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Last year, I started writing about my experiences taking courses on machine learning and artificial intelligence. One of the big, unexpected problems I ran into was calculus and linear algebra. I’ve found that many online courses say you don’t need much mathematics fundamentals to be a programmer, but inevitably, even in beginner courses, the underlying math was important to understand what was going on.
The need for remedial math seems widespread enough that even a simple Google search for ‘calculus and artificial intelligence’ turns up a bunch of blogs and additional courses on how to understand the math underlying these assignments.
After spending a lot of time online trying to sort through this haystack of do-it-yourself calculus blogs, college class PDFs, and other resources, I came away with two websites that were outstanding for teaching basic calculus and linear algebra: Khan Academy and an on-demand tutoring service called Yup.
The first, founded by Bill Gates’s “favorite teacher”, the Khan Academy website breaks down calculus and linear algebra in ways that are just so simple and intuitive.
The thing that Khan Academy does (that almost no one else does) is it gives step-by-step examples for almost every math problem. There’s plenty of free resources online for math, but, in my experience, they’re all littered with abstract variables; few take the time to work out problems by hand, so students are left on their own to do it themselves.
Watching Khan complete calculus problems by hand gave me the confidence to know how to do the problems myself and I also learned a lot of the really powerful techniques that great thinkers like Khan use on a regular basis.
More specifically to machine learning students, the Khan Academy website has a really robust visualized lesson on gradient descent, which is one of the core calculus concepts necessary to understand artificial intelligence. Finally, the website is mobile friendly with plenty of self-directed quizzes, which is nice for people on the go during regular work hours.
But, I found self-directed calculus and linear algebra learning can only take me so far. I’d often get stuck on problems for reasons that weren’t explained in either the videos or the comments.
Yup is a mobile on-demand tutoring service. While the service is mostly for younger students and more elementary math, I found the tutors competent to answer most calculus question. Yup’s real-time accessibility was great for me to stay on track.
The screenshot above shows what the interface is like. Sessions look like chat exchanges, with the added ability to send screenshots and drawings back and forth.
If you like to write math problems on paper, then Yup’s interface will work seamlessly. I like to draw math problems on Evernote on my phone, so I had to come up with a hack to be able to send problems to the tutors oh; I’d upload screenshots of my Evernote drawings to Google Photos and then send them a link to my Google Photos storage. It’s a little cumbersome, but it works.
Highly self-motivated student with enough free time could probably learn all the necessary calculus and linear algebra concepts by themselves, but for folks with full-time jobs, it may be worth investing in a tutoring service to speed things along.
Either way, I think it is entirely possible to learn the math of machine learning and artificial intelligence without ever needing formal classroom experience.
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