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/sci/ - Science & Math

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6182534 No.6182534 [Reply] [Original]

> Marking first year calculus exams.
> mfw everyone thinks 1/(a+b) =1/a + 1/b
> mfw everyone thinks(a + b)^n = a^n + b^n
> mfw nobody uses the chain rule.
> mfw 90% of the students can't into basic high school math.

>> No.6182567

>>6182534
Are you from.... US, by any chance ???

lolface.jpg

>> No.6182573

Well there are people in my master's level analysis courses who couldn't give you the definition of compactness. I don't know how these people pass exams.

>> No.6182584

>>6182573

lol for real there's a couple master's students in my analysis class who are totally clueless. This one guy had no idea what a homeomorphism was.

I did my undergrad in physics and I know more math than them.

>> No.6182588

>>6182567

Canadian, actually. I'm at a mid-tier university.

>> No.6182594

>>6182567
France

>> No.6182601

>>6182594

You're not OP...

>> No.6182608

>>6182534

Engineering calculus is the worst to TA. Not only are they terrible at math, but they think they know everything and refuse to admit they're wrong.

>> No.6182618

>>6182608
> freshman
> think they know everything

i dont believe you
difficult engineers that I know, are difficult because they don't care, because filling out a spreadsheet doesn't require triple integrals

>> No.6182631

>>6182618

Engineers take 2 years of calculus.

>> No.6182650

>>6182584

Some undergrad programs don't touch topology (apart from metric spaces).

>> No.6182664

>>6182573
Lol, I'm in calc 3 and I even know the definition of compact spaces.

>> No.6182677

>>6182588
which one
>pls say waterloo

>> No.6182691

>>6182534
>thinks 1/(a+b) =1/a + 1/b
This happens way more than it should

>> No.6182695

Yeah, it's pretty unreal how bad people are at math. As the math major in my group of friends that consist of more "bro" types, I get asked to tutor them a lot. I realized how poor their skills just in basic algebra are when I consistently would get asked to explain things like pulling a common factor out of a polynomial.

The only thing that I find weirder is that most of them end up passing. Honestly, I can't imagine teaching a class easy enough that they would pass. It practically wouldn't have any math.

>> No.6182698

>>6182584
Rather embarassing to not know what homeomorphism means, but still I think not knowing compactness beats it. I mean, off top of my head, that means the person couldn't use stuff like uniform continuity or extreme values.

>> No.6182704

Wow. This thread's full of mutual masturbatory arse lickers. Who gives a shit what compactness is? I bet you've never licked a wet cunt.

>> No.6182786
File: 76 KB, 397x436, 2+2=KFC.jpg [View same] [iqdb] [saucenao] [google]
6182786

>>6182704

Looks like someone is butt hurt that they failed high school calculus.

>> No.6182792

>>6182677

I went to Waterloo before. It was only a little bit better.

>> No.6182800

The class average of my last calculus exam was 85% . The teacher was like WTF are you fucking serious.

I know ; fucking cool story

>> No.6182808

>>6182704
/thread

>> No.6182818

>>6182704

Haters gonna hate. I lick wet cunts while computing the homology of compact spaces.

>> No.6182880
File: 7 KB, 210x160, download.jpg [View same] [iqdb] [saucenao] [google]
6182880

>>6182792
This one?

>> No.6182888

>>6182534
>mfw everyone thinks(a + b)^n = a^n + b^n
Wait, it doesn't?

>> No.6182890

>>6182888
no, that only works for (ab)^n = a^n b^n
otherwise you have to FOIL or something

>> No.6182899

>>6182890
>that only works for (ab)^n = a^n b^n
That's the same thing in different notation.

>> No.6182900

>>6182698
That is untrue.

Compactness is not strictly associated with uniform continuity or ''extreme values.'' It helps immensely and there's a theorem associated with it, but it isn't exclusive to it.

One can, for example, use the Lipschitz condition theorem to show uniform continuity or simply utilize limit points. Or they can just do something better: Use the straight definition of uniform continuity.

Compactness is, by the way, not necessarily a completely intuitive concept. It's not hard to learn, but it certainly isn't one of those 'obvious' things.

>> No.6182902

>>6182588
British Columbia?

Oh wait they're shit tier

>> No.6182905

>>6182800
>The class average of my last calculus exam was 85%
That's not bad.

>> No.6182909

>>6182899
okay, faggot, I'm not the one that thought (a+b)^n = a^n + b^n like a fucking retard

>> No.6182911

>>6182899
it's the associative property of exponentiation over multiplication.

>> No.6182915

>>6182905
It means the exam was quite possibly too easy. Good exam averages are considered to be in the 70-75 percentage range. Lower than that, it means that the exam was probably too harsh; higher than that means that it was probably too lenient.

>> No.6182919

>>6182915
Subjective. It depends on how difficult the teacher's style is, how they word the questions, etc.

>> No.6182921

OP your picture made me cry of laughter, and the story made me lose it completely, I've had this thread open since 7:45

>> No.6182928

>>6182915
No it doesn't. The correct difficulty of the exam is whatever difficulty accurately gauges students' progress in and understanding of the coursework, such that the grade reflects student understanding. Under this paradigm, the theoretical ideal would be 100% average, but that would be practically worrisome and an 85% average is a pretty good number in general, though there's more that matters than just that.

>> No.6182930

>>6182786
I'm in AP Calculus AB right now, and we just finished derivatives before going on Thanksgiving break. Do you guys have any tips on how to accel a bit faster than my class' current pace? I don't want to learn everything and just sit in class twiddling my thumbs, but I think it'd be good to do some exploration on my own, then ask my instructor about anything I need help with. I'm also planning on entering a university with a rather rigorous engineering program, so any comments on what to expect would be appreciated.

>> No.6182940

>>6182919
>>6182928
While I agree with you from a pedagogical standpoint, I am speaking from the viewpoint of a graduate student who has TA'ed for classes and who has sat in classes where practically all of my professors have stated that they want their exam averages to be between 65% and 75%.

