/sci/ - Science & Math

>mfw when I'm taking BC
>mfw its easy shit

>mfw im taking calc ab, ap stat, ap bio, ap chem, and ap physics c all in one year as a high school senior

stop complaining cancer

>mfw high schoolers BAWWing

they dont even use english anymore in these classes

teacher here describes limit with hyglogryphics

>>3594302

still virgin?

>cal AB

Someone care to explain this acronym?

>>3594318

it's the 1st semester of college calculus spread out into 2 semesters.

Combinatorics

>>3594318
Calculus Anal Buttdevastation.

Entry course for people new to calculus.

>>3594314

yup but mfw i'm a doctor and i drive a bentley and I get bitches whenever I want

>>3594326

Dear lord. Why would they even do that? Biologically, your brain is adult by 18-20 anyway, so it's not like there's a reason to teach it more slowly for high school students.

triple integrals were pretty cool, although my favourite has to be vector calculus. I'm actually using it now in my fluid mechanics course so I'm glad I paid attention.

Mathematical Statistic II

Chapters 8-10 fucked me up

9th grade math
shit was hard

>>3594326
dumbshit, its semester A and B of college calculus.

Went up to vector calculus when doing my BS in physics.

>> mfw when I dropped ODE because I had better things to do
>> mfw I've since taught higher level math at another university

>>3594285

Differential equations/Calculus 3

The hardest high school calc class (can't remember if it was AB or BC) will prepare you well for calc 2 which is the hardest on the track of calculus until you hit diffeq, but if you're a dumbshit at visualization and hate to actually conceptualize math, you'll hate calc 3 more. Differential equations is calc 2 again, but with some easy shit to do before integrating/differentiating. It's also much more formulaic, and the solutions are much more obvious than calc 2.

Tips: Easy shit that you might forget are partial fractions, trigonometric calculus, completing the square (haha, middle school), integration by parts, and uh, most of calc 2.

>>3594302
Hey dumbshit,

Your taking all classes with heavy crossover and similar mindsets, of which often when one has skills and mindset for one it assists them in the others. complain to me when you spread those courses out over the years, so in one year you also have to juggle courses which require completely different sets of skills and objectives. like my senior year

>AP Calc AB, AP Eng Lang, AP Psych, AP Econ, AP Art

>>3594402
>ap art

>>3594285
>mfw when you apfags can't compare to IB superiority

>>3594369
You need to read this.

http://www.maa.org/devlin/LockhartsLament.pdf

>mfw when im a junior taking ap chem, ap physics, and ap us history while teaching myself ap environ. science.

took ap calc last year, it was fucking easy.

>>3594363
no he was correct the first time, it's a college level calc spread out over two semesters.

I believe the only common AP courses that usually count as a year's worth of credits are physics and chemistry

>>3594402

Hey Dickthong, those are only half of the classes im taking, since u asked here's my whole schedule.

AICE reporting in.
>Nobody knows AICE ;_;

Highest I've taken is cal 3, DE comes next for me. So far it has all been easy as fuck.

if you still think there's such thing as a "highest" math class that means you're in the lowest of the low peasant math classes. deal with it

>>3594469
what the hell is AICE anyways?
how does it compare to IB/AP?

Hahahahahaha, AP Calc AB hard. Nigga, I smoked every day the two weeks prior to it and got a 5. It's all about thinking about what youre doing and not memorizing eveyrthing. I can prove every theorem I learned in there using only pythatgorean theorem.

>>3594462
Thank you. You may now continue to complain. But 8 classes? where the fuck do you go to school? Here they don't let you take more than 6 senior year, and try to push everyone into 5.

>>3594421
You got a problem? Lets see you do this shit..

>>3594505

macro and govt are separate semesters so it's 7 classes and 1 lunch period. I'm pretty blessed to go to a high school that lets u take whatever classes u want and has 8 periods..

