Reminder: if you can't do all of these, you don't

I can do 13 of them but i don't know what you mean Newton's method?

>>7020939
I study Astronomy and Physics and I don't know half of these

I learned how to use programs to solve the difficult maths for me

why the fuck would you think any of this is important outside of a Mathematics major?

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>>7020939
Reminder that if you can't do this, you don't belong in academia.

>>7020946
>i didn't take calculus 3

>>7020944
Newton's method for approximating roots. http://en.wikipedia.org/wiki/Newton%27s_method

I can do all of them off the top of my head except for the e^(x^2) one, but I'll probably never try it because I'm too busy with other math.

>>7020951
It's simple polar coordinate transform.
All of those are so elementary it shouldn't even serve as a "reminder".

>>7020951
Oh i just forgot what that was called.
>>7020954
They are simple from a pure math perspective and i know them because i study math but i also study physics and you don't learn most of these outside of math

>>7020948

Solved easily using a triple integral over the domain of all Barnett integrable functions

>>7020946
>I study Astronomy and Physics and I don't know half of these
>I learned how to use programs to solve the difficult maths for me

Data monkeys "astrophysicists" don't belong here.

>>7020939
>if you aren't a math major entering their 3rd year or later then you aren't qualified to post on /sci/
yeah, sure thing

captcha: nicka

>>7020966
>3rd year

All of these are freshman topics even engineers know.

>>>/out/

>>7020968
Pft, when I was born I used my mother's afterbirth to write out solutions to these.

I haven't gone to college yet and I can do
1,5,12,13
Is that good?

>>7020981
>can't do 3
>can't do 14
>can't do 10
>can't even do 4

You're retarded

>>7020981
1 and 5 are simple tricks that it is good to be exposed too.
I am surprised you have seen 12
I am surprised you learned induction in high school too

>>7020981
>cant do 3

get out

>>7020961
Nice meme. This is why /sci/ is shit.

>>7020983
none of my teachers ever showed me lolz

This is /sci/, the math OR science board.

>>7020939
I'm a physics grad student and know all of those easily.

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>implying I'm a fucking math major
kek. Here's one for you mathfags

>>7020939
Why not change to
> Prove 3*5=15 via addition
> Prove zero is smaller than 10/50
Cause you might as well.

Everybody who finished first quarter of the freshman year in any technical speciality knows this. School kids who took AP maths know this before 12th grade. Great requirements, OP.

>>7020998

EPIC LE MAYMAYS xDDD

>99
>dubs checked, ur welcum :^)

>>7021001
Assume there are a finite number of primes { p1, ... , pn }

Can you find a new number that isn't divisible by any of them?

>>7021005
Can't do science without math. CS and Bio majors should not post here

>>7021031
Why do people think CS majors don't do math? Maybe at your shitty institution they just program fizzbuzz for 4 years or whatever but at most schools CS students are usually required to excel at mathematics.

>>7021013
>Everybody who finished first quarter of the freshman year in any technical speciality knows this. School kids who took AP maths know this before 12th grade. Great requirements, OP.

Yet many people in this very thread don't

>>7021052
3rd smartest anon

>>7021040
Because you don't do any math and immediate deflect any criticism of CS with a "shit school" ad hominem.

>inB4 But muh discrete math was soo fucking hard! There's no way I'm could be an idiot so your full of shit

>find the distance from a point to a plane

Why the fuck should I care about this I'm not doing a babbies first computational linear algebra course

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>>7021058
>Never heard of computability theory
>Never heard of algorithm design
>Never heard of group theoretic word problems
>Never heard of Turing machines
I'm not even a CS fag and I pity your idiocy.

>>7021052
I trust you to make the conclusion yourself.

>>7020939
>He thinks God's equation is "truly astounding"

1-1 = 0

so profound

>>7021065
>I'm not even a CS fag

You are HIGHLY overestimating the math required for those topics.

>>7021078
He did call it "nerdy"

>1-1 = 0
>so profound

The multiplicative identity having an additive inverse is the the foundation of ring theory.

>>7020948
Most social scientists wouldn't be able to do this.

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>>7020946
I study physics and astronomy as well and I can do every single one except for 14
Get yourself checked, pleb

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>find the derivative of sin(x)
>transcendental function
>no definition given
I seriously hope you guys point this out to your professors.

>making both mutually exclusive

>>7020939
Missing 7 and 11, however I'm studying Engineering, so I should be partially justified. Will go study them right now.

>>7020939
What is this, calc 1 review?

