/sci/ - Science & Math

>>7080422
Abstract Algebra.
Real Analysis.

>>7080422
Uh, no. Typically 11th graders here are doing Alg 2, and 12th doing precalc or calc 1. If they got into advanced classes earlier on, they MAY be in calc1 junior year

>>7080427
I took Calc 1 and 2 sophmore year.

>>7080571
That is a massive exception to the rule and you should know that.

>>7080422
If you can still visualize it, it's not advanced math.

>>7080573
>visualizing a problem in your head
>not advanced

m8 anyone can imagine a graph of a triple integral or plane topology in their head

>>7080427
>Typically 11th graders here are doing Alg 2, and 12th doing precalc or calc 1.
Not even remotely close where I live. Literally almost everyone gets to at least precalc/trig by junior year. By senior year prolly >=10% are doing Calc III, >=30% are doing Calc II, and the rest Calc I. Except for the minority that can't even handle babby tier shit, they do stats or drop math altogether.

>>7080749
>>=10% are doing Calc III, >=30% are doing Calc II
I meant =< for both

>>7080749
I know you feel really good about yourself right now, but all you have to do is take a look at what is tested on the ACT (up to basic trig.) to know that your situation is vastly different from the average student

>>7080571
That's really cool that you had rich enough parents and the high quality of education to expose you to that. But that's far from the norm, and you know that.

But I mean if you really, really want to feel special and brag about it, feel free. Because nobody in real life will give two shits so boast about it on an anonymous German cartoon forum

At my old school, by senior year, most people are doing discrete math, about 35% do pre-calc, 10% in calc 1, 1% in calc 2.

>>7080753
tru

> linear algebra
Youll have to be more specific. I've used linear algebra all the way from middle school all the way to an upper division undergraduate course. There are linear algebra courses in graduate school. Quantum mechanics can be reduced to an eigenvalue problem.

>>7080577
Confirmed for knowing fuck all about math

>>7080786
Show me a way to visualize De Rham cohomology.

>>7080787
You just gotta, like, do it man, you feel me?

>>7080789
I feel you brah, I feel you.

>>7080787
>here's something in higher level math you can't visualize
>this means all upper level math is impossible to visualize

>>7080787
a million dicks fucking you senseless at the same time

>>7080791
>this means all upper level math is impossible to visualize

I didn't say that, man. Lebesgue theory is considered upper level and it's very easy to visualize and very beautiful. My implication is: impossible to visualize => upper level, not the other way around.

>>7080422
linear algebra is above, calc 2 is the last math american highschoolers take if theyre at all good.

some also take intro stats.

once you reach vector calculus and ordinary differential equations you are finally free of the pure hatred of american high school maths.

>>7080422

>>7080422
A very large fraction of high school age students in the U.S. don't even graduate at all. The drop out rate is over 50% across some very large areas of the country.
Anyone have better stats on this?
They're not role models, but let's keep some perspective of what's average.

Triple integrals

>>7080749

what school is this?

>>7080884
A public one.

>>7080888

What's the school called?

>>7080796
No, that's exactly the opposite of what you (or whoever they were responding to) said.

>>7080577
>If you can visualize it, it's not advanced math

>>7080761
What school did you go to? I don't believe you.

>>7080918
Well, that's because I'm retarded. I meant otherwise.

>>7080427
this was the case with my school.
other 12th grade students took finite math (basically watered down discrete), statistics, or retook a more remedial math class.

>>7080577

That feel I can visualize Trig or Calculus.

>>7080917
Malibu High School.

>>7080925
*can't

>>7080577
I completely disagree. There's a few good essays (by mathematicians) on how professional mathematics think on StackOverflow:

>I've used the metaphor of an egg yolk frying in a pool of oil, or a jetski riding ocean waves, to understand the behaviour of a fine-scaled or high-frequency component of a wave when under the influence of a lower frequency field, and how it exchanges mass, energy, or momentum with its environment. In one extreme case, I ended up rolling around on the floor with my eyes closed in order to understand the effect of a gauge transformation that was based on this type of interaction between different frequencies. (Incidentally, that particular gauge transformation won me a Bocher prize, once I understood how it worked.)

http://mathoverflow.net/a/38882

>>7080917
Why's its name of relevance?

>>7080926
>>7080933
http://en.wikipedia.org/wiki/Malibu_High_School

Was just looking where it ranked. Must be nice being in a top 100 school in the entire country.

>>7080942
Honestly wasn't even aware of its rank.

>tfw you were taking calc I in senior year when some of your friends were taking calc III and Dif Eqs

>>7080577
You can draw pictures of schemes. They look weird, but they make sense. Same goes for some noncommutative spaces.