>math

>>3594510
Yeah, pretty much, my school only has seven periods, AP classes are almost always in the same period, so its near impossible to get full schedule of them, they don't let anyone except freshmen take all seven periods, AND all courses are year long. Its the shits man.

>implying AP shit counts for medical/grad school

stay beta kiddos

>>3594488
Advanced International Certificate of Education. Basically, Cambridge (London)'s version of the AP tests. I found AP courses more challenging, but then again I took AP physics, bio, chem and AICE English, Critical thinking, Writing, etc.
As a comparison, I took AP Bio 10th grade and passed with a 5, then took the AICE Bio exam two years later with no preparation, winged it, and still passed.

PhD in Pure. It's great, you should try it. Be prepared for a lot of very intelligent by odd people - odd in an interesting way, not in a try-hard "goofy" way. Not a single female doing pure, some doing applied, and heaps doing stats.

>>3594440

Before I embark on this many paged PDF, can you tell me why I should read it? Are you mocking me or will it underpin my points? Is it something that you think I'll like or do I need to read it and learn to stfu.

God damn, you americans have confusing high school course setups. Why not just stuff all the math into one whole course? Don't really understand what the point of it is when it's divided it up.

>>3594685
european math approaches are dogshit. i know, i'm at an ivy and they try to push that same dumbshit methodology.

differential equations 1... but ive never even seen math as difficult, only a game for children to play.

in similar words, i've always seen math as a childish game... answers can usually be found much more effectively with computers.

high level engineering courses are much harder.

you highschoolers and your formulas... you have no idea how the real world works. so naive.

>>3594713
>in similar words, i've always seen math as a childish game... answers can usually be found much more effectively with computers
fuck you're dumb.
>implying computers don't run on math
>implying you're smart because you can call a computer function written by someone smarter than you to give you an answer

>>3594713

Was I sleeping, while the others suffered? Am I sleeping now?

Tomorrow, when I wake, or think I do, what shall I say of today? That with Estragon my friend, at this place, until the fall of night, I waited for Godot? That Pozzo passed, with his carrier, and that he spoke to us?

Probably.

But in all that what truth will there be?
(Estragon, having struggled with his boots in vain, is dozing off again. Vladimir looks at him.)
He'll know nothing. He'll tell me about the blows he received and I'll give him a carrot.
(Pause.)
Astride of a grave and a difficult birth. Down in the hole, lingeringly, the grave digger puts on the forceps. We have time to grow old. The air is full of our cries.
(He listens.)
But habit is a great deadener.
(He looks again at Estragon.)


*At me too someone is looking, of me too someone is saying, He is sleeping, he knows nothing, let him sleep on.*

diff eq, calc III, mathematical physics

>>3594285
aerospace engineering phd student here. graduate coursework in linear algebra (banach spaces n shit), real, complex, and functional analysis, PDEs, and numerical methods.

>>3594685

I'll probably get flamed but I'm Canadian. Over here we have only 3 types of math courses.

1. Data Management (statistics, analysis, counting etc)

2. Advanced Functions & Intro to Calculus

3. Calculus & Vectors

This is for the final year, all the other years it's pretty much just one class.

It seems more effective to me at least.

>>3594726
look. im not trying to undermine the math, im saying theres alot more out there to worry about than mathematical techniques. it's probably a good idea to understand the techniques once, but we have bigger fish to fry in the engineering world. we don't need to learn 10 proofs to find the area of a circle is what im saying. we can trust that its pi*r^2. you obviously haven't been around long enough to see things my way. physicists and mathematicians don't run the world, engineers run it. and it really disheartens me to see engineers being called faggots on this online board. but what do i know.

>>3594742
it really disheartens me to see engineers being called faggots on this online board

son you got trolled

God this thread is full of butthurt math failures trying to discredit the hard work others have put into their math courses.

>>3594713

I just want to note that engineering classes at "higher levels" are just manipulating calculus a bit and tooling a bit with some equations.

I always have a few students who tell me they don't want to do "math" because all math can be done by computers. By this, of course, they mean all math that engineers need can be done (easily) with computers. Which is, for the most part, true.