>>7021235
hahaha wildberger taught my first year discrete maths class a couple of years ago. Was not expecting this picture

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>>7020939
I might not be able to do those, but I can guarantee you can't do this. We all have different talents. Doesn't mean I can't enjoy discussions about scientific topics that come up here.

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WTF is this high school shit? OP sure sounds underageb&

>>7021244
This should be on the sticky

Most of them are high school stuff and couple of them is for freshmen. Indeed you should be able to solve them all or gtfo shitposter.

Reminder that anyone who wants can post here. For all you know I'm a mentally retarded 15 year old.

>>7021110
I'm not the person you've been corresponding with, but you are highly underestimating the math required for those topics. Unlike your shitty university, my university host outstanding mathematicians which studies fields in recursion theory, etc. It is apparent you go a shit university, because I can go ahead and eliminate that you do not attend schools such as Berkeley, Chicago, Cornell, Michigan, etc. These universities offer courses in mathematical logic, and if you ever took a few graduate courses in recursion theory, reverse math and so forth then you'd realize your 'muh undergrad rigor in analysis etc., etc.' will seem like child's play.

I mean it's fine to not attend a university as such, but you have a narrow world view, and it isn't your fault your math department is outside the top 10/doesn't teach courses beyond the vanilla standard.

Even if you did attend such a university, then you won't be taken seriously in the field. I certainly wouldn't.

>>7021298
>you don't belong here
Confirmed for edgy college faggot. Why would a scientist need to prove there are infinitely many primes?

>>7021367
>For all you know I'm a mentally retarded
All right
>15 year old.
You need to be at least 18 to visit 4chan

ITT: Butthurt Math Majors

>>7021244
Report submitted! This window will close in 3 seconds...

>>7021244
your tears are delicious

>>7021248
>Missing 7 and 11, however I'm studying Engineering, so I should be partially justified

>Numerical methods
>Fourier methods
>Not important for engineering

What scam school do you go to?

>>7021376
>Undergrad CS courses will take you to postdoc level in the topics at a good school!
>I'm totally super cereal at the moment!

Yeah, no. Even at Berkeley and Cornell, the undergraduate CS courses are pathetic.

>>7021378
What in that post made you think I was edgy? I'm just an artist with a somewhat sciency day job who browses 4chan in quiet times and enjoys reading these threads. If anyone's trying to be edgy here it looks like it's you.

>>7021244
life on academia may be hard but that doesn't mean you don't have to try harder. it's where we enhance our intrinsic godmode mentality.

>>7021435
>Yeah, no. Even at Berkeley and Cornell, the undergraduate CS courses are pathetic.

I'm not a CS major. I'm a math major that took math courses in recursion theory. I'm pretty sure they were more rigorous than the CS counterparts, but they cover the same topics in terms of computability. So, no, those courses are not 'pathetic'.

>>7021378
>Why would a scientist need to prove there are infinitely many primes?
It's high school math. Every self respecting scientist can do math. If you can't proof it, you shouldn't call yourself a scientist.

>>7021453
>because science has existed for like 1% of the time religion has

>>>/out/

>>7020939
I'm an hybrid between theoretical physics and engineer. Is it bad if I can't really come up with a way by myself to formally prove things like 4, 5 or 14? I'm pretty sure I could understand the concepts in half an hour at most but it's just not things I've never had to think about.

>>7021454
>It's high school math

It's 6th grade elementary school math at best and really should be done by the 3rd grade.

>>7021458
>Is it bad if I can't really come up with a way by myself to formally prove things like 4, 5

Yes because they are so trivial and straight forward you should be able to do them.

for 4 see >>7021027
for 5, assume √2=p/q with GCD(p,q)=1. Can you tell if p and/or q is even? Do you see the contradiction?
for 14, just show [0,1] is uncountable. Assume f(n) can count them all and let d(n) be the nth digit of f(n). Can you find a new number in [0,1] that was missed for all n?

>>7021512
I like this. Lets post the solutions for these properly so our fellow /sci people can understand.

The Euler Formula proof via power series is explained pretty nicely on this link.

https://www.youtube.com/watch?v=jcrQ3rPUYjc

No i don't
I'm not a math major, i'm a psychology major

>>7021555
>Lets post the solutions

Lets NOT. If they can't figure it out, they don't belong here.

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>>7021561
>i

>>7021568

It turned into a L, what the fuck

>>7021564
just trying to be productive man. We can help enlighten. It's in the spirit of /sci/

>>7020988
>exposed too.

to*

If you can't do it, learn it. Simple as that.

