I'm a freshman in college right now, and I'm getting ready to take my Calculus II final here later this week. I've always been very good at math, but this last semester was by far the most difficult math I've ever taken. For the first time in my life, I'm actually having to study outside of class, and I'm not certain of at least a high B on this test.
From talking to some of my sophomore buddies and a few of the teachers I'm on good terms with I've heard that Calc II is about the hardest math I will ever take. Would you guys agree? If not, what was the most difficult math for you?
Yeah, I think that's why I haven't simply 'got' Calc II like I did all my other maths through high school. Theres a lot of what just feels like tedious memorization, rather than the logical thinking I'm used too.
The nice thing about single-var calc is that the theorems are so easy, you can prove most of what you need while you're writing the test. If you think BASIC INTEGRATION is a lot of memorization, try PDEs. The most conceptually difficult undergrad math is far from first-year; try Galois theory, second-semester RA or complex, algebraic geometry, ...
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Anonymous2007-12-10 13:05
>>3
The fact that you don't understand the line of thought doesn't mean it's not logical. If you think calculus is a lot of memorisation you need to get out of mathematics now.
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Anonymous2007-12-10 14:39
analysis was pretty hard, but really you can get by in classes like that with a good understanding of pertinent theorems and their proofs.
calculus can be hard if you don't have a good prof. i found that it made a lot more sense when the lectures stopped pandering to the superficial applications and delved a little deeper into more rigorous calculus (because for some, the purely applied stuff seems pointless).
to be fair though, there were several courses in undergrad math that I took that were easier than calc II.
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Anonymous2007-12-10 22:48
Why not try looking into some astronomy and physics, then maybe the reasoning behind calculus will make a little more sense.
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Anonymous2007-12-10 23:38
>>7
That's like saying looking into plumbing will make the reasoning behind hydrostatics make more sense.
regardless, uni math will be hard until you stop thinking of it as hard and start thinking of it as "different"
The theorems and proof are actually very simple in lower division math, it's just that they're always written in mathematical legalese which you are not used to coming from high school, so that's why it seems difficult.
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Anonymous2007-12-11 7:44
>>8
Well not exactly, as plumbing existed long before hydrostatics, however in the sense that hydrostatics allowed for a much more in depth understanding of complicated plumbing systems, then yes, I believe knowing a bit about how piping systems work would make understanding hydrostatics quite a bit simpler, and hydrodynamics while you're at it.
Calculus was a tool developed to understand astronomical phenomena, and has since proved that it has applications in a wide range of other areas. Being familiar with the mechanics of those areas would give a good grounding point for conceptualization of things like vector calculus. I know I didn't really understand why vector fields were important until I understood the physics it was designed to describe.
Linear algebra is easy, galois theory pig disgusting, etc.
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Anonymous2007-12-13 7:37
>>1
Calc II isn't hard at all. It's all basic integration.
Linear algebra is the hardest thing I've taken yet, and that was only because I didn't do the work for the class. PROTIP: It's not high school anymore, prepare to have to actually do work.
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Anonymous2007-12-13 22:39
Calc II hard... riiiiight, some people who accell at math, hit a barrier with calculus, or a better way to put it is that they reach thier maxium math potential. Not everyone's brain ist equiped to handle calculus.
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Anonymous2007-12-13 22:53
>>15
Just like not everyone's brain "ist equiped" to handle English, amirite?
Calculus is dead simple. If you don't understand it, it's entirely down to a shitty teacher.
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Anonymous2007-12-13 23:02
HOW CAN YOU FUCKERS FAIL AT CALCULUS? Seriously, any serious person could be competent at Caclulus I & II in about 4 weeks of studying.
>>18
Ever hear of 1 typo in every 10 words, mixed with a failure to write well?
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Anonymous2007-12-14 2:29
>>18
There's a difference between a typo and so many of them you might as well be illiterate.
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Anonymous2007-12-16 16:58
Well when you get almost fluent in a second language come and talk to me.