If you want to see what mathematicians do, you might want to get your feet wet by looking up something like "topology" or "abstract algebra." These is by no means an exhaustive list.

abstract analysis

>>3594755
mathfag, i do computational fluid dynamics. i tackle the pinnacle of challenging math problems using a combination of advanced numerical methods, nonlinear pde analysis, physical insight, software engineering, and high performance computing. of the millennium problems, navier stokes and P/NP are the only ones whose solution could immediately affect even those who don't understand them.

i'm an engineer. mathematicians suck. do something useful.

Wow, high school everywhere. Cancer.

If you haven't already taken Calc IV, you don't belong on this board.

>>3594742

Currently, many of the engineers who are making groundbreaking changes to the world we live in are also well-versed in either pure or applied mathematics. The ones which are not skilled in mathematics are not so common.

Also, there is a definite difference between learning mathematical techniques [eg, calculus, algebra], learning proof techniques [eg, undergrad algebra, undergrad analysis, etc.] and learning to explore mathematical structures to find new theorems lurking about [research].

Also note that mathematics, as an exercise, allows one to "mature" in a method of thinking which is productive to creating and realizing new and fruitful ideas.

>>3594782

If you are well-learned in CFD, then you should know that Solid State and Fluids, as a study, developed from a long line of mathematical thinking which was, for the most part, theoretical. Recent applications of quantum dynamics to FD is (primarily) computed theoretically, but the results are visible macroscopically.

I'll admit FD is currently one of the tougher of the sciences, but computationally it is do-able. I don't know why you cite the MProblems as the be-all-end-all of mathematical problems (especially since there are significantly more recent and interesting lists) but I'll just cite some questions that recently came up at a conference: what happens to fluids on surfaces which are not Ricci-flat? This may seem like a purely theoretical exercise, but note that general relativity predicts some interesting possibilities --- and that many structures behave as liquids under certain circumstances. Neat stuff.

>>3594788
Calculus IV?
Fuck kind of wizardry is that? My uni only goes to Calc III

And yes, I agree with your post so sage

>>3594812
a long time???

im taking fluid mechanics next semester and my textbook covers only newtonian fluids in ch1-3.... chapters 4+ are quantum mechanical principles.

and we all know quantum mechanics isn't OLD. its quite new.

>>3594812
>developed from a long line of mathematical thinking which was, for the most part, theoretical
no, that's quite bullshit. the navier stokes equations, euler eqns, and potential flow were well studied for half a century prior to the advent of computers. numerical methods were developed for these before computers even existed in the sense we think of them now.

fluid dynamics is one of the most elegant physical problems in the universe, even recognized by physicists and mathematicians. it is not fucking theoretical in any sense at all. the pioneers of the field were very much engineers in every sense. taylor, prandtl, reynolds, fourier, every thermodynamicist in the 19th century... this is as "applied" as application gets.

also, computationally it is not "do-able". direct numerical simulation has obscene computational requirements such that a full aircraft an't be simulated in such a manner for centuries.

>>3594285

taking pre-calc this yearn and AP physics.

so far everything is going just fine, my only problem is when if i get something wrong the first time, i begin to think i'll never get it right.


But then of course i think of Andrew Wiles and it gives me confidence to keep trying, then i normally get it right.


I wouldn't say it's hard though, you just have to be in the right mindset when doing some of the work.

>>3594833

I'm not entirely sure my post was understood. Yes, QM is relatively new, QD is also new. Fluids is quite old, but Newtonian fluids is (as you will find out) not a great approximation. Nonetheless, theoretical mathematics was able to find new and useful ways of representing fluids since then.

To discredit mathematics by saying it wasn't or isn't useful in such discoveries is sort of silly.

A little off topic, but what movie is OP's picture from?

