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brailsafe

> We assume no math knowledge beyond what you learned in calculus 1

Anyone got recommendations for self-studying and testing Calculus 1?

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Calculus Made Easy - 1910. It is even entertaining.

"What One Fool Can Do, Another Can. (Ancient Simian Proverb.)"

https://calculusmadeeasy.org/

They are probably terrible for self-study, but I want to mention them anyway. I am a huge fan of David Bressoud’s Calculus (and analysis!) books. His first one doesn’t have exercises and his second one has a lot of physics.

They are all heavy on written narrative and interlaced with history. I find all four of them absolutely fascinating.

Calculus: https://www.amazon.com/Calculus-Reordered-History-Big-Ideas/...

https://www.amazon.com/Second-Year-Calculus-Undergraduate-Ma...

Analysis:

https://www.amazon.com/Approach-Analysis-Mathematical-Associ...

https://www.amazon.com/Lebesgues-Integration-Mathematical-As...

Better explained[1] articles that explain the “what” part, such as the meaning of “e”, from the first principles.

I have a reasonable handle on Calculus-1 but those articles really helped me connect the dots. After reading them I realized that all I knew was “how” without having a clue about “what”

[1] https://betterexplained.com/

1) go into knowing that the terminology is the hardest part to learn. The arithmetic is fairly easy, but the word salads can get daunting.

2) khan academy, coursera, MIT open courseware, whatever books your library has. Piece together multiple sources, b/c you don't have a professor to ask questions to, you'll need all the different sources and how each source explains the same idea differently for everything to 'click'.

I refreshed on linear algebra and multi variable calculus through Khan Academy before I took a theory-based machine learning class. For me, it was a really good experience and I can’t overstate my appreciation for Sal Khan’s teaching style.

I found the book "Calculus: a complete course" very nice. It's very cheap and extremely unpretentious while also giving you a subtle taste of a bunch of interesting applications (Deep learning... bleh, give me electromagnetism!)

Nothing beats taking a good university class on it - https://ocw.mit.edu/courses/mathematics/18-01-single-variabl...

To begin, try to get a really high level explanation for differential and integral calculus. Look at videos, illustrations, etc.

Then, once you have a mental image of what you will be doing, get into the math from the ground up.

When I was like 14 years old one one my math teachers explained to us what calculus was using zero equations. He made everything look really easy.

At college, it was the complete opposite. My professor started with limits and convergence, didn't even bother to explain why we were studying the subject.

Kudos for people who actually explain things.

I never got a high level explanation for what calculus was because the business model of my school involved having a passing rate below 30%. If the passing rate was too high, teachers got fired no matter what the reason was.

My high school physics teacher explained calculus to me by plotting a velocity curve, then saying the tangential line at a point (derivative) is acceleration and the area from 0 to that point under the curve (integral) was the distance travelled. Made all of calculus very easy for me to grok going forward.

I missed the day where the word tangent must have been explained, then failed basic trigonometry and felt like an idiot for the rest of high school.

I found outlier.org to be fantastic.

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