>> No.6182941

>>6182928
>has no idea what he's talking about because his answer has no basis in statistics
Please, shut the fuck up

>> No.6182946
File: 5 KB, 140x100, youtube-meh7.png [View same] [iqdb] [saucenao] [google]
6182946

>mfw everyone thinks 1/(a+b) =1/a + 1/b
>mfw everyone thinks (a + b)^n = a^n + b^n
mfw nobody is able to assign
a = b = n = 2 in order to verify

>> No.6182947

>>6182940
>pedagogical
why do you type so smart

>> No.6182951

>>6182946
why wouldn't you do a = b = n = 1?

>> No.6182954

>>6182941
I don't think he's talking about it from a statistical viewpoint, but from a moralistic one. I'm assuming the anon in question thinks that if everyone is learning the material correctly at a decent pace, everyone should get a 100%. It's more of a pedagogical viewpoint than anything else, I think.

In an ideal world, I'd like it if I could give everyone 100% on HW assignments and exams. Sadly, that isn't the case.

>> No.6182956

>>6182954
>I'd like it if I could give everyone 100% on HW assignments and exams.
really? why?

>> No.6182963

>>6182956
I don't want to give anyone an F, a D or a C. I don't derive any pleasure from watching someone fail at a course or perform dismally. Maybe others enjoy witnessing such tragedies, but I don't. I do it because a) it is academically unjust of me not to assign the grade it deserves and b) because quality should come first and foremost before any emotional attachment. That being said, it still doesn't mean I don't want them[the students] to succeed.

Do you like assigning bad grades?

>> No.6182967

>>6182940
Well, a pedagogical standpoint is what I was looking at it from, as an aspirant teacher myself. Where do you TA? It might be cultural. Around here (California) people would mostly be happy with a 85% average, but we had a yankee teacher and she was different.

>>6182941
no u

Also
>implying an average with no standard deviation listed is relevant at all for statistical purposes

>>6182947
Why do you type so dumb?

>>6182954
Yes. Of course, I recognize that a class of perfect students taught by a perfect teacher is far from realistic, but it would be ideal, and I don't really see how anyone could hold otherwise.

>> No.6182970

>>6182956
So that he gets appraised as a better teacher,

His students are apparently failing, and if his students fail school-standard tests more than students of other teachers, then he gets flagged as an ineffective teacher

>> No.6182971

>>6182963
>Do you like assigning bad grades?
I'm in high school

>> No.6182973

>>6182888

LOL. You never learned binomial theorem in high school?

>> No.6182979

>>6182970
>So that he gets appraised as a better teacher
Why is it inconceivable that someone would want all their students to excel?

>> No.6182983

>>6182930

Read ahead and learn to integrate.

>> No.6182981

>>6182970
Completely off the mark. I'm not a HS teacher; my salary/income is not dependent on how I grade. I am a graduate student; my funds are strictly dependent upon how well I do in my grad classes and how I progress in my research.

In an ideal world, I'd like to give students straight 100%s because I don't like assigning bad grades. Most of the time, the students don't even know who's grading their papers; they just know their professor isn't.

>> No.6182982

>>6182979
What if they're smarter than you?

>> No.6182986
File: 31 KB, 319x443, dr seuss.jpg [View same] [iqdb] [saucenao] [google]
6182986

>>6182534

OP here again. Just found the second exam where some idiot wrote infinity/infinity = 1.

>> No.6182987

>>6182940

>tfw calc 4 at my university has had more Fs than any other grade the last ten years

>tfw I'm gonna ace it in nine days

They really make hard exams, way harder than equivalent exams from average american unis from what I've seen

>> No.6182991

>>6182971
Oh, I see.

In general, I just don't like assigning bad grades because I'd like to see everyone do well. I know that the real world doesn't work like that and, as such, I grade the exams accordingly. Like I said, I place academic standards and rigor above my emotional yearnings regarding grading.
>>6182979
/sci/ is home to a multitude competitive individuals whose collective motto is, "it is not enough for me to succeed, but you must also fail." The hivemind thinks that everyone believes in drivel.
>>6182967
I'm a northerner.

>> No.6182993

>>6182982
Then they should be able to earn a better grade? What's the problem?

>> No.6182994

i couldnt take the second derivative of a rational expression to get the concavity to sketch a curve because i dont know how to factor 80 term long expressions

>tfw retarded and going to state uni

>> No.6182997

>>6182986
Yeah, just like 2/2 = 1 or n/n=1 or 0/0 = 1.

>> No.6183001

>universities want diversity
>be african american with a good GPA and decent SAT scores
>realize that even though my scores aren't well into the middle 50 of a particular school, I could still probably get it if my background is taken into consideration
>struggling with intense feelings of inadequacy because the realization that being good in high school doesn't mean shit in university or the real world is too much
>scared to apply to any of the top schools because I feel as though I'd be the dumbest person there

>> No.6183004
File: 53 KB, 475x533, 1370570298811.jpg [View same] [iqdb] [saucenao] [google]
6183004

>>6182997

>trying to start this shit for the infinity/infinity 'th time

>> No.6183003

>>6182994
80 term long?

sounds like hyperbole really, if anything its just plug and play after writing out a bunch of terms..

>> No.6183007

>>6183001

> Go to Harvard.
> Get degree

...

> Fuck bitches in bathtubs full of money.

Go for it.

>> No.6183011

>>6182930

What does "AP" stand for? Anal penetration?

>> No.6183012

>>6182915
No , same exams every year, my group is just full of fucked people.

>> No.6183014

>>6183001
Just apply.

You won't be the dumbest person there as long as you work arduously and shed stereotype threat. You'll never know if you don't try.

>> No.6183015

>>6183001

If you can work hard being good at high school is enough. as long as you have a little talent discipline will carry you the rest of the way.

