so a wonderful thing happened to me at the weekend I was doing some research on Twitter research yes research okay I was wasting some time on Twitter when I saw this tweet from Steven Strogatz interest piqued I clicked on Robert breasts Twitter feed and I’m very glad I did because I saw this thread how I teach the Kalman filter to first-year undergraduate engineering students at Penn a thread it goes on when teaching multivariable calculus.
I use matrices and linear transformations from the very beginning with nice payoffs in derivatives and integrals now this really piqued my interest why yes why-why did it pique your interest tell us because when I was learning calculus and linear algebra they were taught to me as two separate subjects so over here you’ve got linear algebra and here is calculus they’re not connected and really.
I was never shown how they were related to each other and I think that’s a big problem with the way a lot of maths is taught you’re taught how to do things but you know that student is left to develop that insight and intuition themselves and you and that can be a very long and winding path and some of us never develop that intuition what would be really useful would be as if the instructor gave you that insight and intuition or at least some of it or a road map for that insight and intuition right at the beginning and that doesn’t happen very often but in this course.
it does so I visited his YouTube channel and his course on multivariable calculus is one of the best if not the best course on calculus that I have seen I agree with that it’s also the best course that I’ve seen that’s two of us he’s clearly very knowledgeable but you need more than that to be a good teacher he’s a good communicator he obviously loves his subject and he’s aware that is a difficult subject to learn a lot of people that teach maths you know have become very good at it and they’re not aware of the difficulties that exist when people are learning the subject themselves but Robert Grist hasn’t forgotten that he knows it’s a typical subject and he’s sensitive to that he gives you insight he gives you intuition and the production values of this course are just superb.
I mean take a look at it pick a point X on the hyperplane look at the vector X minus X not take the dot product of that with N and set it equal to zero that is the implicit equation for the hyperplane and when you look at his YouTube channel you get a sense of just how much work and effort has gone into these videos I mean this is a really comprehensive course on calculus and one of the other things I like about it is that most of the videos are under five minutes long so they really hold your attention and look I mean the number of videos in each playlist over a hundred and thirty there are currently 3 playlists.
I think another one is coming and if you want to get a full rundown of what the course covers then just visit his homepage at the University of Pennsylvania and you will be able to see that so who is Robert Crist well he’s an American mathematician known for his work on topological methods in Applied Mathematics he’s currently professor in mathematics and electrical strokes systems engineering at the University of Pennsylvania and if you want to find out more about him you can go to his homepage at the University of Pennsylvania or look at Wikipedia now you can’t expect a video course to do all the work for you you’re gonna have to go off and you know with a pen and paper and understand this stuff and work through it and do some problems you’ve got to put the effort in you have it doesn’t matter.
How well explained it is you still have to put the effort in that’s just how maths is but it will give you a road map to that insight that you might not otherwise develop or you know at least not for a very long time and that’s what I really like about this course I’ve linked these videos in the description below I really would urge you to take a look and then I discovered also that he’s done a course on single variable calculus to which I am working my way through now there’s a link to that as well go and take a look at it really these are the best courses on calculus that I have seen and they are free.
I’ve also linked to some problem sets in the description as well because you know you’re going to need practice doing problems to really understand the subject but I don’t think you will find a course than this on calculus I don’t think you’ll find a better course either it’s fantastic so if you’re interested in machine learning and data science and artificial intelligence and all that wonderful stuff and you need to learn the maths take a look at these courses these courses do require you to have had some exposure to calculus in the past but nothing at you know a really high level and you’re expected to be familiar with algebra 2 but it’s nothing that you couldn’t go and learn of the Khan Academy now after a couple of weeks so if you haven’t quite met that level go off and do a couple of Khan Academy courses and then come back to this but bookmark these courses if you need to learn calculus go to them first they are superb I’m going to go and watch some now