My highschool offered advanced functions, data management and calculus and vectors for grade 12. And in calculus, the chain rule wasnt even in the cirriculumn.

>>7082669
I live in Canada fyi.

>>7080863
>series, sums before Calculus
>nonsense like QM in high school before OChem

ctfu bruh Im fckin rollin lmao

In my high school the students at normal grade level did pre-calc their senior year.
Many people were a year above that, and many more, of course, were also a year below that.

>>7080427
>>7080571
American highschool seems so much different than Canadian highschool

>>7082669
Ontario?

What is the right age for someone to start taking calculus>>7080427
I'm american. I took Calc 1 sophomore year of high school.

>>7080571
Lol same. Also went to american public school

>>7080427
In Virginia (the Hampton Roads area, anyway), the standard is:
7th grade: algebra 1
8th grade: geometry
9th grade: algebra 2
10th grade: precalculus
11th grade: AP calculus AB (1 and 2)
12th grade: AP calculus BC (2 and 3) or AP statistics
Unless you drop out of math, in which case you stop after algebra 2.

>>7080761
We had a course called "discrete math" at my high school. It was a class for seniors who needed one more math credit to graduate, but had dropped out of math. The class is little more than addition and subtraction. Perhaps it was the same at anon's school?

>>7083002
Wait, BC is 2 and 3? I guess that means that I took Calc 2 and 3 as sophomore

>>7083025
From what I understand, there are a few concepts in calc 3 that are omitted from BC, but most topics are covered in varying degrees of detail. I just skimmed through
http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx
and I remember doing almost all of this in high school.

>>7080881
Where are you getting this from? I could probably have found something better if I cared to look, but
http://www.governing.com/gov-data/high-school-graduation-rates-by-state.html
doesn't have any states having a graduation rate lower than DC's 59%, and this doesn't count students who leave high school and then get a GED (which isn't dropping out). Perhaps the rates have dropped significantly in the past 4 years, but I'm not seeing a dropout rate of over 50% anywhere, and certainly not "across some very large areas of the country."

Additionally, we aren't really concerned with what the "average" student takes; we're talking about being above a high school level. A lot of students dropping out doesn't (well, shouldn't; legislators screw this up) affect the standard of a high school education. If there are high school students taking calc 3 within their schools (rather than at a community college or something) then calc 3 is still within high school level math, regardless of how few students actually go ahead and take it.

>>7080422
But to answer, I would say that's about 11th grade, yeah.

The highest anyone teaches at my school is calc bc, but it's a select few.

>>7082972
Somewhere between sophomore and junior year seems to be the prevailing opinion. It probably differs based on state requirements.

>>7083100
My state usually takes it senior year at the earliest.

>>7080422
Probably around differential equations.

>>7080427
the school i went to in New Jersey was pretty much
9th grade:algebra 1&2
10th grade: geometry & trigonometry
11th grade: pre calculus
12th grade: Calc AB
also calc BC and multivariable available if you skipped courses
i skipped combined algebra and Geometry Trig and went Pre calc->AB->BC->multivariable

>>7080787
through poincare duality. you basically consider only forms which are cell-representable, then they can be visualized as the dual cells of classical algebraic topology.

forms are the hard part to visualize. but you can think of them as hyperplane fields i guess.

>>7080571
My high school didn't even have Calc 1.

the term calc1 calc 2 don't mean much
neither does discrete math

even the difference between calc 1&2 for business students is greatly different than calc 1&2 for Stem students


same with discrete. some levels are just curriculum filler others are for people a year away from building robocop

Grade 9: Algebra 1 or Geometry
Grade 10: Geometry or Algebra 2
Grade 11: Algebra 2 or "Math 4"
Grade 12: "Math 4"
They used to have pre-calc, but removed it before I was a senior because they didn't want to pay the one teach qualified to teach it more money.
But that was just my shitty Ohio school.

>>7080422
Multiplying and not making mistakes

Interesting, the most my hs had was precalc, some complex variables (not even functions though, just algebraic manipulation), matrix operations and linear systems off linear algebra (didn't enter on vectorial spaces etc) and that's it. A bit of probability, too. And of course, basic 2d and 3d geometry and basic algebra and vectorial algebra.
The first touch I had with calculus itself and deeper linear algebra was already in univeristy.

>be scheduled to take precalculus in my sophmore year
>dad says "I took calculus when I was your age" and drives me to local university for summer math classes three days each week
>finish half of undergraduate math curriculum at that place before graduating high school a year earlier than everyone else and heading to uni to get a math degree
I love my parents.

>>7083002
Nigga, don't even front. That's not standard in Hampton Roads. Most students didn't go past Alg II at my school.

