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Related note: Strang's essay on the imbalance in education in favor of Calculus over Linear Algebra is (in my opinion at least) a great read, for those interest

Related note: Strang's essay on the imbalance in education in favor of Calculus over Linear Algebra is (in my opinion at least) a great read, for those interested in the pedagogy of mathematics. http://web.mit.edu/18.06/www/Essays/too-much-calculus.pdf http://web.mit.edu/18.06/www/Essays/too-much-calculus.pdf

jimbokun 7y ago
I think Strang's videos should also be used as examples of all around great pedagogy, independent of the Linear Algebra content. He does more with some chalk and a big black board than any modern courses using fancy presentation technology.
- abhgh 7y ago
  Definitely - I went through some of his lectures after I had read up on Linear Algebra as part of a course (from [1]) and had used it in a bunch of applications, but I still found the lectures worth going through if only because his fantastic exposition helped me visualize things better. [1]we followed Huffman-Kunze https://www.amazon.com/Linear-Algebra-Kunze-Hoffman/dp/9332550077 https://www.amazon.com/Linear-Algebra-Kunze-Hoffman/dp/93325...
sadlion 7y ago
Interesting read; what are good calculus resources that achieve Strang's outlook? I do know Strang has a free calculus book. I've taken calculus years ago and have forgotten most of it. I hated that it was taught to me in a rote way. I am looking for resources that teach the essence well similar to 3blue1Brown.
- fishmaster 7y ago
  I would also be interested in this, since I find Strangs style great.
msla 7y ago
I already love this essay because I've been saying the same thing for years, and he even mentions "statistics and discrete mathematics" as something we should be doing more of; in short, calculus is useful for physicists and engineers, primarily, whereas statistics and discrete mathematics, properly taught and motivated, are useful for everybody. For example, if there's a certain probability of people with cancer getting a positive test result, what's the probability of a positive test result meaning you have cancer? Too many people absolutely cannot approach that problem in any intelligent fashion. (Side note: More classes should accept "there isn't enough information to give a coherent answer" as a correct result.)
- srean 7y ago
  You will need calculus for any non-trivial statistics though, unless you want statistics distilled into cook book style pre-canned formulas and recipes. Those are fine when you are dealing with a situation that has been anticipated 'just so'.
  - msla 7y ago
    > You will need calculus for any non-trivial statistics though, unless you want statistics distilled into cook book style pre-canned formulas and recipes. It's a matter of focus: The point isn't to derive statistics, any more than the point of a first semester course on differential calculus is to derive the real numbers and the infinitesimals. Calculus isn't useless, it's just not as useful unless you go into specific fields.
    - jacobolus 7y ago
      Statistical distributions and methods were all designed by humans for a particular purpose. If you understand calculus, you can start with a statement of the desired goal, and then work backwards to derive the formulas you need. The final form you get then makes sense, and you have some ownership of it. In a pinch you can re-derive it for yourself, but even if you look it up in a book you understand what the parts mean. If you don’t know calculus, someone has to tell you the formulas, which will seem like mysterious completely arbitrary magic. Memorizing them will be a pain in the butt. When you try to use statistics you will make small mistakes which will lead to wrong or even entirely incoherent results, but you won’t notice because you’re just following a recipe you don’t understand. Of course, to do real statistics you need linear algebra as well.
inasio 7y ago
I taught a bunch of undergrad level Calculus courses and one or two Lineal Algebra classes using Strang's book. By far the most fun class I've taught, and it's very easy (and in my opinion almost mandatory) to add some numerics to it. Ok, cool, you can solve by hand Ax = b of a 3x3 matrix, now let's do it for a 1000x1000 matrix for one of many real world problems. There are also tons of very complicated advanced calculus and differential equations concepts that have direct "discrete" analogues in linear algebra, and this become glaringly obvious when trying to say discretize and solve a partial differential equation.

jimbokun 7y ago

I think Strang's videos should also be used as examples of all around great pedagogy, independent of the Linear Algebra content. He does more with some chalk and a big black board than any modern courses using fancy presentation technology.

abhgh 7y ago
Definitely - I went through some of his lectures after I had read up on Linear Algebra as part of a course (from [1]) and had used it in a bunch of applications, but I still found the lectures worth going through if only because his fantastic exposition helped me visualize things better. [1]we followed Huffman-Kunze https://www.amazon.com/Linear-Algebra-Kunze-Hoffman/dp/9332550077 https://www.amazon.com/Linear-Algebra-Kunze-Hoffman/dp/93325...

sadlion 7y ago

Interesting read; what are good calculus resources that achieve Strang's outlook? I do know Strang has a free calculus book. I've taken calculus years ago and have forgotten most of it. I hated that it was taught to me in a rote way. I am looking for resources that teach the essence well similar to 3blue1Brown.

fishmaster 7y ago
I would also be interested in this, since I find Strangs style great.

msla 7y ago

I already love this essay because I've been saying the same thing for years, and he even mentions "statistics and discrete mathematics" as something we should be doing more of; in short, calculus is useful for physicists and engineers, primarily, whereas statistics and discrete mathematics, properly taught and motivated, are useful for everybody. For example, if there's a certain probability of people with cancer getting a positive test result, what's the probability of a positive test result meaning you have cancer? Too many people absolutely cannot approach that problem in any intelligent fashion. (Side note: More classes should accept "there isn't enough information to give a coherent answer" as a correct result.)

srean 7y ago
You will need calculus for any non-trivial statistics though, unless you want statistics distilled into cook book style pre-canned formulas and recipes. Those are fine when you are dealing with a situation that has been anticipated 'just so'.
- msla 7y ago
  > You will need calculus for any non-trivial statistics though, unless you want statistics distilled into cook book style pre-canned formulas and recipes. It's a matter of focus: The point isn't to derive statistics, any more than the point of a first semester course on differential calculus is to derive the real numbers and the infinitesimals. Calculus isn't useless, it's just not as useful unless you go into specific fields.
  - jacobolus 7y ago
    Statistical distributions and methods were all designed by humans for a particular purpose. If you understand calculus, you can start with a statement of the desired goal, and then work backwards to derive the formulas you need. The final form you get then makes sense, and you have some ownership of it. In a pinch you can re-derive it for yourself, but even if you look it up in a book you understand what the parts mean. If you don’t know calculus, someone has to tell you the formulas, which will seem like mysterious completely arbitrary magic. Memorizing them will be a pain in the butt. When you try to use statistics you will make small mistakes which will lead to wrong or even entirely incoherent results, but you won’t notice because you’re just following a recipe you don’t understand. Of course, to do real statistics you need linear algebra as well.

inasio 7y ago

I taught a bunch of undergrad level Calculus courses and one or two Lineal Algebra classes using Strang's book. By far the most fun class I've taught, and it's very easy (and in my opinion almost mandatory) to add some numerics to it. Ok, cool, you can solve by hand Ax = b of a 3x3 matrix, now let's do it for a 1000x1000 matrix for one of many real world problems. There are also tons of very complicated advanced calculus and differential equations concepts that have direct "discrete" analogues in linear algebra, and this become glaringly obvious when trying to say discretize and solve a partial differential equation.