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I would recommend watching 3Blue1Bown series on calculus. Its very easy to understand and somes with some great visuals.

https://www.youtube.com/watch?v=WUvTyaaNkzM

The perfect video companion to learning Calculus is 3blue1brown’s Essence of Calculus series: https://youtu.be/WUvTyaaNkzM

To answer your main question - "what level of maths" do you need is more about what topics: a couple introductory classes in Calculus, Linear Algebra, and Discrete Mathematics will make that sentence understandable.

I'll give some definitions and resources, but think about how you would explain multiplication/division/algebra to a kid. At some point, you just have to work through some problems and the math just makes sense. So I'll explain the terms above, but best bet is to just take a few courses on the topics I mentioned above.

Quick definitions: - Exponential: is the constant e to the power of some number. e, like pi, is a ubitiqous constant in mathematics and nature. You run into pi when doing geometry, and e when doing calculus.

- A function in mathematics is similar to a function in programming, but not exactly. A course in Discrete Mathematics helps here.

- F-apostrophe is notation used in calculus to show the relation of one type of function, called a derivative to another. f and f' are related. How, though, is better explained by taking calculus.

- An eigenfunction exists in a system of equations. Think of it like a 'balance' point. Linear Algebra will help make sense of this term.

Resources - Essence of Calculus: https://www.youtube.com/watch?v=WUvTyaaNkzM - Essence of Linear Algebra: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...

Those 2 video's will do a good job of giving you the 'intuition' behind Calculus and Linear Algebra. Like programming, though, you just have to actually work some problems out by hand for the stuff to sink in. For that, do something like MIT opencourseware or a local online college course.

3blue1brown channel on calculus:

https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...

Well, there's always 3Blue1Brown: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw Take a look at his course, Essence of Calculus: https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ... I'm not fluent in math, but I find it fascinating to watch, for some reason. NancyPi is also great: https://www.youtube.com/channel/UCRGXV1QlxZ8aucmE45tRx8w Oh, and don't forget the Mathologer: https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg What a great guy! While I'm at it, go watch Numberphile too: https://www.youtube.com/user/numberphile Is there anyone I forgot? :D

I know of no better way to both learn, truly understand, and enjoy calculus than the visual approach of 3Blue1Brown in the Calculus series of videos: https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...

⬐ edjrage

I swear one day I'm going to write a WebExtension whose sole purpose is to auto pin comments about 3B1B's videos on calculus and linear algebra HN threads.

⬐ hackermailman

I found the best way to truly understand and enjoy calculus was to learn it as it was historically developed https://youtu.be/HRD9X-2Bmdw and then learning about the problems they ran into and how we ended up with modern Calculus after Euler and Lagrange tried to correct these problems https://youtu.be/fCZ8jJCVinU (these lectures cover Stillwell's book Mathematics and it's History)

Interesting in the second lecture is how Australia does 'photo radar' on one stretch of highway, where it records you going through a gate at one point, then many kilometers away records you again from another gate, then establishes your average velocity between the two gates using Calculus and sends you a ticket if your calculated average shows you must have exceeded the speed limit during some point between the gates.

⬐ krick

> best way to truly understand and enjoy calculus was to learn it as it was historically developed

In fact, I'd argue it's the best way to understand almost anything, especially in math. Many topics I found somewhat confusing at school or university or whatever got really simple once I learned about their history. Little by little I come to feel that most of great inventions or discoveries made by people we regard as geniuses are often brilliant at how clear, beautiful and somewhat unexpected the solution was, but it's actually very rarely complicated and usually seems like the most natural thing in the world, when told about how Fourier/Laplace/Leibniz/etc discovered it, and not hidden behind standard school math curriculum.

That's a part of why I love 3Blue1Brown videos so much, and why I love Morris Kline books. And it always makes me kind of sad feeling how much time I wasted trying to come to terms with something that always was just unnatural explanation.

⬐ gshubert17

Morris Kline's book "Calculus: An Intuitive and Practical Approach" is still in print. I prefer the paper version because the Kindle version has many formatting problems.

Grant (the 3Blue1Brown guy) has an uncanny ability to explain difficult concepts and the fundamental intuition behind them. In many of his videos, he explains topics from the perspective of a person inventing that topic (such as in his first Calculus video [1]). I can't recommend his videos enough.

[1] https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...

⬐ haskellandchill

It works for a lot of people, I'm just looking for something else, exercise-based computer-checked proofs to teach mathematics, something like that. Want it bad.

+1

And definitely follow through his "pause and ponder" sections. If you want to build up your maths skills, it is crucial to learn how to think in the maths way. Like becoming a good programmer involves writing lots of code yourself, or to become a good dancer you need to practice your steps. For maths it's abstract thinking. Appreciation of maths is one thing, having the discipline to self-study a whole other.

Edit. Regarding your 2nd Edit: His videos are made for the broadest audience possible. I'd recommend picking any video whose topic interests you the most at the moment. You will see what knowledge you lack (take notes of these!) and can expand from there. Be it to watch his maths fundamental ((1)) series [0],[1] or just rewatch.

((1)): As in any other things, knowing your fundamentals is significant to the understanding of a topic. It won't help you at all if you can apply (copy paste) some machine learning techniques if you don't know about linear algebra at all.

[0]: https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

[1]: https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...

https://www.youtube.com/watch?v=WUvTyaaNkzM

check out this series (he also has a really good one on linear algebra)

After that, I'd check out Khan academy.

⬐ mrcactu5

this book seems to complement the earlier HackerNews book about the "Calculus Made Easy" -- that is certainly the book I first learn from... it really tries just to get the basic ideas across without being too careful.

I look at it now, this book is wonderful. https://news.ycombinator.com/item?id=14161876

⬐ nafizh

This is just wonderful. I watched his essence of linear algebra series, and that just opened up a whole new universe I never knew existed. I was yearning something like this for calculus. I am salivating at the thought of watching these. Better finish my work.