>> No.6183016

>>6182994

> Not using Faa Di Bruno's formula to take repeated derivatives.

Stay pleb.

>> No.6183019

>>6183011
Advanced Placement. They're SUPPOSED to be the equivalent of freshman college-level classes that can be taken in high school for students who want to challenge themselves.

>> No.6183024

>>6183003

well its more like 10-15 or something but you have to factor it to get where x is zero for the inflection points but i was too shitty at algebra but whatever i got a B+ anyway

>>6183016

i coulda just known algebra better to do it as well

>> No.6183025

>>6183001
Instead you should refrain from applying to "top" schools because they're fucking expensive and you can get the same education cheaper in most other places. Just do two years at a community college and then transfer.

>> No.6183027

>>6183025

hes black he gets to go to school for free man

>> No.6183029

>>6183025
Do not listen to this person.

Apply to the top schools that you can whilst going for scholarships. Also apply for a few safety schools, schools that will DEFINITELY give you a full ride/ample scholarship and will help you out if you're still unsure about the monetary prospects of the top school(s) you're looking at.

Top schools, safeties, the middles, etc. Aim middle, aim higher, then highest.

>> No.6183030

>>6183027
This guy is probably joking, but this is more or less true, especially since our income is sub-60k a year.

>> No.6183034

>>6183030
>mfw I grew up in a household where the income was between 10k-15k a year.

Going from shelter to math grad school sure is a trip.

>> No.6183033

>>6183029
Thanks

>> No.6183045

>>6183034
what's your iq

>> No.6183057

>>6183001
i love being the dumbest person in my top-tier grad program!

>> No.6183082

>>6182951

(1+1)^1 = 1^1 + 1^1

>> No.6183093

>>6183082
which is true..

>> No.6183099

>>6182888
sure it works if n is prime and a, b are in Zn

>> No.6183102

>>6183057
what are you studying?

>> No.6183103

>>6183029
That shit is only really necessary if you don't know where you're going, or didn't actually work hard enough to get where you want to go. I've never applied to more than one school at once, nor been rejected.

>> No.6183109

>>6183103
>never applied to more than one school at once
That's just abject planning.

>> No.6183113

>>6182584
There are a lot of analysis courses that use the concept of homeomorphism, but don't bother to define it.

>> No.6183115

>>6183109
No, it worked so it's perfectly good planning. If I was some kind of incompetent who couldn't get into the school I wanted, it would be bad.

>> No.6183122

>>6183113
why are university courses so cruel in this way? i can understand that they expect certain concepts to be understood beforehand, but shouldn't certain things that are crucial to your subject of study at least be mentioned to clear any confusion?

>> No.6183125

>>6183115
>it worked so it's perfectly good planning
Patently false.
>If I was some kind of incompetent who couldn't get into the school I wanted
*shrug* you don't seem very smart

>> No.6183127

>>6182691
Worse is (a+b)/a =b

>> No.6183147

>>6183127
Worse is (a+b) -(c+d) = (a+b) -c+d

>> No.6183154

>>6183147
That's not an error someone in calculus could be making.

>> No.6183155

>>6183147
Worse is (x-4)/(4-x) = 1

>> No.6183159

>>6183154
But I see it all the time

>> No.6183163

>>6183155
Worse is f'(x) of f(x)=x^2(sin(x)) = 2x(cos(x))

>> No.6183164

>>6183155
>>6183147
>>6183127
>>6182946
>>6182534
The thing is, I wonder why most textbooks don't include this kind of thing. Like, common errors.
Intro books should have THIS instead of rigorous proof bullshit.

Why don't you guys write a CC-Licensed math text-book, /sci/?

>> No.6183165

>>6183159
No, I shall decline to believe that.

>> No.6183168

>>6183099
Really? Can you direct me to a proof? Google's coming up dry. Unless it's really simple and I'm missing something...

>> No.6183184

>>6183168
fermats little theorem

>> No.6183187

>>6183164
>rigorous proof bullshit
Why are you taking a maths class then? That's what maths as a subject is.

I think the US and anywhere else that have the same classes for mathmos/engies/physicists/economists etc. should take after the uk (and again, other countries that do it, wherever they may be): we have seperate maths classes for each degree, so the engineers don't waste their time on such "bullshit".

>> No.6183198

>>6183187
I mean in intro books. You know, for high school kids. Before they could do anything even close to proofs, they need to learn common bullshit to avoid. You know, like the ones highlighted by the posts I chose.

This is the reason why people think it's hard to get into maths. They think it's so damn hard, when all they do is just repeat the same mistakes.

>> No.6183203

>>6183198
Can someone explain how to do a delta-epsilon proof?

>> No.6183213

>>6183184
Ah, cheers. Lowly Physicists don''t learn such things.

>> No.6183218

>>6183198
I see. It's funny, because in the UK our high school system DOESN'T do any rigorous proof; it's pretty practically based. Although I get the impression the "proof" in the US is a bit more like memorisation/regurgitation than thoughtful mathematics...?

>> No.6183223

>>6183203
what are you trying to show?

>> No.6183225

>>6183218
I ain't even US.
I'm just concerned about how maths is generally taught. There is little emphasis on teaching the actual rules of maths. Like, I haven't actually seen any method of schooling where they DIRECTLY just go like "See this movement here? The way I move the x across the equation like that? THAT'S WRONG."

>> No.6183227
File: 147 KB, 484x453, fuck you.jpg [View same] [iqdb] [saucenao] [google]
6183227

>>6183164

> Rigorous proofs bullshit

Herp derp why don't they just tell us the formulas and we can memorize and regurgitate them on demand without understanding why they're true?

You're a fucking retard.

>> No.6183228

>>6183227
see
>>6183198

>> No.6183229

>>6183203

Look in an analysis textbook. Lay's book is very good.

>> No.6183233

>>6183225
I wasn't assuming you were, that's just the only other country I can comment on as an example without making a bunch of shit up.

