Differences between math and other subjects

[truste1]

Ouch.  The history class looks painful!

Uh...it looks basically like Western Civ.

Yeah, painful!  I really dislike history courses. :)

I'd say the same thing about Math and Science courses, but then certain members on this forum would say how that makes me stupid.

[Sidoh]

Ouch.  The history class looks painful!

Uh...it looks basically like Western Civ.

Yeah, painful!  I really dislike history courses. :)

I'd say the same thing about Math and Science courses, but then certain members on this forum would say how that makes me stupid.

Maybe some would.  I wouldn't.  I might have in the past, but I don't think I would now. :)

I think the thing that makes history painful for me is it's almost entirely memorization.  It's not that I don't find history in itself interesting, but the only real way you can test a person's understanding of history is to bombard them with a bunch of questions and expect them to have memorized the answers.  This is one reason I've grown to love things like math and computer science.  Concepts or rules are taught, and you're expected to have a very good understanding of them, and be able to apply them to situations that are almost completely foreign to what you've seen in the past.  If you remember a very small grain of information (a "trick" used to do something), then you can almost reconstruct your entire knowledge with nothing more.

It's not that I'm bad at memorizing things.  I'm actually pretty good at it.  I just find it completely boring compared to other subjects which basically reduce to elaborate exercises in problem solving.

[truste1]

I agree. I think the bad thing about history courses, though they interest me in the short-term and are easy for me, is that it's nothing more than a learn & dump method of learning. Our requirement for western civilization consisted of three semesters worth of material, and I did well in each course...but I remember only a few key things, vaguely, from each of the three classes. It's just nothing something that you use very often. Unfortunately math has just always been a pretty hard thing for me and thus I've shyed away from it, where I've excelled at writing and those sorts of classes. Math (especially mental math) is something that I intend to slowly improve at though.

[Sidoh]

I agree. I think the bad thing about history courses, though they interest me in the short-term and are easy for me, is that it's nothing more than a learn & dump method of learning. Our requirement for western civilization consisted of three semesters worth of material, and I did well in each course...but I remember only a few key things, vaguely, from each of the three classes. It's just nothing something that you use very often. Unfortunately math has just always been a pretty hard thing for me and thus I've shyed away from it, where I've excelled at writing and those sorts of classes. Math (especially mental math) is something that I intend to slowly improve at though.

Yeah, I'd probably be the same way.  In fact, I'm the same way with math too.  As I mentioned before, though, you can reconstruct your understanding of a subject given a very small hint, so you don't need to remember very much to be able to make use of most of what you learned in a math course.  I suppose you could say knowledge is much more hierarchical in maths than it is in other subjects.

I was never bad at math, but I wasn't good at it until I began liking it.  I think seeing some of the wackier applications is what drew my interest.

This is a bit of an aside, but my philosophy professor briefly mentioned Gödel's incompleteness theorems today in class (which, in essence, show that given a sufficiently powerful mathematical system, there are things that are true within the system, but cannot be shown to be true).  He phrased it as something like "Gödel proved that there are some things that you can't prove to be true."  I think about 50 heads exploded.

[Ender]

History is about much more than just memorization!

[Sidoh]

History is about much more than just memorization!

Maybe.  Especially in intro level courses, though, it rarely involves much else.

[Blaze]

History is about much more than just memorization!

Maybe.  Especially in intro level courses, though, it rarely involves much else.

History courses are generally critically thinking about situations you have to remember.  I always did well in those courses.  You are right that a portion is remembering everything, but one could say that about many professions.

[Sidoh]

History is about much more than just memorization!

Maybe.  Especially in intro level courses, though, it rarely involves much else.

History courses are generally critically thinking about situations you have to remember.  I always did well in those courses.  You are right that a portion is remembering everything, but one could say that about many professions.

Sure, I'm sure there's a significant amount of critical thought involved, but it's not the kind I'm interested in.

[truste1]

History is about much more than just memorization!

Maybe.  Especially in intro level courses, though, it rarely involves much else.

History courses require memorization of facts, but more importantly the courses consist of lots of analysis of events, seeing the big picture, and cause and effect relationships. All subjects require memorization, for example math formulas.

[Rule]

History is about much more than just memorization!

Maybe.  Especially in intro level courses, though, it rarely involves much else.

History courses require memorization of facts, but more importantly the courses consist of lots of analysis of events, seeing the big picture, and cause and effect relationships. All subjects require memorization, for example math formulas.

Except the memorization in math is negligible.  At higher levels, you should be able to derive most formulas essentially from first principles.

[deadly7]

Except the memorization in math is negligible.  At higher levels, you should be able to derive most formulas essentially from first principles.

Even at lower levels you can do that. Chain ruling the product formula cause you forgot it while deriving shit? For the win.

[Sidoh]

Except the memorization in math is negligible.  At higher levels, you should be able to derive most formulas essentially from first principles.

Definitely.  I think there's something that's fundamentally different about mathematics and most other subjects, and this is a property of that difference.  Being able to reconstruct a ton of knowledge from very simple facts and observations is not something that's present in many other subjects.

Even at lower levels you can do that. Chain ruling the product formula cause you forgot it while deriving shit? For the win.

Haha, for sure.  There was a problem on one of my calculus exams a few years ago that required the use of integration by parts, which I had almost no memory of.  I did remember the simple trick that was used in its derivation, though, so I was able to reconstruct the result and answer the question.  I remember a bunch of my classmates whining about not remembering how to do IBP. :)