1. Just remember the equation and fix it to ax^2+bx+c=0.
2. Mark the integral with "I" and find I^2 as double integral.
3. Drav a square and divide it with 4 secants.
4. Antithesis, there are finitely many primes. Multiply them all and add one, none of them divides the number, so it has dividers that doesn't belong to that group.
5. Antithesis, square root of two is rational p/q. square the equation, multiply by q^2 and look if the sides are divisible by 2.
6. For x^n use definition and binomial equation. For sin(x) use trigonometrial identities and the limit of sin(x)/x=1.
7. Draw a picture buy Newtons method also has many drawbacks.

im a biologist and i dont know how to do any of those

i also dont need to

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>>7021766
you also don't belong

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>>7021766
>biology
>hard science

I can do these except for 2, 11 and 12. I'm going to school for engineering next year.

A-a-am I going to make it /sci/chan?

>>7021792
2 is really really really really easy. You could absolutely do it you just have to know the trick. Look up "Gaussian Integral" on youtube and you'll probably be able to find a video showing how to solve that integral.

>>7021766
I'm a biologist and a chemist. I can do half of these things. Can I stay guys??? Please??

>>7020966
Not in uni and can do 1, 3, 5, 6, 8, 9, 11, 13
The questions should be harder

>>7021113
and on a list of the most profound things in the universe, ring theory comes right after my belly button lint

>>7021792
>I can do these except for 2, 11 and 12
>I'm going to school for engineering

Gaussians are fucking important in engineering
Euler identity is really fucking important in engineering
Minimizing error with least squares (point to solution "plane"/space) is fucking important in real life engineering

I hope you were trolling.

why would I want to prove half this shit

who cares how many primes there are

>>7021829
>The questions should be harder

Can't really do that without favoring one major over another.

>>7021837
>No love for abstract algebra

get >>>/out/

>>7021843
>who cares how many primes there are

Cryptographers

>>7021849
I didn't ring theory wasn't interesting, but it's hardly profound

God's equation is a meme equation was my point

>>7021849
Abstract algebra is pretty autistic and useless. I mean it's okay to know how to use the most important results from algebra to apply them in other fields of math, but doing algebra as an end in itself is wasted time, almost on par with philosophy.

>>7021849
>Cryptographers

I was seriously expecting you to come up with a better example than that. Thanks, gave me a laugh

>>7021912
It's almost as if you're such a retard that you don't understand how important cryptography is to the modern world.

Good luck doing any online banking without those "useless primes"

>>7021908
>coming up with novel unifying theories encompassing the entirety of several scientific fields
vs
>solve some basic 2nd year undergrad level problems that are so trivial they wouldn't even be on a math exam outside of maybe babbys first proofs class

Yeah, no I think you're just retarded.

>>7021919
I don't do any online banking, thanks though

try again

>>7021925
That's because you're poor. Opinion invalidated.

>>7021931
No, it's because I'm not autistic and don't fear social interaction.

>Opinion invalidated

thanks, I really care about your validation ;)

>>7021951
>No, it's because I'm not autistic and don't fear social interaction.

>on 4chan

>>7021912
I'm not even him but how data is secured right now is by primes.

>>7021912
>>7021843

I think >>>/sp/ is more of your kind of board, bro.

>>7021924
well, I've done 1) and 2) they're really not that hard. Everyone else looks retarded to me.

>>7021951
You say that, but all we hear is:
>No it's because I feel like I was born in the 1800s and enjoy massively inconveniencing myself.
Also, fear of social interaction? Seriously? The bank tellers probably think "oh, there's that massive douche who hits on us when he comes in every week" whenever they see you.

>>7021956
I understand thats a difficult concept for you to understand given your personal experience, but I encourage you to broaden your horizons and entertain the idea that some people who post here are, in fact, normal functioning members of society.

>>7021970
...and why should I care what a bank teller thinks of me?

This kind of thinking is why you're a basement dweller

>>7020939
I'll be back in four or so years, after I start and finish college. Wait for me, /sci/!

>>7021978
>such a luddite you don't even use online banking in 2015 let alone mobile banking like the rest of the world
>normal functioning members of society
Yeah, no fucking way anon.

>>7021993
Oh, I see, you're "that guy" on campus.

>>7020939
1st year Math....
Every math major should've done this over 3 years prior....

>>7021298
Anon, some of these guys are so dysfunctional outside of a few specific classrooms that it's very important to them to feel superior to everyone who ignored them it high school.
Pretending 4chan matters helps them suffer through.
Let them have it.

>Science & Math
>can't post here if you don't into maths

3rd smartest board...

I'm a fairly successful lawyer, meaning I've had as much if not more (and more difficult) higher education and certification exams than 95% of the posters on this board. I can't into maths for the life of me. The last math class I took was calc 2 in freshman year of undergrad.