Maybe it depends on your teacher. I remember doing exactly what you just mentioned at school, although I'm fairly sure that wasn't in the textbook.

>> No.6183243

>>6183218
At the University level, proofs are considered very rigorous.

In the HS level, we have some quasi-proof style that students use in Geometry. It's line by line, no real thought process involved.
>>6183203
Do you even know the definition? The main reason people mess up with epsilon-delta proofs is because they don't know the definition too well.

Protip: You're supposed to find/''construct'' the delta, given the information you know.

>> No.6183250

>>6183243
That's what I thought. There are proof of limits as well thou, right? Like that guy is asking? How rigorous are those at high school level?

>> No.6183258

>>6183250
I don't know. I was homeschooled.

I didn't do epsilon/delta proofs during my HS days, though. Generally, epsilon/delta proofs are usually passed over by most freshman calc professors/instructors. There's a lot of ideas going on with epsilon-delta proofs that people don't realize.

For example, to do epsilon-delta proofs ''correctly,'' you must really know what a delta-neighborhood is, a limit point, an isolated point, The Archimedes principle, etc. You also need to be adept at what I call ''approximations,'' i.e., inequalities and 'tricking the math' so to speak. Anyone who has done epsilon proofs knows what I'm talking about.

>> No.6183274

>>6183258
are you good at them? were they hard to learn?

>> No.6183283

>>6183274
They're not so bad. It's just a matter of practice and refining your proof writing style.

Epsilon-delta proofs aren't hard to learn, but they are indeed different.

>> No.6183284

>>6183258
I did ε/δ proofs my first year of uni in the UK. δ-neighbourhoods, isolated points and the Archimedian property were all covered in the first semester. Probably not perfectly to be fair, but I wouldn't know, I gave up on joint honours and switched to straight physics after first year.

>> No.6183344

>>6182930
A. Read the rest of the school textbook.
B. Read the sources on the sci sticky, it has lots of good free books on math.
C. Read Wikipedia on math topics.

>> No.6183362 [DELETED] 

>> boards.4chan.org/b/res/518036841

>> No.6183367
File: 43 KB, 320x320, look of disapproval3.jpg [View same] [iqdb] [saucenao] [google]
6183367

> mfw when 100 more exams to go.
> mfw when n00b thinks 1/0 = 0
> mfw when same n00b thinks exp(2x)/(2x)=exp(x)/x

>> No.6183376
File: 111 KB, 576x720, mfw_dog.jpg [View same] [iqdb] [saucenao] [google]
6183376

>>6183367

> mfw when I have to loom for some reason to give these dumbasses part marks or else they'll come bitching to me.

>> No.6183383

>>6183367
1/0 = positive or negative infinity ;)

>> No.6183386

>>6182608
>>6182631

where do you people get this? I'm a chem E and need to solve PDEs a lot of times to solve problems, use differential forms for thermo, some vector calc theorems for fluid mechanics. Hell. I'm going took a complex analysis class, (not the one for math majors mind you, an applied version), calculus based probability. Calculus of variations is used in finite element analysis a ton. Need tensor calculus for transport phenomena problems.

Why do you math majors (pure) try to shit on us so much, sure I don't know all the formal definitions like you do, but what do you know about any other subject except math? If I had to learn all those theorems and prove them too, why would need we mathematicians.

>> No.6183388

>>6183383

Nope. It still doesn't mean anything in the extended reals. Only when you go the real projective line (or Riemann sphere) does it have any meaning, in which case 1/0 = infinity.

>> No.6183391

>>6183388
derivative of 3x^4 = 12x^3

>> No.6183398

>>6183391

And how is this relevant? 1/0 is still totally meaningless unless you're working in the one-point compactification of R or C.

>> No.6183400
File: 83 KB, 500x355, 30rock136.jpg [View same] [iqdb] [saucenao] [google]
6183400

>>6183007
>pic related

>> No.6183403

>>6183164
You sound like one of those retards who shouts "I never use pythagorean theorem irl, why am I learnin it in hs??"

>> No.6183417
File: 1013 KB, 281x288, Decomposition of Hydrogen Peroxide.gif [View same] [iqdb] [saucenao] [google]
6183417

>>6182534

Show no mercy, OP. Let them suffer. They are not worthy of the knowledge of the universe.

>> No.6183438

Sometimes I forget rules but then I think is 1/6 the same as 1/3 + 1/3? Of course not.

I don't know why people use rules that are clearly wrong

>> No.6183442
File: 306 KB, 1280x960, 1382169565352.jpg [View same] [iqdb] [saucenao] [google]
6183442

I failed pre-calculus twice in high school.

If I took Calculus in college (im 23 now) would I have a decent chance at passing it. Is regular calc easier than pre-calc? Figured this thread would be appropriate to ask

>> No.6183444

>>6183442

Yeah...you need to know pre-calculus to do calculus.

>> No.6183450

>>6182534
>> mfw everyone thinks 1/(a+b) =1/a + 1/b
I was grading papers for my Linear Algebra/Differential Equations midterm last week and I saw this twice.

Why.

>> No.6183460

>>6183438

you'd be surprised how many people cannot do operations on fractions.

What do people who have done higher level math think about teaching high school math? I have this vision to go back to teach high school math after my career. I have this idea that if students are taught in a way that allows them to see the applications in math, that they will consider majoring in physics, math, engineering, etc.

like say, we learn about some basic trig. Then we can use the learned trig to model some EE applications. Of course there would be limits, I wouldn't talk about fourier series or anything, but I would just show trig functions and complex numbers can model real world problems. They assignments/problems would be adjusted to so that students could solve them.

or say you just learned about the exponential function, this function shows up every field that calls itself a field. You can show some equations used in chemistry, physics, etc..........