>calculus AB
>hard

chooseone.png

>>3594302
I did
AP Calculus AB
AP Physics AB
AP Statistics
AP Literature
AP Government
AP Macroeconomics
and AP Microeconomics
all my senior year.
>mfw 4.91 year gpa

Fucking religious/conservative government teachers.

>>3594879
A Serious Man. The main character is a physicist, but the movie isn't about physics or math beyond a few scenes. Disappointing.

>>3594859
> new and useful ways of representing fluids since then.
NO IT FUCKING HAS NOT. holy shit. it fucking has not. theoretical mathematics is fucking worthless and predicting the most fundamental of turbulent flows.

>>3594879
a serious man

>>3594302
yfw when you get no sleep and only get 3's with no college credit

Astrophysics you niggers.

suck it up, it's not that hard
i took ap calc as a sophmore, i was 14 at the time

ring theory

>>3594859
im the same student whos taking fluid mechanics next semester, and ive already looked enough ahead to see what you're saying is bullshit. newtonian approximations vs. quantum approximations depends on the mean free path. please read up before you speak.

pre-algebra B

DiffEq. I have a feeling I would have liked it if it weren't for it being a T/TH 8:00AM class, the instructor having a monotone voice (did too many drugs when he was my age) and teaching from powerpoints, and the textbook's narrator being a total smartass and not explaining anything.

fuck

that

class

Taking Differential Equations this fall, and Calc III (which is Vector Calculus, Multivariable Calculus, vector algebra, etc ) in the spring.

Normally they're taken in reverse order but my major recommends doing differential equations first.

>>3594302
Lucky you, my high school cancelled all math classes beyond algebra 2 (even AP classes) in order to bring it's test scores up.

I tried a bit of the cool stuff, but one does not simply walk into algebraic topology. I rather code recursive functions all day and call it condensed matter physics, than drown under all those theorems.
The little I can understand I think is very nice though, I am secretly jelly of mathematicians

>mfw I had to take Calc 1 in university
>mfw I went to a shit tier high school

Mathematics of Compound Interest, you start dealing more with Black-Scholes, geometric summation, and other financial fun. Outside that, probably calc 3 or linear algebra (fuck linear)

After multivariable calculus there is no clear order to rank the math courses.

As a math major, I've done the standard undergrad math curriculum. That is: analysis, abstract algebra, number theory, chaos theory, statistics, probability, numerical analysis, etc.

The difficulty of a course usually depend on the level of abstractness and the level of the proofs.

>>3595235
which of those did you find most difficult?

>>3594713

Depends what kind of answers you seek. Sure, if you want to build a pumping station or a bridge, computers will do most of the calculations for you.

But that's not what pure maths is about. It's about the infinite possibilities of existence - exploring what it means to think and what objects can be built from pure thought. Computers tell you how to build things you already know about. Maths teaches you new ways of thinking.

>>3594285
At U of M, math 525, abstract algebra. Shit was hard. It was the only time I was legitimately challenged in a math class.

>>3594742

Lol you goofball. Math isn't proofs, it's ways of thinking. When all you can do with linear equations is crank them out and row reduce them, that's ALL you'll ever do. But when you have a whole toolbag of ways of looking at them, such as transformations between vector spaces, and projections, and plain old linear equations, and you understand WHY these are all the same, you'll be able to reason much faster and with greater power.

Math isn't about proving things, or calculating. It's about understanding things.

>>3595262
>most basic of all real math classes

well well well.

Numerical methods.

>>3595288
50/50 you're trolling. Hard to tell. It's not what you think it is.

>>3595310
I'm a doctoral student
>guess again

If I'm not in the american system, how do I know what is treated in each part?

Anyway, I think mine would be about topology or multivariable calculus.

>>3595324
Your trolling shall not work on I.

>>3595324

Sure, PhD of Communications.

>>3595335
I'm only in my first year but I certainly know exactly what abstract algebra is all about.
I'm 'working' in the field of topology and leaning possibly toward geometric algebra (though I'm a bit naive about the subject)

>>3595365
It wasn't your standard abstract algebra course. Was taught by a professor who specialized in the subject. I was an undergrad when I took it. Started out with maybe a dozen grad kids and I. Ended up with 3 other grad kids and I for the final, with one auditing the class. It really was vicious.