But I'm on this board and theres nothing you can do to stop me. I can discuss and enjoy abstract physics, astrophysics, and astronomy with no higher understanding of math because muh theories do not equate to muh data research

suck it, peons

>>7022044
>I'm a fairly successful lawyer, meaning I've had as much if not more (and more difficult) higher education and certification exams than 95% of the posters on this board. I can't into maths for the life of me. The last math class I took was calc 2 in freshman year of undergrad.
HAHAHAHAHAHAHAHAHAHAHAHAHAHHAAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA
Some of my best friends are lawyer but you sir are so full of yourself

>>7020968
Why should/would a freshman engineer (non autist) be able to prove that R is uncountable? Or even how to solve a ODE

>>7022078
They wouldn't, which is why engineers and freshman do not belong here.

>>7022078
If he's a CE or CS student I'm sure he knows how to prove R is uncountable.

Math majors sure do think they're special snowflakes. :^)

What do you guys think? Is sci legit or is it just a lot of fronting mostly? Honestly, Im in my second year at a good university, math major. I am no expert and I def not compare to what people on sci claim is the norm. for example from this list as of now, I could only do 1 3 4 5 6 8 10 12 and maybe some easy problems with 13? Any legit response?

>>7022084
Why? What are you talking about? What course would a first year CS or CE student take that teaches R is uncountable..?

>>7020939
i can do most but about #2, does the solution involve the taylor expansion and just integrating the infinite polynomial terms?
i cant see how polar coordinates would help

>>7022090
Undecidable problems use cantor's diagonal argument as proof of their undecidability. It's trivial to use that to show that the reals are uncountable.

>>7022088
Yeah, /sci/ and 4chan in general is mostly dickwaving, trolling and trying to fuck with people.

If you take people seriously when they say stuff like "enjoy being a low iq beta pleb who has a small 7 inch peen and will never amount to anything in life. I bet you can't even squat 3x your bodyweight.", you have bigger problems than proofs.

>>7020939
It never occurred to me that a^2 appears. Anyone care to explain why |a| is not needed?

>>7022108
Okay, but why would a first engineer know that? what course? Im at McGill and know lots of intelligent engineers, I doubt any of them would know what that even means. Im sure there just dumb compared to you, who clearly solved poincares conjecture at age 11 and followed up with a quick proof of P=NP before the end of middle school

>>7022111
Nah its not that I take it seriously, its just I think that if it true that some people really are that much smarter at such a young age is a little scary

>>7022078
>be able to prove that R is uncountable

They all see it in their Intro to Probability and Random Processes courses. (Assuming they don't go to a scam school like ITT Tech and are really engineering technicians)

>Or even how to solve an ODE

You can't even do babies' first circuits analysis without being able to solve 1st and 2nd order ODEs. Of course all engineering freshmen know it.

>>7022123
>They all see it in their Intro to Probability and Random Processes courses. (Assuming they don't go to a scam school like ITT Tech and are really engineering technicians)

Care to show an engineering program that requires such a rigorous course?

>>7022119
>>7022119
Haha, I'm not >>7020968 at all. I actually despise that kind of dickwaving on /sci/

I'm just saying that you should have some understanding of Cantor if you major in CS or CE, imo.

McGill is a great school, by the way.

>>7022102
>i cant see how polar coordinates would help

It's really just a cute trick: Let Z=∫exp(x^2)dx, then Z^2=∫exp(x^2)dx*∫exp(y^2)dy = ∫∫exp(x^2+y^2) dx dy

>>7021007
You posted this in another thread and nobody gave a shit about it there either.

Nobody's impressed.

>>7022127
All of them

>>7022150
Care to provide a specific program?

Can't do 7 or 9 because I don't give a shit about differential equations.

The only proof I know for pythagorean's theorem is the visual one, but I guess that's good enough. Actually, I suppose I could proof it using sin and cos after defining them by their taylor series, but I feel like that is cheating.

>>7022150
More like absolutely none of them. dude I hope your 14 or something and not seriously this delusional

>>7021007
>temperature of the electrons
why not throw in volumes of protons and pressure of neutrons in here as well?

>>7020939
can do 1, 3, 4, 5, 6, 11, 12, 13, 14

>>7021007
Anyone realized that this is just this guys homework. good bait tho

This thread confirms why you guys are future Elliott Rogers, and rage at stupid shit that no one cares. This HURRR DURRR MUH FIELD IS BETTA THAN YOOOURS, is retardation, not autism. You guys fight over things someone else has solved, and claim it as your. This is fraud behavior, not intelligence. Any monkey can learn these proofs, but can you solve existing problems with no solutions? Also if you're in America, good luck getting funding its going to get deeper budget cuts. Ted Cruz is the chair of the science, space, and whatever the other thing is called.

