51–60 of 126 posts
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For calculus I-III, look at Professor Leonard on youtube. He is the best. His channel can be found at https://www.youtube.com/channel/UCoHhuummRZaIVX7bD4t2czg
His videos look great. How do you get in practice problems following his class?
Kind of inauspicious to see this kind of thing on page 5: A (standard) unit vector is a vector with all elements equal to zero, except one element which is equal to one Huh? I've never heard the term "standard vector" before, and a "unit vector" is a vector whose magnitude is one. There is no requirement that one element be equal to one. Maybe that's why the download is free...
> A (standard) unit vector... I know this as "an element of the standard basis," B = {e_1, e_2, ...), where e_1 = (1,0,0,...), e_2 = (0,1,0,0,...). You could view it as inauspicious that the treatment doesn't begin with abstract vector spaces, but there is always Axler. For what it's worth, I find it inauspicious that after taking three (pure-math oriented) Linear Algebra courses I never saw least squares nor the SVD…
Kind of inauspicious to see this kind of thing on page 5: A (standard) unit vector is a vector with all elements equal to zero, except one element which is equal to one Huh? I've never heard the term "standard vector" before, and a "unit vector" is a vector whose magnitude is one. There is no requirement that one element be equal to one. Maybe that's why the download is free...
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I was really bad at rearanging terms/formulars and this came up in calculus exams all the time, but not so much in linear algebra exams.
That's another thing I observed teaching calculus: a lot of students who have problems, are having their difficulties with the algebra they supposedly know, and not so much with the "new" material. In theory, we expect students to already be fluent in this sort of algebraic manipulation; in reality, we recognize that a calculus class provides our students an opportunity to improve at this. I'm not sure I have any sug…
I successfully finished my CS degree.
But I often have the feeling that my math problems are getting in the way of getting on the next level, hehe.
Kind of inauspicious to see this kind of thing on page 5: A (standard) unit vector is a vector with all elements equal to zero, except one element which is equal to one Huh? I've never heard the term "standard vector" before, and a "unit vector" is a vector whose magnitude is one. There is no requirement that one element be equal to one. Maybe that's why the download is free...
But there is the requirement that the other elements be equal to zero. It's right there in the sentence you quoted.
True enough, thanks -- fixed.
Still a completely bogus definition.
> 2-vector (x1,x2) can represent a location or a displacement in 2-D... Isn’t this fundamentally faulty? Same notation describing a point and displacement. From this, we may conclude that, a point and a displacement are the same thing because they are described by the same notation. Shouldn’t mathematics be free of such contextual interpretation?
I'm a self taught programmer with a very weak maths background. What's the best learning path for me if I want to be able to understand and create ML based applications?
There's a practical course for this http://www.datasciencecourse.org/lectures/ anything you don't know, like linear algebra, look up the topics here for a 1-2hr crash course https://www.youtube.com/playlist?list=PLm3J0oaFux3aafQm568bl... There's a playlist for a math background in ML for anybody who wants to try a more rigorous ML course https://www.youtube.com/playlist?list=PL7y-1rk2cCsA339crwXMW... More information…
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A bit weird to add a negative review, but here goes: https://www.coursera.org/learn/linear-algebra-machine-learni... Is _not_ a good introduction. The instructors are all over the damn place, and you will spend much of your time finding better explanations from other sources. Wish I hadn't started with this. On the plus side, you will get a certificate at the end.
Indeed weird, because the course you mentioned is actually excellent. However, it was designed for people who had (somehow) already seen the subjects in an abstract and unapplied setting (such as a math class at uni). They refresh or refocus the subjects with a geometric intuition and with some concrete applications in mind; which I found quite useful and beautiful. This class is more like a more developed version of…
What 3b1b does still brings a lot of value, so I don't want to take away anything from his work.
> 2-vector (x1,x2) can represent a location or a displacement in 2-D... Isn’t this fundamentally faulty? Same notation describing a point and displacement. From this, we may conclude that, a point and a displacement are the same thing because they are described by the same notation. Shouldn’t mathematics be free of such contextual interpretation?
In mathematics, we abstract by forgetting about what the things are, and retain information about how they behave, and about what abstract properties they satisfy. The insight is that 2d locations and 2d displacements have the same abstract properties, which are modeled by a certain algebraic object: 2-vectors.
I went though the slides. Super fun material! I've seen all the methods long ago, and much deeper than in the slides, and published on some of the most advanced material, and much more, but, still, it was fun material because of the many examples and really good graphs. From their other books, clearly they are real experts. The slides, then, are a careful path where minimal theory gives a LOT of nice applications. Th…
Also see http://www.axler.net/DwD.html.