Error correcting codes. Spanning distance. Covering spheres. Crazy group rules that I've since forgot - which is unusual. I usually remember most things of math I learn, but this class was above my level.

>>3595365

To a PhD, sure abstract algebra is no big deal. But for an undergrad, it's pretty intense the first time you see it.

>calc AB
>hard
Nigger you best be joking

Never took notes

Never did homework

74

3/6 on my AP exam

I was an AP kid though, I was hospitalized for a week for a depressive episode or something, it's hard to remember that year

>>3595403
ADHD* kid. For example, I was allowed to sit on my desk and stare out the window in the last few months of school because I had brain problems.

>>3595377
ah yeah. I remember in undergrad I took a set theory course and the professor totally reamed everyone's asses. Wasn't the standard undergrad set theory course.

I'm not sure what you mean by "error correcting codes". What is this?

>>3595380
I wont have a PhD for another 4 years or so. I'm just in grad school. That's what "doctoral student" means.

>>3595417
Communication theory. What if you have to send a message (in bits) over a "wire" where there's a probability that some bits will be flipped randomly to the other bit.

An error correcting code is a transmission code so that it is tolerant of errors. If you have every message differ by at least 2 bits, then it's possible to detect an error during transmission of 1 bit off. If you have every possible message separated by 3 bits, then any single bit failure of a message is correctable at the receiving end. The covering spheres refer to an error tolerance and for each message in the code the set of messages within that error tolerance of the message. If no two spheres intersect, then the code can correct up to that number of errors of the error tolerance.

>>3594302
Ohhh sonn, calc ab, ap stats, ap spanish, apush, apel, ap physics junoir three years ago. Too many classes at one time fist bump

Highest level math? Like it's a linear track the whole way up.

After Calc 2, you go anywhere you want, generally into the trinity of stat, applied, and pure. My "highest" is M.S....derp.

>>3595434
There was some crazy group analysis in there for some of the proofs that I've long since forgot.

>>3595417
Lol, basic number theory. Checksums, dude?

Shit they run before the credit card you swiped gets set out into the big wide world. Come on...

>>3595450
You want to do proofs concerning G256 by hand to prove that certain subsets are error correcting codes with a certain tolerance? Good luck sir. That was just a very small part of the class. I've repressed most of it.

>>3595434
by 'bits' do you essentially mean strings of words over a given alphabet?

this sounds like a simple application of modular arithmetic. If I understand correctly. Though that is quite interesting. More interesting than my algebra class I took in undergrad. We stopped at silow's (sp???) theorems but didn't even prove them

>>3595450
>Lol, basic number theory. Checksums, dude?
To continue, no not basic checksums. Checksums are a form of data redundancy. They let you know if the message has been corrupted, up to the strength of the hash used to generate the checksum. The really interesting/hard parts comes when doing it for obscure groups, without brute forcing the answer, using some high level group algebra theories that I've long since forgot, to prove that some codes are error correcting up to X errors.

>>3595460
In this case it was bits. The strings would be mappable via an encoding to bits. The messages were strings of bits.

>Sylow theorems
http://en.wikipedia.org/wiki/Sylow_theorems
Oh god, it's starting to come back to me a little bit. Totally was in over my head with that guy.

The hard part about the class was that he would do some proofs, but unlike most math classes where it was just regurgitation and application to a kind of templated problem, the shit he pulled involved other fun parts of math that I knew little to nothing about. The problems were never straightforward.

I took some mathematical methods for electrical engineers class after vector calculus and ODEs so I guess that's the hardest.

I remember jack shit about it but I think it was a really dumbed down complex analysis course that only taught a few things relevant to electrical engineering. It was harder than any math I did before but I'd imagine it was much easier than a normal complex analysis course.

