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naraburns  nihil supernum  1yr ago (text post)   4347 thread views

Small-Scale Question Sunday for December 4, 2022

Do you have a dumb question that you're kind of embarrassed to ask in the main thread? Is there something you're just not sure about?

This is your opportunity to ask questions. No question too simple or too silly.

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For example, if you want to integrate a polynomial fraction, the most common questions involve completing the square, long division, and partial fraction decomposition. In my observation, LR unis will have questions requiring only one technique. MR will have two. And HR will often have all 3.

Which one of these tasks is computationally hard? Linear algebra and statistics have been the most computationally intensive courses I've taken. Multiplying two 4x4 matrices is 16 * (4 + 3) = 112 additions or multiplications. Computing standard deviation for a sizable dataset is, again, a lot of arithmetics. And in uni calculus most questions have an answer that reduces to something neat, so if you get an unwieldy polynomial for an answer you've probably made a mistake. A matrix or a sigma looks just like any other value you can get.

I meant relatively. Subjectivity withstanding.

None of them are particularly hard. But I have seen polynomial fractions that look fairly unwieldy and need 2 of the following to simplify. Subjectively that is more computationally intensive than just multiplying and adding a lot of numbers.

Also, your professor is insane for putting matrix multiplication on exams, it's just wasting time; if you can multiply 2 2x2 matrices, you can multiply any mxn matrices. There is nothing gained other than knowing how to add/multiply numbers fast. My lin algb exams were very theoretical and didn't require crazy computation.

If you're looking at linear algebra as the study of matrices then you're thinking about it in completely the wrong way. Linear algebra is the study of linear maps from vector spaces to other vector spaces, end of. The book "Linear Algebra done right": https://www.amazon.co.uk/Linear-Algebra-Right-Undergraduate-Mathematics/dp/0387982582 is a very good teaching aid, it explains what's actually going on properly while minimising matrix bullshit.

I think so as well. Which is why I said its insane to include large matrix multiplications in a lin alg exam.

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