>>7022088
You should REALLY be able to do 11 and 14. The former is basic calculus, and the latter is one of the more famous proofs out there, not to mention that diagonal arguments apply in a lot of other situations in other ways.

2 is famous so you should learn it - it's a really cool proof and quite short. It's an exercise in Rudin (with hints given)

I think for 13 the image is only implying that you should be able to do basic ones, obviously there can be vary hard induction proofs.

>>7022166
it was from an exam a year ago

>>7022150
I know you're just some punk kid who think he's hot shit. Well you're not, you are taking someone work as your own, and then saying others are stupid, because you learn how to copy someone answer. Newsflash engineers in general don't have great math rigor. Some maybe able to do ODE, or higher, but in the industry you're mainly doing at best third semester calc. Your bosses will not trust you to do your own work, because of human error. So you need a computer to do it for you. By the way this younger is dumber than their parents. There are a lot of studies on this subject. Even in tier 1 universities, the kids have poor rigor in their subjects.

>>7022160
http://en.wikipedia.org/wiki/Electron_temperature

>>7022164
>can't do 10

wtf?

>>7020939
I can't do one. I attended nigger tier schools, and never got any help, because teachers were in general not interested in helping. So i just gave up, before I even enter the race. Now its too late to learn all of these proofs and maths in general.

>>7022044
>I can discuss and enjoy abstract physics, astrophysics, and astronomy with no higher understanding of math

Nearly as well as a person with no conception of the English language can enjoy Keats or Blake. Yes, I'm sure you can parrot all sorts of neat theories you've heard discussed by qualified individuals, but don't presume to have any real understanding of any of the things you listed while discounting mathematics.

>>7022044
lel I know a lawyer and he said his undergrad in engr was way more difficult than anything he had to do in law school. i know this is pasta but just letting you lawfags know your shit is piss ez

>>7022088
I'm not a mathematician, I'm a chemist, I can do 1, 3,4,5,6,7,8,and 14.
Probably one of my weakest points is proof by induction. I only know these answers because I've seen the answers from somewhere else. I would've never been able to come up with these myself . I don't understand all this elitism of being able to solve these.

>>7022200
>Nearly as well as a person with no conception of the English language can enjoy Keats or Blake
by this logic we shouldn't even bother to learn how to read, because we won't understand reading as linguistic professors. To be fair, even the professional don't know what they're doing. Half the time, they don't understand what they're looking at.

>>7022200
Hail dubs!

>Yes, I'm sure you can parrot all sorts of neat theories you've heard discussed by qualified individuals

This. Just like the teachers who did the "gifted" program at high school. Watching NOVA documentaries does not give you an understanding of anything.

>>7020939
>Things every math major should know
Is this a joke?

It asks for wishy-washy "interpretations" of derivatives and integrals instead of the rigorous ones a math major should know.

It asks for a "discussion" of a simple result, rather than a proof.

it asks for a derivation of an algorithm in numerical analysis, it asks for no conditions/proofs of convergence. it asks for shitty graphical illustrations.

The rest of it is stuff you can do by the end of your first term of a maths degree in the uk. Most of it people can do before they go to uni.

This list reads more like "stuff people who have a vaguely math related major" should be able to do. (read: engineering, physics)

>>7022208
>I don't understand all this elitism of being able to solve these.
They went to college, and realized they're not hot shit and someone else is better than them at their field. They like to take credit for someone else work to make themselves feel better.

>>7022212
>Most of it people can do before they go to uni.
No one in my BC calc class could do any of that, beside perhaps 9 and 13. UK schools must be some hot shit.

>>7022209
These topics aren't anywhere close to being advanced. It's like requiring the ability to read at the 6th grade level to post here.

Stop defending butt hurt and incompetency.

>>7022212
>Is this a joke?

No

>This list reads more like "stuff people who have a vaguely math related major" should be able to do. (read: engineering, physics)

Which is why
>if you can't do all of these, you don't belong here
since this is
>/sci/ - Science & Math

Obviously it should be way below real math majors.

>>7022221
>These topics aren't anywhere close to being advanced

They're not suppose to be, but OP picture is just a circlejerk of Austimo asshats who don't know what real maths is in real life. This is for high school kids, but most high school kids aren't given proper math rigor. American schools don't teach diddly, nor do Britbongs. You're the one that's getting butthurt, because you are upset a lot of people can't do this, but are scientists. You are by definition Austimo general.

