An Intuitive Guide to Linear Algebra (2012) • Hacker News Board

Re: An Intuitive Guide to Linear Algebra (2012)

#101

Post by JadeNB » Wed, Feb 26, 2020, 8:20 PM UTC

alacombe wrote: post #81

JadeNB wrote: post #31

Earlier quoted context omitted.

> solutions in search of problems... This sounds like it was meant to be pejorative, but it's what (applied) linear algebra, and applied mathematics more generally, is . Anyone can learn about a certain mathematical topic upon realising it's the one relevant to the problem they're facing—and learn it way more quickly, due to motivation and focus, than they would in a general-purpose course on the topic; the art is in…

Of course it was meant to be pejorative and that pretty much summarize my experience through university. In this particular case, the teacher wasn't giving a rat arse about his class and was merely there for the safe job, pension, sprinkles by some "research". Anyhow, I disagree with that top-down approach, which seems to be very... European. I much prefer to follow a more logical path where the problem preclude the…

> Anyhow, I disagree with that top-down approach, which seems to be very... European. I much prefer to follow a more logical path where the problem preclude the introduction to the solution.

I agree that it's easier to learn that way, but it's not much use when solving real-world problems; you can learn the techniques relevant to the solution once you know what they are, but, if you haven't met them before, you won't recognise that they're the right ones.

Re: An Intuitive Guide to Linear Algebra (2012)

#102

Post by trentnelson » Thu, Feb 27, 2020, 1:22 AM UTC

hintymad wrote: post #45

adamcharnock wrote: post #36

I... I still really struggle with this. I'm a smart person, I've got a bachelors of engineering, I've been a professional software developer for around 14 years now, and I've built a house. But there is something about degree-level maths and beyond that I find deeply unintuitive in a way that software development isn't. Through comments here I found 3blue1brown's (clearly much loved) videos. By the third video I was…

This is typical for many people. You love pre-college math because you have intuitive understanding, while college-level maths offer a new level of abstraction that you may not feel familiar with from the get-go. It's perfectly okay not to learn linear algebra, by the way, especially when you don't find any incentive to do so. Otherwise, you'll find linear algebra to be one of the most intuitive tools to model so man…

Got any similar recommendations for college-level probability/stats stuff?

Re: An Intuitive Guide to Linear Algebra (2012)

#103

Post by abdullahkhalids » Thu, Feb 27, 2020, 5:09 AM UTC

mattkrause wrote: post #97

abdullahkhalids wrote: post #78

Earlier quoted context omitted.

Unfortunately, for a lot of people, including undergraduates, the dopamine hit they get from watching a video or passively reading a textbook makes them believe that these are adequate substitutes for doing thousands of exercises. In my university, undergraduates have admitted that they have done fewer than 50 questions throughout the entirety of my math course. Their grades obviously reflect that, but they will do t…

Can I press you to explain what you think dopamine is/does? I'm curious because I'm a neuroscientist who occasionally works on dopaminergic stuff and "passively reading a textbook" is so far from the canonical examples we use for dopamine activity, but the idea of dopamine/dopamine 'hits' has taken on a life of its own that seems quite different from the neurotransmitter.

I am a physicist, so I will dare not make any technical neuroscience claims. I meant "dopamine" in the causal sense of people feeling pleasure from passively reading a book because they think it is useful work.

Re: An Intuitive Guide to Linear Algebra (2012)

#104

Post by hintymad » Fri, Feb 28, 2020, 11:44 PM UTC

trentnelson wrote: post #102

hintymad wrote: post #45

Earlier quoted context omitted.

This is typical for many people. You love pre-college math because you have intuitive understanding, while college-level maths offer a new level of abstraction that you may not feel familiar with from the get-go. It's perfectly okay not to learn linear algebra, by the way, especially when you don't find any incentive to do so. Otherwise, you'll find linear algebra to be one of the most intuitive tools to model so man…

Got any similar recommendations for college-level probability/stats stuff?

No. I took only a few courses on probability and mathematical stats. The books are A First Course in Probability and some some textbook on Mathematical Stats. The courses were probably not advanced enough, as I found them reasonably straightforward. I struggled a bit on what exactly is a random variable, but once that was internalized, everything else followed. I heard that advanced courses like random processes were really hard, but I'm not at that level.

Re: An Intuitive Guide to Linear Algebra (2012)

#105

Post by FabHK » Sat, Feb 29, 2020, 4:06 PM UTC

JadeNB wrote: post #100

FabHK wrote: post #95

Earlier quoted context omitted.

Or not span the space, for that matter.

Well, it depends on what "the space" is. Every set of vectors (in a common ambient space) spans some space—often called the column space of a matrix, if they are the column vectors of the matrix.

Sure, every set of vectors will span the space they span. But the requirement that a basis span the space refers to the space it’s in, not the space it spans (otherwise every linearly independent set of vectors were a basis, spanning the space it spans.) I could go on :-)