integrals. In my experience it's the other way around.) For scaling, getting the first few right should hopefully make a template others can take and run with. As long as we're dealing with text, it's infinitely editable and updatable. (Why are we so enamored with video? We can't fix our inevitable mistakes!) I'd love to chat more if you like! Just ping me at kalid.azad@gmail.com.
Sakiina_ 10y ago
This looks amazing, and is so timely! I'm taking a supply chain management class. Though the pre-reqs said basic algebra was fine, they mention a lot of Calculus and I feel like I'm not fully understanding the material without it. One of my biggest frustrations about learning math is that I don't get the concept, and it makes it hard for me to just work through equations. So your approach looks fantastic to me. The motivation level and how much time is available-- that's exactly what I need. The 1 minute breakdown was perfect. I learned something immediately, and more importantly-- I was then excited and intrigued about learning. I seriously can't thank you enough for this.
- kalid 10y ago
  That's awesome to hear, thank you. The goal of education should be to spark the fire so we learn more. Really glad to hear the intro made the rest more intriguing :).
shams93 10y ago
Yes this is really the best course on calculus I've ever run across thank you so much for this amazing guide!
- kalid 10y ago
  Thank you!
skapadia 10y ago
Kalid - also your explanation of complex numbers is absolutely amazing. Sure I could manipulate them by memorizing rules, but I never really knew what they meant or why they were important. I also love the Numberphile explanation of quaternions (building up from real to complex numbers, etc.) - https://www.youtube.com/watch?v=3BR8tK-LuB0 https://www.youtube.com/watch?v=3BR8tK-LuB0 -Sujan
- kalid 10y ago
  Thanks Sujan! I've been poking around with quaternions, appreciate the pointer :).
pitaa 10y ago
I just wanted to jump in here and add that trig never made sense to me until I read your "Intuitive Trigonometry" page. I was well in to calculus and (even after getting an A in my college trig class) suddenly realized that I didn't have even the slightest idea what a sine, cosine, or tangent actually was. Some googleing led me to your page and it suddenly made sense!

by kalid 10y ago

petra 10y ago

Kalid, thanks for your amazing content! Reading this from the link you provided:"In my ideal world, every Wikipedia topic would have a guide that took you from the 1-minute version to a full technical understanding. Go as far as you wish, make meaningful progress at each step, and have fun along the way.". Have you though how to build/scale it ? Because it would seem like an amazing site, and maybe a good startup.

defen 10y ago
> "In my ideal world, every Wikipedia topic would have a guide that took you from the 1-minute version to a full technical understanding. Go as far as you wish, make meaningful progress at each step, and have fun along the way." This is my biggest gripe with Wikipedia for mathematical topics - as it stands, it's only useful if you already know the material, in which case you probably shouldn't be using wikipedia as a reference / refresher except as a last resort.
- kalid 10y ago
  Exactly. Wikipedia helps me remember things I've forgotten, but it's slow going when trying to learn a new topic. The first paragraph includes a set of links that you recursively follow.
kalid 10y ago
Thanks Petra! I've been kicking around ideas for an "intuitive wikipedia", guides explicitly (and realistically) designed to get you from curiosity to mastery. Wikipedia has a few problems: * Too much detail for beginners (to be fair, it's a reference, not a tutorial) * Too difficult to contribute. Even excellent contributors have to fight to get changes in. * Generic, boring, academic "tone of voice" (kills the fun for me) Previously I'd tried to make apps, forums, etc. to help aggregate this, but it was over-engineering. My idea: 1) Have a topic like the Fourier Transform 2) Write a tutorial (http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/ http://betterexplained.com/articles/an-interactive-guide-to-...) 3) Collect feedback [see comments on article], examples, diagrams, etc. Make it easy to contribute an insight. 4) Weave the final result into an honest, realistic guide from curiosity to mastery. (I don't have one built yet for the Fourier Transform.) I'd prefer to organically grow the guide out of our shared experience vs. "imagining" what a hypothetical student needs. (The hypothetical student should study limits for weeks, then derivatives, then integrals. In my experience it's the other way around.) For scaling, getting the first few right should hopefully make a template others can take and run with. As long as we're dealing with text, it's infinitely editable and updatable. (Why are we so enamored with video? We can't fix our inevitable mistakes!) I'd love to chat more if you like! Just ping me at kalid.azad@gmail.com.

Sakiina_ 10y ago

This looks amazing, and is so timely! I'm taking a supply chain management class. Though the pre-reqs said basic algebra was fine, they mention a lot of Calculus and I feel like I'm not fully understanding the material without it. One of my biggest frustrations about learning math is that I don't get the concept, and it makes it hard for me to just work through equations. So your approach looks fantastic to me. The motivation level and how much time is available-- that's exactly what I need. The 1 minute breakdown was perfect. I learned something immediately, and more importantly-- I was then excited and intrigued about learning. I seriously can't thank you enough for this.

kalid 10y ago
That's awesome to hear, thank you. The goal of education should be to spark the fire so we learn more. Really glad to hear the intro made the rest more intriguing :).

shams93 10y ago

Yes this is really the best course on calculus I've ever run across thank you so much for this amazing guide!

kalid 10y ago
Thank you!

skapadia 10y ago

Kalid - also your explanation of complex numbers is absolutely amazing. Sure I could manipulate them by memorizing rules, but I never really knew what they meant or why they were important. I also love the Numberphile explanation of quaternions (building up from real to complex numbers, etc.) - https://www.youtube.com/watch?v=3BR8tK-LuB0 https://www.youtube.com/watch?v=3BR8tK-LuB0 -Sujan

kalid 10y ago
Thanks Sujan! I've been poking around with quaternions, appreciate the pointer :).

pitaa 10y ago

I just wanted to jump in here and add that trig never made sense to me until I read your "Intuitive Trigonometry" page. I was well in to calculus and (even after getting an A in my college trig class) suddenly realized that I didn't have even the slightest idea what a sine, cosine, or tangent actually was. Some googleing led me to your page and it suddenly made sense!