>>7022219
Must be. I'd seen 1,4,5,6,7,8,9,10,12,13 in class as part of the course before I became an undergrad.

I'd seen 2 because I had a substitute who thought we might appreciate it.

>>7022209
>by this logic we shouldn't even bother to learn how to read

That's a very poor and inaccurate interpretation of what I was trying to get across. We should all strive for understanding. That doesn't imply some sort of specialized expertise. Going back to the analogy; it would make little sense to claim you understand a poem, a sonnet, or whatever else, without having a decent grasp of basic grammar.

>>7022228
I was more commenting on the fact the title of the picture is "things every math major should know", not what op wrote.

I suppose it's technically true, every math major should know these things, it's just a laughably tiny subset of what they also should know.

>>7022229
>but are scientists

[citation needed]

>>7021512
>It's 6th grade elementary school math
Nah, 11-12 years old shouldn't be able to do this.
If you can't do it 17-18 yo, then science is nothing for you though.

>>7022233
I assume they meant: Should know before starting a math major

>>7022232
>We should all strive for understanding. That doesn't imply some sort of specialized expertise.
That's exactly what you didn't say. You told other anon he can't understand it, because he has no training in the subject. He can understand it, to an extent. But you're being an absolutist on the matter.

>>7022240
Well a lot of math majors don't have the kind of education to teach them proofs, before going to college. A lot of public schools just teach the standardized crap given to them.

>>7022238
I was too busy smoking weed and fucking sluts to care about math at 17, but now I'm in a fairly prestigious graduate program

u mad

>>7022242
Nowhere in my post did I say he can't understand it. I only implied that he didn't. That doesn't exclude him from being capable. And I'll stand beside what I said before. Being able to describe theories or put concepts in lay terms, no matter how well-meaning, cannot be mistaken for true understanding.

>>7022256
Sorry, I misread your post as he didn't understand it. You want him to understand the data, jargon, and ideas in an articulated matter. I know what you mean. Although I never major anything related in STEM, I do know what you're trying to say about theories being described in lay terms.

>>7022230
>Not knowing 3

How? Even the President of the United States was able to come up with his own unique proof of it.
http://math.kennesaw.edu/~sellerme/sfehtml/classes/math1112/garfieldpro.pdf

>>7022238
>Nah, 11-12 years old shouldn't be able to do this.

They have been doing just that for over 2000 years. This is very basic material from Euclid.

Just because modern schools within the last century decided to become daycares instead of educational facilities does not mean kids are incapable of learning the material they once learnt.

>>7020939
Make me leave, faggot
>oh wait you can't can you? LOL deal with it fuckin' squints

>>7020939

This is a pretty decent list, although some of these need to be scrapped because they should be known to every kid in high school with any interest in mathematics (for example 1 and 3).

Also, you definitely need to add the following:

>Know at least one proof of quadratic reciprocity.
This is like the Pythagorean theorem for undergraduates, because there are a ton of proofs for this relatively simple but profound result.
>Be able to prove the central limit theorem.
This is one of the most important results in mathematics/statistics, with a remarkably simple proof.
>Know the proofs to the fundamental theorems of algebra, calculus and arithmetic.
You might have mentioned some of these in your OP, but they are all important, and should be trivial to prove, apart from maybe the algebra one.

>>7022271
>They have been doing just that for over 2000 years. This is very basic material from Euclid.

Just because modern schools within the last century decided to become daycares instead of educational facilities does not mean kids are incapable of learning the material they once learnt.

Education in the past was reserved for those who could afford it or tested into the schools. Today, everyone is just pass to the next level because the government wants to compete in the ranking system with other countries as dick measuring. Anyone can learn, but most people have no interest in math or science. If they do, they have been beaten down by school, and just want to move onto getting a job.

>>7022268
No, no, it's perfectly fine. I understand the need for things like that, and it isn't inherently a bad thing. It's simply that when I see somebody claiming knowledge of physics (or any other STEM field) based purely on superficial facts or explanations, I die a little inside.

>>7022290
I'm trying to learn it as a physicist would learn physics. The thing is, my fucking attention span prevents me. But I can understand your feeling toward a passionate subject being bastardized. I try my best to read the literature. But I can't do a proof to save my life. Was never given proofs in my life, just do this problem and output the return.

>>7022123
ODE's is a sophomore level class everywhere except your school. Sorry man.

>>7021007
If you can't render your shitty course notes into LaTeX then you're as pleb as >>7020946

>>7022336
it's from an exam, not notes, and why would i spend the extra time to do that when all i need to do is snap a picture

>>7022324
Most STEM kids do AP calculus or at least rub it out the summer before their first semester. Otherwise you're stuck during your 1st year without being able to take any relevant courses since they all require it.