Basic topology.

Starting Graduate level Analysis in the fall, measure theory and all that fun stuff along with honors abstract algebra, Galois theory etc etc.

AB calc is easy as shit btw. Especially the actual test. No seriously I've never been less challenged in a course.

>inb4 hur why didn't you do BC. My HS didn't have it niggers.

>>3594841

>no, that's quite bullshit. the navier stokes, etc.

I don't know what the problem is here. I'm saying that these things were theoretically derived first, which is exactly what you're saying. Before, when I noted that much of the work is done on computers, it's because many of these methods are applied to extremely large samples and things in order to compute specific details.

>fluid dynamics is one of the most elegant physical problems in the universe,etc

I also don't know why you are arguing here; I'm essentially agreeing with you. Maybe my notion of "theoretical" is boggin' you down: that is, theoretical is generally used to describe derivations using logic from basic statements; applied, on the other hand, is actual numerical calculations or calculations which lead to a calculus of the subject. Of course these Giants of mathematics were applying their mathematics, but much of it is "theoretical" in the sense that it generalizes to spaces and arguments which are not readily applicable to real life. For example, if you take an RT-instability, of course we can apply it to the real world, and in this sense it is applicable. The theoretical sense was the derivation of the equations which guided this, which were, in turn, guided by observations. I'll assume you've read the landmark papers, but I will remind you that most of these papers derived these equations from basic mathematical principles in physics and sometimes used difficult and exotic (not in the sense of RT, but in some other areas) mathematics (like differential topology).

I think our only tiff is the difference between pure and applied, and this notion is fuzzy at best.

Differential Equations was the highest math course I took.

The hardest was calcII though. Order of difficulty was CalcII>DiffEQ>CalcIII>CalcI.

I'm glad I didn't have to take Linear Algebra. I'm kinda okay-ish at math but I dislike it a lot.

>>3594897
>>3594938

I'll answer these in one fell swoop. I don't know why you guys get so mad on /sci/, especially if one of you hasn't even taken a single course on the subject yet. Note I did not say anything about QUANTUM APPROXIMATIONS. I am simply noting that quantum dynamics and fluid dynamics are beginning to be investigated together. This is absolutely true; search on arXiv. The portion I was noting was that Newton's original ideas of fluids [as blocks] are not appropriate in dealing with every sort of fluid.

As for the rage-aholic who hates theoretical mathematics for whatever reason, I have always taken the [general] NS equations to be in the realm of pure mathematics, though specific cases are certainly applied. I will not respond to the claim that theoretical mathematics cannot predict turbulent flows since the subject evolves; the only approximations I've seen for such things involve extremely specific cases and rigid constrains, so it would also be fair to say applied mathematics is also having trouble with this problem.

>>3594285
>>3594294
>>3594302
you guys are literally so gay right now

people who say that math that isn't differential equations or graph theory or any 'tradional' applied math is worthless bullshit are narrow minded, like a hillbilly who hasn't stepped an inch out of his town. you work all day on what YOU do, and you see its results. but you don't realize that your work is just a FRACTION of what science actually is.

there's a difference between what people actually do in a field, and what a field can do. parts of math like abstract algebra and topology seem worthless to engineers because, while they have their head stuck so far up their ass in their computational work, they only see mathematicians as people working to tweak and refine some proofs that are completely unnecessary. they don't realize that not all mathematicians do this (or they do, but not all day), and that there are many in these fields who actually apply their work to real life, in places like dynamical systems.

some people work their entire lives in one field, and that's fine and all, but it's much better to work in a few different fields that are closely related yet diverse in their approaches (possibly at the same time; you won't miss anything, but you'll actually gain more) to get a better perspective about what's going on. it may or may not make a difference to one's academic status (if you are successful in them it will make a huge difference actually), but it will stop mathematicians from hating on engineers/physicists for being sloppy with proofs once they see that proofs are not the only beautiful things that come out of math, vice versa, etc.

What high schools did everyone attend?