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Comment by Retric | Hacker News Reader

'Learn' can be fuzzy.

IMO, most undergrads taking an undergrad DifEq course will have little understanding of what they are actually doing and just treat it as symbol manipulation. I have seen people encounter the same problem with calculus, matrices, or even simple algebra. And you can keep pushing, but at some point if you want to progress you need to revisit older topics and hopefully gain new understanding.

It's like revisiting multiplication and division in binary and suddenly understanding why a similar process in base 10 works.

PS: Pure symbol manipulation is still powerful, but intuition takes a little more.

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I'm not sure I understand any of this. The person asking is trying to understand the difference (and required effort) between Khan Academy and what's linked on the page - basically 'Maths textbooks for curious undergraduates'. That's a good and sensible question and whatever you think the answer to it is, it surely isn't (as suggested by the person responding) 40 years of ferocious training in the Arctic with Doc Savage.

To be more clear, I agree the foundation is within reach of a dedicated 20 year old student.

But, there is a huge gap between being able to pass a test on X after taking a class and being ok when someone writes the same idea in yet another notation. Or worse reading something when they go step 20 -> step 21 and yes you can get from A to B with an hour of concerted effort and step 20 -> step 21 and see what they mean and could get there the long way in a few minutes of calculation.

Now personally, I only got just enough understanding of Math to read a QM book and recognize how much work it would be to get more than a vague I kind of see what your doing thing going. But, sure if you mean the starting point for monumental effort then yea a solid undergrad math background is 'enough'.

I think he was just trying to be more clear on what we define as "learned" in the context of math. Many people "learn" math and do well on tests because they have memorized ways to manipulate equations to resolve the problem without actually understanding abstractly what is going on, and are thus often less creative with their maths. Ironically, I've found that those students who appear to excel in maths are usually the ones who are less curious about the why and how of math. Maths is usually taught in a way that it discourages the people who seem to struggle with it when they are often just trying to understand the depth of it more. I was one of these students in high school, and thought I just wasn't gifted. Fortunately I had the discipline to learn it and eventually had a really good teacher.

I got that, I just don't think it has anything to do with the question (or the bad answer I was replying to).

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