>>7022337
Because nobody can read your shitty handwriting asshole

>>7022366
it's my professors handwriting and it's very clear

>>7022344
This board isn't for hobbyists who can sip wine and listen to Mozart and "appreciate" the advancements of scientists, it's for people who aspire to do science. You don't know jack shit about physics. Lurk, but don't post.

>>7022368
Anon you really need to promote your standards of excellence.

>>7022371
Actually, this board is for people like me.

I can post whenever I want, and you can't stop me. Does that bobble your knobbies?

If and when I decide to post, it's clearly in a context where I can add to the conversation. Most often, it's about theoretical space travel or existential concepts too abstract for math. Also known as science is just for academics, you toolbox.

If I did decide to post in an inappropriate context where I cleary don't know what in talking about, that's called trolling and is pretty rare (and obvious) on this board. Trolls get called out and ridiculed. Kinda like your post, pleb

>>7022394
>>7022394
>>7022394
>Most often, it's about theoretical space travel or existential concepts too abstract for math
So you're the ones making all the stupid threads. Please just stop making threads. Please.

>>7021065
>>7021110
>>7021376

The only one of those that is really serious is Computability Theory. That said, Computability is really legit shit and it's a really big deal in mathematical foundations and other parts of mathematics. Here are some lecture notes detailing the introductory material.
http://www.personal.psu.edu/t20/notes/fom.pdf

Computability also leads to the development of a bunch of other hardcore badass "computable" versions of normal math stuff.

Some other big topics that CSfags get into are Category Theory, Type Theory, and Homotopy Type Theory.

That said, most CS students do not take these courses and instead choose to stick to more practical courses.

>>7022344
>I can know plenty of advanced physics and astrophysics without ever picking up a calculator.
This is totally true... if you replace all those calculations with algebra.

>>7022415
>That said, most CS students do not take these courses and instead choose to stick to more practical courses.
Because they want to make money some dough, instead of advancing the field. Also most cannot hack higher level maths.

>>7022394
The whole purpose of physics is the creation of predictive mathematical models. Science never is concerned with the underlying nature of the world.

By the very rejection of mathematics, you reject science.

>>7022460
Well most people have never done mathematics in their lives. They do arithmetic in school, but never given the chance to do maths.

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>>7022466
>Well most people have never done mathematics in their lives.
>but never given the chance to do maths

Maybe we should, I don't know, give them the chance to learn it in school.

>>7022484
>that screencap
autistic as fuck. cut that shit out. you need to learn more in school than fucking math. you fucking faggots make me sick

>>7022484
>modulo before division
simply great

>>7022344
And that's why nobody likes lawyers.

>>7022484
Oddly that's a system I envision a few years ago. I never seen this picture before, but kids are amazingly resilient and eager to learn. They can learn higher level maths at a young age. The concept of limits can be taught to third graders. Teaching them proofs will help their analytical skills. But you need to add in linguistic, history, geography, political science(legitimatize, not clapistan style). The math is correct, but kids need more than STEM subjects.

>>7022489
>you need to learn more in school than fucking math

Doesn't excuse not learning math

I'm not mad. I smoked weed age 14 to 20, I stopped now but I was always top of the class in math.

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>>7022593
>I'm not mad. I smoked weed age 14 to 20,
retard.

>I stopped now

Now that the neuronal development has ended and your brain has fully matured, you've quit smoking and you think that will change anything. LEL. Damage was already done, kid. You've fucked up your brain when it was growing maturing. You've probably shaved 20+ IQ points with weed.

>but I was always top of the class in math.

kek'd hard. top of the class in some shithole full of other potheads and morons.

>>7022271
>They have been doing just that for over 2000 years. This is very basic material from Euclid.
I agree for 1,3,4,5,10,12 and 13. But you can't expect kids 10-11yo solving diff. eq. and integrals while understanding the theory behind them. And no, they didn't do that 2000 years ago, since analysis wasn't a thing until the 17th century. Hence>>7022238

this thread is why this board is shit.

>>7022615
I was talking about the proof that there are infinitely many primes. Not all of them.

>>7022619
Ah ok makes sense, then I agree lol.

>>7020939
Problem solving skills trump knowledge any day. Forget that entire picture. I've got a much simpler criteria.

If you scored below 20 on the Putnam or didn't take it at all, you don't belong here.

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>>7022614
turbofaggot.

> 'Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.'

>>7020939
So, how do you do 14?
Besides Cantor's diagonal whatever

>>7022489
>autistic as fuck.
>not recognizing obvious bait

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>muh secret internet sperglord club

you guys are pathetic.