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Anonymous2007-12-16 18:18
>>20
There's a difference between a typo and a misspelling.
For example:
Theer (there)
Their (there)
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Anonymous2007-12-16 18:24
Actually, I would say that typos form a subset of misspellings.
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Anonymous2007-12-16 18:37
Calc II is just scratching the surface. The hardest math you will ever take you can't even dream of.
As a good example of some genuinely hard math, go to any university library, and pick up any book that has a yellow cover with a white top to it that says "Graduate texts in mathematics," or whatever the hell they're called. Or if you just want a subject that will kick your ass no matter what you do, try differential forms.
There's really only ten integrals that you ought to have memorized, then a bunch of rules for integration. Not that hard. The limit shit is harder IMHO
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Anonymous2007-12-17 23:42
>>26
Actually, I think that the limit shit is much easier. All you have to do is first assume that the conditions are satisfied, and then find the appropriate expression for delta, and then go on proving that delta works.
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Anonymous2007-12-18 3:25
>>23
Fair enough, but if one would spell the word the same way on paper, it's not a typo; it's a misspelling.
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Anonymous2007-12-20 11:07
Category theory.
With Peter Freyd.
Impossible.
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Anonymous2007-12-20 17:11
>>27
well probably part of it is due to using derivatives and integrals much more often than limits. Limit stuff is usually limited to evaluating something easy where substitution or l'hopital's rule work, while the harder stuff (like whether some godawfully complicated limit is finite or not) is never done. While differentiating and integrating is done like, all the time in my signals class and often in mechanical systems.
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Anonymous2007-12-21 6:02
Memorization is for niggers. Either you've used an analytical rule so often that you don't have to go through the conscious effort of memorizing it or you read it off your calculator. The thing has memory for a reason.
What IS the hardest math all round according to Anon?
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Anonymous2007-12-21 8:16
>>31
Number theory is quite hard.Proving Riemann's hypothesis also :).Actually almost all math is quite hard for me.
Whats considered to be the hardest math classes at my university are "Vector Calculus" and "Functions of a Real Variable".
Vcalc is fairly self-explanatory, I did well in it but had mono that quarter so I can't remember it as well as I probably should (especially the later more theoretical stuff like wedge products and the stuff for replacing dot and cross product in R4 and above, but those are the less important stuff for other courses like electromagnetic fields etc).
Functions of a Real Variable is just getting ridiculously thorough with single-variable calculus (or so I heard).
Theres also boundary value problems, which is basically "diffEq 3"
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Anonymous2007-12-22 14:41
>>29
I'll second that.
There is no easy way to prove Baire, let alone any of the results that follow.
Albeit different course, different prof.
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Anonymous2007-12-23 0:38
>>34
WTF? Baire is so easy to prove, all you need to do is to make use of the Cantor's intersection theorem and just make a closed set not intersecting with each nowhere dense set (easy to do, just get an open sphere to do the job since it is nowhere dense, and then take a the closure of the open sphere), and make the (n+1)th closed set be within the nth (possible, since the nth closed set is itself complete), and intersect all of them, which has a non-empty intersection which in the set, and is not in any of those nowhere dense set.
>>35
"...just make a closed set not intersecting with each nowhere dense set (easy to do, just get an open sphere to do the job since it is nowhere dense, and then take a the closure of the open sphere)..."
This makes no fucking sense, are you high? Are you implying that an open sphere is nowhere dense? Or that its closure doesn't intersect with any nowhere dense sets?
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Anonymous2007-12-31 18:27
>>38
I mean that it's closure doesn't intersect with any nowhere dense sets. Why? Because the closure of the nowhere dense set is a closed set containing no open set, so within any open set, there is at least one point not within its closure. This means that there is an open sphere centered upon that point not intersecting that nowhere dense set. Choose one such open sphere, take the open sphere with half its radius, and then take the closure of that sphere.
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Anonymous2007-12-31 19:51
>>39
Ok, I get you now, the wording was just a little skewed.