>> No.6183494

>>6182704
This thread is about math. I wouldn't go into /fa/ and tell them that they're all ottermode instead of athletic
wouldn't go to /mu/ and tell them they know nothing about mlp

>> No.6183495

>>6183442
why would you think that? no, of course it isn't

if you can't do basic algebra then adding more shit into it won't work

>> No.6183510

>>6183460

That might be interesting. But teaching is constrained by both poorly motivated students and the mind-numbing structure of high school. Better to volunteer for outreach with motivated students - we do that in graduate school.

>> No.6183520

>>6183495

Sometimes going back later in life to study something relatively simple like calculus works for some people. I don't actually think most people are bad at math. True, they aren't necessarily good, but I think with hard work anybody can be average. A reasonably intelligent person, say someone able to get a degree from a good school, can definitely master calculus. Sometimes you just need the right teacher and the absence of an oppressive mindset like high school.

>> No.6183550
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6183550

>>6182588
Lemme guess. UofC?

>> No.6183551

>>6182951
>why wouldn't you do a = b = n = 1?
Lrn2counterexample, pleb

>> No.6183583
File: 37 KB, 662x663, 1385342349168.jpg [View same] [iqdb] [saucenao] [google]
6183583

>mfw people can't solve

x = 7x + 8x
x = -3x * 9x

>> No.6183592

whats worse is

(A+B)/(B+A) = 1/ln(-A-B)

>> No.6183595

>>6183583
x=0
x=-1/27

>> No.6183596

>>6183583
x = 15x

>> No.6183631

>>6183165
Just never go to grad school. Taste grading makes you lose faith in humanity.

>>6183258
No honestly I have no idea what you're talking about for the most part. Where does the archimedian property or isolated points come into play? The worst thing I can think of that most people need to learn is the triangle inequality and epsilon/3 trick.

>> No.6183848

>>6183592

LOL.What in the actual fuck?

>> No.6183854

I used to think that stuff in high school until I tried teaching myself calc 1 in my senior year and realized I didn't even know basic shit

>> No.6183874

>>6183386
Wow a well thought out and mature answer. I agree.

>> No.6183918
File: 22 KB, 500x285, Huh.jpg [View same] [iqdb] [saucenao] [google]
6183918

> mfw when 10+ hours of marking already
> mfw people think 1/0 = 0
> mfw people think -exp(-x)=exp(x)

>> No.6183935

>>6183386
Because I look at the courses required at my university for chemical engineering and see no courses covering that sort of math in any depth whatsoever. I have 2 friends who do both mechanical engineering and physics as a double degree, and another who does civil engineering, and they all say it's easy as fuck in comparison and that the math is completely plug and chug

>> No.6183941

>>6182691
Please explain me why this is wrong.

>> No.6183946

Is it true that 1/4 = 1/(2+2) = 1/2 +1/2 = 1?

>> No.6183949

>>6182534
A Serious queston: Is there any resource on how to learn this?

>> No.6183953

>>6183935

Yeah especially in chemical engineering you have very little math involved. My brother is studying chem eng and my dad has a PhD in it and they don't know any more than the basics of calculus and ODE.

>> No.6183957

>>6183949

High school math books. Possibly also elementary school math books for the fractions stuff.

>> No.6183961

>>6183949

Maybe Kahn academy has some stuff on grade school math. Check there.

>> No.6183962

>>6183957
Is there any one you can especially recommend?
>>6183961

Thanks to you bouth!

>> No.6183964

>>6183962

I personally don't know any good basic math books, but someone asked about this on stackexchange:
http://math.stackexchange.com/questions/69060/what-is-a-good-book-for-learning-math-from-the-ground-up

>> No.6183977

>>6183964
That reply is bullshit. That book is only useful for an undergraduate. I am in a similar dilemma, and there is nothing in that book which teaches basics. I can recommend Lang's Basic Mathematics, it starts from the really elementary maths, and moves fast enough so that you don't get bored. Saw some posts in the textbook thread as well, check that out.

>> No.6183993

>>6183977

There were MULTIPLE books recommended, dipshit. Do you not know how to scroll down?

>> No.6183995

>>6183099

(2+1)^3 = 3^3 = 27
(2^3) + (1^3) = 8 + 1 = 9

doesn't work

>> No.6183997

>>6183918
is exp suppose to be e....

>> No.6184000

>>6183995

1 is not a prime.

The obvious reason this cannot be true is that it contradicts Fermat's last theorem for n>2

(a + b)^n = a^n + b^n

>> No.6184001

>>6183977
>>6183964
I'll look into both stuff, thanks again!

Just to explain my situation: I currently taking Analysis I next to school and I have serious trouble with the basic stuff, like the mistakes described in this thread.

>> No.6184002

>>6183993
eh none of them are very good for the ground up treatment that anon wants. Would you honestly recommend Spivak's Calculus to someone who wants to go over fractions?

>> No.6184006

>>6183997

Yeah that's pretty obvious...

>> No.6184055

>>6183997
Sometimes it's useful to make a distinction between the exponential function and exponentiation from base e.

>> No.6184062

>>6184055

Like when? The reason you often see exp is because if you have a complicated argument it's hard to read, and sometimes you use e for something else like the electron charge.

>> No.6184086

>>6184002
Just learn the basic laws and play with numbers. By the way, the 12 basic properties (Commutative laws, Associative laws, etc) are in Spivak's Calculus, page 9.

>> No.6184102

>tfw I had 2nd derivative and primitive in high school so first year of uni in USA (after I moved) was easy as shit..

>> No.6184114

>>6184102

They teach this stuff in Canadian high schools but still most people I'm grading clearly don't know shit. Teachers just feel obligated to pass students who deserve to fail.

>> No.6184125

>>6184114
they better drop out then

>> No.6184169

>>6184125
The problem is high school teachers pass them in the first place because they are pressured to by school boards and parents

>> No.6184185

>>6184062
When you want to think of the exponential function as a function.
There is a lot of baggage associated to the constant e.
For instance, I'm currently working with exponential generating functions, and it is much more intuitive to count structures with exp(A) rather than e^A.
Intuitively, if A is a combinatorial structure, then e^A is silly.