>>7085150
There's a fair amount of effort these days to take the smart kids and get them somewhere else.

I would literally have killed someone if it would've gotten me into a non-normie school. Literally genius IQ (as tested by child protective services) when I was 5, AND ten years later when I joined Mensa, but no, I had to be put with the normalfags and literally if I tried to read books or something kids would TAKE SHIT FROM ME. Literally I was like 7 putting a 100 piece puzzle together, and half the class watched me, and a kid stole a piece from me. My experience with humans is what makes me antisocial.

Seriously what the fuck is with normalfags attacking anyone trying to do anything that isn't "normal"?

>>7082972
>What is the right age for someone to start taking calculus

All elementary schoolers should have mastered calculus at least before entering high school.

http://www.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/
http://wordplay.blogs.nytimes.com/2010/10/04/numberplay-calculus-for-the-second-grader/?_r=0
http://www.educationreimagined.org/2012/06/calculus-by-third-grade/
http://wildaboutmath.com/2008/02/20/calculus-in-4th-grade/
https://isellerfinance.wordpress.com/2012/03/12/dont-all-fifth-graders-know-calculus/
http://www.fairmontschools.com/news/fairmont-6th-and-8th-grade-whiz-kids-join-ranks-among-the-youngest-students-nationwide-to-take-the-a P Calculus Exam

>>7085183
>Seriously what the fuck is with normalfags attacking anyone trying to do anything that isn't "normal"?
Jesus I know exactly what you mean. I had to take a health class in high school, and it was my only non-honors class. It sucked so fucking hard. One day I literally just got up and left and never went back. Teacher didn't say shit and I took the C (0s on everything for the last quarter of the class, 100s on everything before)

>>7085183
I went to a school for gifted children until high school, like you had to have a 135+ IQ and it was literally just rich Jewish kids. It was so lame. I was the only black kid there and they really were mean to people because they weren't as rich as them

Anyway this has been my high school math experience. Pretty normal cause I had no choice:

8th grade- Algebra I
9th grade- Geometry (hated)
10th grade- Algebra II/ Trig god-tier class, got 100 average even though my teacher was a huge pedophile (inb4 i prostituted myself for grades)
11th grade- Pre-Calculus, AP Statistics
12th grade- AP Calculus AB

I took AP Physics in 11th grade too. I wish I could have been more advanced in math

>>7080422
OK OP

Americans allow high school students to take introductory post-secondary credits. This is the "Advanced Placement" (AP) system.

There are a number of reasons for AP courses which basically boil down to
a) college is expensive, if you can do some of it in high school you pay less $
b) rich/needy parents want their kids to get a leg up

The consequence of this is that "striver" kids will get exposed to a lot of first year math pretty early.

BUT
The caveat is that AP courses aren't really good at what they do and people end up having to retake/dropping math altogether because their foundation is so weak.

So when you hear that American high schoolers are doing linear algebra/real analysis, don't be too impressed.

THAT SAID

This is a huge country with the biggest concentration of wealth and smart people on the planet. There are some extremely sophisticated schools that are highly selective about their students and prepare them ruthlessly.

>>7083002
In Colorado (Denver), the standard is more like:
7th: Pre-algebra
8th: Algebra
9th: Geometry
10th: Algebra 2
11th: Trig/precalc
12th: Calc 1 or "Algebra 3" or "College Algebra" i.e. algebra 2 again with a little calc 1, but this time they make sure you actually know it

This is the route about 70% of highschoolers will take.

Those in "Honors" take the path that you described

Those that are "gifted" will start geometry in 8th grade and finish their senior year doing calc III. If they're particularly fancy, they'll go to a community college nearby and take lin. algebra and maybe diff eq.

>>7080422
If you can work with fractions, you're more advanced than most high-schoolers in America.

>>7080571
>>7080427
>>7080749
Where I live in central Florida it's quite fucking rare to see someone in precalc and only one kid of the whole 1500 kid school passed calc 1 a year. Only one class of about 15 doing calc 1 and anything beyond is unheard of. Where the fuck do you guys live?

>>7082484
Algebraic Geometry is baby tier

>>7085515

For me it was:

7th grade: Pre-algebra
8th grade: Algebra I

9th grade: Algebra 1 again (first half of year was a review)
10th grade: Geometry
11th grade: Algebra 2/trig
12th grade: I skipped precal and went straight to cal. Did okay.

>>7082970
I live in Ontario and we do chain rule. Idk what school this guy is in.

>>7082713
>>series, sums before Calculus

Literally nothing wrong with that.

>>nonsense like QM in high school before OChem

There's no point in learning Organic if you're never going to use it.