>> No.6184197

>>6184185

Good point.

>> No.6184217
File: 23 KB, 288x499, why.jpg [View same] [iqdb] [saucenao] [google]
6184217

>intro to Macroeconomics
>"what are the 5 main things that can change demand for a product or service"
>somebody says demand

>> No.6184225

>>6184217
Whoops. meant to say
>somebody says price

>> No.6184255

>>6184197
I do hope I got the point across.
It's more of a conceptual distinction.
e is a concrete "thing" while exp is more floating in the air.
It helps with abstraction.

>> No.6185008

>>6184217
>implying that's wrong
I can see you've never observed a Steam sale.

>> No.6185039

>>6183941
'no'

>> No.6185059

>>6182534
>clear indicators of shit tier uni

>> No.6185063

>>6183164
>rigorous proof bullshit

How goes your job at McD's?

>> No.6185075

>>6183935
>>6183386
>6183386

It also just depends how much you as a student puts into it. Currently about to finish my masters in Aerospace and some of the classes are a joke, but the professors also give you deep knowledge if you take the time. Some of the homework problems I've solved, I've used lie groups to make the problem trivial (since it was), where other students were just breaking it down from a purely plug and chug the high school algebra shit.

If you want to utilize math as an engineer, you can, but a lot of the times the classes dont force you.

But you're in college and if you love the topics, you'll fucking take the time to learn.

>> No.6185084

>>6182608
Im in engineering taking first year calc and all my engineer bros including me are topriding the class

except that one fucking asian kid who doesnt even show up. Only for exams, of which he leaves halfway through

>> No.6185090

>>6183596
So 1 = 15
A*

>> No.6185154

>>6183935
>>6183953

are you trolling?

every decent chem E program makes you learn about PDEs and transport phenomena (requires tensor calc).

If you're still convinced that hurr engineers only knows calc 2, look at BSL - transport phenomena, it's pretty much our bible. Yea it's probably not as much as a physics/math major, but it comes very close.

My list of math courses taken:
single variable calc
multivarable calc
vector calc
calculus based probability
linear algebra 1 & 2
applied complex analysis (not the one math majors take)
ODE
numerical methods
PDE

>> No.6185184

>>6185090
no, x = 0
are you a fucking idiot or something

>> No.6185222

>>6182534
>> mfw everyone thinks(a + b)^n = a^n + b^n
It's called being a freshman.

https://en.wikipedia.org/wiki/Freshman%27s_dream

>> No.6185267

The most surprising thing is the number of people who think 1/0=0. Why.

>> No.6185292

>>6185267
(1/0)^-1 = 0

>> No.6185296

The thing about more complex math that I don't like is that, if you're not using it constantly or at least refresh your memory from time to time, you'll forget how to do it.

>> No.6185302

>>6185184
x = 15x
x/x = 15x/x
1 = 15
idiot

>> No.6185311

>>6185302
> dividing by zero
idiot

>> No.6185313

>>6185311
I divided by x, not 0

>> No.6185314

>>6185313
See
>>6185184

>> No.6185317

>>6185314
You don't know that x = 0 until you already solve. I divided both sides by the same thing which is allowed in algebra. Fuck off.

>> No.6185326

>>6185317
>You don't know that x = 0 until you already solve
Until you get to x=15x. You should know how zero times anything works before you get to algebra.
>I divided both sides by the same thing which is allowed in algebra
Unless that thing is zero.

>> No.6185330

>>6185326
Please, prove that 1 = 15 is false

>> No.6185331

>>6185317

Dividing by a variable doesn't make sense unless you assume that variable is not 0. You can't divide by 0 in a field.

>> No.6185338

>>6185330
Additive identity
A+B=A
iff B=0,

A+B=C
If B=/=0, then A=/=C

>> No.6185369

The problem is in high schools. The teachers are often incompetent (i.e., humanities majors who barely passed high school mathematics themselves), and end up "teaching by the textbook" which ultimately ends up with students memorizing formulas rather than understanding math. And then those who are incapable just end up perpetrating the cycle. The students who get high marks are the ones who get into engineering and such, and produce mistakes like the ones you are currently marking.

Students no longer get a "feel" for numbers when learning math, only a rigorous procedure to follow, which is why such simple "pitfalls" are so common. Of course, the government is too lazy/cheap to set higher standards for teachers, so this will only continue to harm students unless they have the fortune of having a good, competent teacher.

>> No.6185394

It's the nature of mathematics that lends to difficulty in it's instruction.

I was at the top of my class, mastering just about everything save for mathematics. I was and still am knowledge hungry, but the assumptions and inter-connections in mathematics grow at such an astonishing rate that I couldn't piece them all together and make all my knowledge fit together precisely. I didn't and couldn't take math at face value because of that.

It took a pretty big paradigm shift to finally get it. I pretty much had to take down my ego to 0, and accept that I couldn't have all the answers via all my current inter-working factoids of knowledge.

I had to re-root myself as a very ignorant person and build the ground work, and take nothing for granted. I am now very close to getting my BS in mathematics and finance and I couldn't see myself do anything else.

>> No.6185399

Well they are first years after all.

>> No.6185401

>>6185394

Poster of the above

>>6185369

I have to agree, and I left it out my response. Mathematics is taught very shittily. It's either you're a master at it by being very narrow-focused like being programmed by a computer, you kind of get it, but are a very good logician and can "BS" your way through to the answer a high enough % of the time, or you just don't get it at all.

>> No.6185479

>>6185008
it's a common misunderstanding of phrases, demand refers to the demand curve, which is a graph of quantity demanded versus price, a change in price doesn't move the curve itself.

>> No.6187056

can someone who's been through precalc/calc/calc II etc explain why you actually study a separate course in differentiation/integration and to what level each of those stages are? in the UK and completely lost as to how this works

>> No.6187063

>mfw know 0 mathematics
>mfw get by fine in life

>> No.6187078

>>6187063

I guess my dog is pretty happy too even though she can't into math.

>> No.6187088

>>6187078

>mfw if you live in america you've probably eaten a broccoli i've touched

My job is more important than yours. If I'm a dog, you're a sea urchin.

>> No.6187099

>>6187088

So you're an illegal mexican immigrant picking vegetables?

Someone with zero skills whose job could be done by literally anyone?

>> No.6187115

>>6187056
We dont, Calc 1 is introductory and you learn about both integration and differentiation

>> No.6187119

>>6187063
>never get into skilled labor

how's the psychology masters treating you at starbucks?

>> No.6187169

>>6185154

Decent list. Transport phenomena is interesting. Theoretical astrophysicist coming from a B.S physics, mathematics background, so I'm interested in pretty much all physics, especially that traditionally neglected by physicists (reaction kinetics, fluid dynamics, simulation, as well as obscure branches of the main kinds of physics.) They don't always neglect it, but (as an example) kinetics is really useful but few B.S. physics students ever learn it unless they are also chemists. I would say that transport phenomena is similar, at least to physicists.

I understand your anger, since I understand the arrogance of physicists and mathematicians; they seem to think astrophysicists are a lesser breed, which is bullshit. But if you demonstrate your skills to them they will, for the most part, acknowledge your scientific abilities and render respect. Thats what I did.

>> No.6187172

>>6183400
Hey wait a minute, that fictional character doesn't fuck bitches while bathing in money at all! Even though part of his character is that he went to harvard!

>> No.6187176

>>6185313

Listen up, chode. When you cancel a variable from both sides, you implicitly acknowledge that x = 0 is a solution. After that, you are looking for further solutions.

>> No.6187191

>>6187169

> Fluid dynamics
> Neglected

Seriously? Fluid dynamics is huge in applied math. Every applied math department has a lot of fluid dynamics researchers.

>> No.6187234
File: 128 KB, 496x496, 1385502068353.png [View same] [iqdb] [saucenao] [google]
6187234

>>6187088

WOW!

>> No.6187237

>>6187191

I know, but I said physicists, not applied mathematicians, and anyway there weren't any fluid dynamicists in my math department. (accident of fate, I guess.) To the *physicists*, which are dominated by string theorists, fluid dynamics isn't as interesting, so they don't teach it to their students. You are lucky to get a class from the math department; I didn't. You would have to take it from engineers, and they have a different focus.

This kind of schismatic approach to physics is part of why I left Physics, and joined Astronomy/Astrophysics. Many physicists call astronomers/astrophysicists "failed physicists." False. A theoretical astrophysicist must be conversant with all the branches of major physics except beyond quantum field theory, and there are several who are with that. Moreover, a physicist doesn't necessarily learn fluid mechanics in grad school; the typical curriculum is like undergrad, with grad classes instead of undergrad classes and classes in your specialty (QFT, string theory, or solid state, or AMO, or nuclear...)

>> No.6187247

>>6187237

Weird. At my university, we didn't have a single string theorist in the physics department, which was dominated by material/astro/medical physicists.

>> No.6187251

>>6187247

Also, every single upper-year physics course we had (other than labs) was cross-listed with applied math.

>> No.6187265

>>6187247
>>6187251

Interesting. I guess department cultures do vary widely.

My physics department was dominated by AMO and nuclear experimenters, with some string theorists (I was a particle/mathematical physicist before I switched in grad school.) The math department was dominated by linear algebra and differential equations/nonlinear analysis, with algebraists making up a substantial minority. A few oddball faculty here and there doing their own thing (it was a math department after all.)

My astronomy department (I consider myself an astrophysicist, not an astronomer, since I work on theory) is dominated by radio and optical observers. Actually its kind of annoying, since there are few theory talks, and those that are are rarely in my field. I do work in planetary interiors/atmospheres, as well as MHD work, and whatever the hell I feel like working on.

>> No.6187322

>>6187237
Fluid dynamics is a huge part of biophysics and other physical fields, it was most certainly taught as a physical course to me.

Certainly most physicists are not string theorists. I don't know where the fuck you went but it's not the case in Europe.

>> No.6187348

>>6187322

I agree with you. Most physicists aren't string theorists, but they dominate the field - particle physics is the largest enterprise in physics, and the theoretical particle physicists are dominated by string theorists. You should know this, since CERN (a fucking city of physicists) is in Europe.

Mostly my complaint is that fluid mechanics is rarely a required course in physics, at least in America. It is essential to describing most of the physical world.

inb4 stupid shit about going to school in America

>> No.6187372

>>6187348
>Mostly my complaint is that fluid mechanics is rarely a required course in physics
At my school at of the fluids stuff is in the engineering departments

>> No.6187373

>>6183045
higher than yours

>> No.6187574

>>6187348

Actually, condensed matter is the most active area of physics research by a fairly large margin. Particle physics is second, followed by astrophysics, and then atomic and molecular physics.

I saw more recent stats somewhere, but I couldn't find the doc, so here are the 2008 stats for PhD physics graduates by field of study. http://www.aip.org/statistics/trends/reports/physgrad2008.pdf

>> No.6187576

>>6182534
why does this surprise you ? in my personal experience math classes are about memorization and not about mathematical concepts.

>> No.6187582

>>6187576

I guess you've never taken a pure math course.

>> No.6187697

>>6182792
Only Dalhousie kids are that retarded.

>> No.6187704

>>6183001
>feel as though I'd be the dumbest person there
Well it'd be kinda silly to go to university if you already knew everything. You're in an enviable position - if you were the dumbest person, you'd have the most to learn.

>> No.6187707

>>6183550
That would be a fun coincidence. I just got my calc midterm mark back today.

>> No.6187711

> mfw everyone thinks(a + b)^n = a^n + b^n

it's not?

>> No.6187713

>>6187711
...binomial expansion...

>> No.6187741

>>6187697

lol

>> No.6187744

>>6187711

If you assume this is true then

4= 2^2 = (1+1)^2 = 1^2 + 1^2 = 1+1 =2

Therefore 4=2, which is obviously retarded.

>> No.6187769

>>6184102
How can you have "second" derivative? If you know first you know them all.

>> No.6187969

>>6187744
Maybe math is retarded and flawed?

>> No.6188031

>>6187744
You can't distribute the exponent…

>> No.6188033

>>6187969
Yes

>> No.6188227

>>6187969
It's true that we don't know whether math is completely consistent, but if the inconsistency was to be found in a simple squaring of a sum of really small numbers we'd have found it already.

>> No.6190146

>>6188031

I know, that was the point, dumbass. I was showing that distributing the exponent leads to the retarded conclusion 4=2.

>> No.6190165

>>6182534
If mathematicians are so good why can't they prove mathematics is consistent within its own framework?

Checkmate matheists

>> No.6190166

>>6190165

In case you're not trolling, because of Godel's incompleteness theorems.

>> No.6190169

>>6190166
>theorems
And what axioms are these theorems built upon?

>> No.6190176

>>6190169

I am an analyst, not a logician. You can read a sketch of the proof yourself on wikipedia.

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

>> No.6190188

>>6190176
>I'm a mathematician but I'm not a mathematician
I think I just discovered an inconsistency in the framework of your posts.

>> No.6190200

>>6190188

I'm a physicist turned mathematician. Most of my experience is in analysis and dynamical systems. I have not taken a course on foundations, and I have not read Godel's proof myself. Like in every field, different mathematicians have different specializations.

The material is out there if you want to check Godel's proof for yourself.

>> No.6190206

>>6182534
Jesus Christ, I'm failing Calc A right now and I don't make these mistakes.

>> No.6190207

>>6183388
Actually, this follows pretty simply with the basic rules of doing fractions. For example:
1/2=0.5
1/1=1
1/0.5=2
1/0.05=20
1/0.005=200
SO as the denominator gets smaller (eg, closer to 0), the quotient gets bigger. When the denominator gets infinitely close to 0, the quotient should be infinitely big.

>> No.6190209

>>6190188

>I think logic is a subset of mathematics

>> No.6190213

>>6190209
Logic is just a trivial application of homotopy theory.

>> No.6190219

>>6184169
The problem is also the idea in society that "I'm not a math person" excuses people from being fucking morons. "I can't make change. I'm not a math person." " I can't do fractions. I'm not a math person." Try pulling out "I'm not an 'English person'" when you say something stupid.

>> No.6190220

>>6190207

I can tell you're in high/middle school. Think about what happens when the denominator approaches 0 from the negative side.

Dividing real or complex numbers by zero only makes sense in the one-point compactification of the real line or complex plane. It should be obvious why.

>> No.6190236

>>6190220
Okay, as the denominator approaches zero from the negative side, it gets closer to negative infinity, with x=0 as a vertical asymptote. Either way, the quotient goes to an infinite extreme, so it follows that the quotient is infinitely big, in either the positive or negative direction.
I wasn't trying to get into the whole proof of this concept, but it is a way to explain the "1/0=infinity" concept to a student say, in an algebra class, without using Riemann spheres.

>> No.6190246

>>6190236
I was trying to relate the point that a concept as complex as 1/0=infinity can be explained in a simpler way, so that someone can grasp the concept. It's this kind of intuitive connections that need to be taught in lower-level math classes, in grade schools particularly. I've seen students in an Algebra 1 class use intuitive methods of finding patterns in a set of numbers to write linear equations. The class did a lot better with this than the method shown in a textbook, and they were doing it in their heads.

>> No.6190248

>>6190213
How so?

>> No.6190250

>>6190246

1/0 does not equal infinity if you are working with real numbers. That is wrong, you enormous n00b.

>> No.6190254

>>6190246
>I've seen students in an Algebra 1 class use intuitive methods of finding patterns in a set of numbers to write linear equations.

Yeah because it's so hard to write a linear equation. How else will people figure out the slope of a line without knowing 1/0 = infinity? (which is fucking wrong except in one-point compactifications of R and C).

>> No.6190260

>>6190248
Do you even univalent foundations?

>> No.6190273

>>6190260

For someone who is good with logic, you aren't very good at deducing things

>> No.6190283

>>6190254
Actually, it is pretty damn hard for an 8th grader who is being taught by someone who is following the cookbook method of "find the slope as m=(y2-y1)/(x2-x1). Then substitute the slope and one of the points into the point-slope formula..... Then solve the point-slope formula for y." When a student can spot the patterns in two ordered pairs, to find how to make the x get to the y for both of them, it's a hell of a lot easier, and the cookbook method can reinforce what they already know in their heads. Plus, get a good look at a struggling Algebra 1 student's face when they realize that they can actually do this. It can turn their whole academic career around.

>> No.6190297

>>6190283

You must have been one retarded 8th grader.

>> No.6190301

>>6190297
Nope, but I knew quite a few retarded 8th graders. Kids who weren't "math people" and are now fucking idiots. On the other hand, I saw some find quite a lot of success once they realized that they could be "math people"

>> No.6190307

>>6190301

Telling people 1/0 = infinity does not create mathematical intuition. It's retarded.

>> No.6190558

>>6190307
It's time to stop posting.

>> No.6190720

>>6190169
>And what axioms
And you can do you own homework, faget.

>> No.6190724

>>6187744
>(1+1)^2 = 1^2 + 1^2
>which is obviously retarded
Obviously. Lrn2exponent, retard.

>> No.6190833

>>6190724

You clearly have zero reading comprehension. I was showing the guy here

>>6187711

why you can't distribute the exponent.

>> No.6190852

>>6182930
How old are you?

>> No.6190854

>>6182930
>rigorous engineering program

Isn't that an oxymoron?