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>>7022614
>2015
>doesn't smoke weed
>makes fun of people that do on an anonymous image board for math and science
>is a giant faggot

Enjoy your life you fucking loser.

>>7022639
It's more to do with quality control on this board.

If we could actually enforce OP's requirements, then this board would easily be one of the best places on the Internet.

>>7022642
>let's just talk about faggy math shit
fuck that

>>7022303
>>7022290

You two are shitheads.

Also, how do you prove that the reals are uncountable? If I was given infinite time I'm pretty sure I could count the reals.

if a math teacher is charismatic and can relay the important information to his students effectively, but isn't the best mathematician - isn't that still a good deal?

>>7022651
A math teacher is to a mathematician as a gym teacher is to Michael Phelps. You get paid to regurgitate material selected from a book and to answer stupid questions, you aren't paid to think.

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>>7022658
i see your point, but I don't agree with "paid to regurgitate material selected from a book and to answer stupid questions"

A math teacher should be expected to be able to run the math club/gifted program in my opinion. I guess that is why there are multiple math teachers in a given school district.

>>7022648
Numberphile it or read a textbook on set theory.

>>7022658
I would say that as a math PROFESSOR you should be.

I can't do 3/4ths of this and I'm in my 3rd year of Chem E at UC Berkeley, lel

>>7022637
Let P(ℕ) be the power set of ℕ.
Define f:P(ℕ)↠R as follows.
For an element s∈P(ℕ), order the numbers in s by size so s(n) is the nth largest number.
Create a decimal 0.2_2_2_2.... where the nth blank is filled by s(n) in binary. If s is finite, end with all 2s.
Clearly this is an injection of an uncountable set into R.

>>7022648
So, say that you give me a (infinite) list of numbers in [0,1] indexed by the naturals. Represent them as decimal expansions that do not end in an infinite number of nines.

Consider the nth digit of the nth number on the list. We can define a new number whose nth digit is unequal to the nth digit of the nth number on your list (and doesn't have a 9 in its decimal expansion). Is that number on your list?

So yeah, if you're just sitting there, "counting reals," you'll never be able to exhaust all of them (since you can't exhaust [0,1]).

>>7022667
A professor's primary job isn't to teach. Fucking undergrads.

>>7022671
>doesn't have a 9 in its decimal expansion
what?

>>7022641
>Being a degenerate
>AD 2015

>>7022684
Trailing 9s

got a bsc in math and im too lazy to even look at these, probably couldnt solve one.

>>7020939
These are ALL mathematical proofs. The name of the board is Science & Math. Where's the science?

>>7022688
Who actually uses >muh degerenacy. Stop being a grandpa and have a little bit of fun in your life. For someone that's on a science board you sure seem to ignore the science done showing that marijuana is not harmful to your brain with moderate use.

>>7022723
Can't do math without proof

>>7022671
>>7022684

It is a joke. They are implying that 0.9999 repeating is not equal to 1.

>>7022766
No, it just fucks up the proof if you switch them.

>>7022723
>These are ALL mathematical proofs
>2 isn't proof.
>6 isn't proof.
>7 isn't proof.
>8 isn't proof.
>9 isn't proof.
>10 isn't proof.

>>7022679
>he thinks a professor's primary job Is research

Laughingsluts.jpg

>>7022873

>imblyging professors do any work

What is a grad student or postdoc?

spoiler: a slave.

>proving stuff that have already been proven
like im going to do that

>>7020939
Mfw im elen undergrad and can so atleast 10-12 ofnthose

>Econ major
>Can't do a damn thing on that list
>At least I guess, I didn't open the image
>Just come here to shitpost and browse dank memes

Life is good, /sci/. Life is good.

>>7022642
I guarantee you with 100% certainty there is an autistic math board out there you could join.

This is a fucking math AND science board. That includes all the shit you don't like. Biology, geology, psychology are all included by the rules of this board--not by your own personal ideals. Get over it bro.

>>7022897
>>>/biz/rael is that way

>>7022784
>2 isn't proof
What the fuck do you think "Show" means?

>>7022904
Calculate it.

M.A. in sociology here, can't solve any of this. I still browse this board regularly and occasionaly shitpost.

You STEMfaggots mad?

>>7022154
At Worcester Polytechnic Institute in MA CS majors learn to prove R is uncountably infinite by Cantor's diagonalization freshman year.

>>7020939
Question number 2 you forgot the constant...also it's 1/2 sqrt(pi)

>>7022614
>tfw I smoked weed at 14 and still have a 142 iq
eat shit fucko.

>>7022921
Nope:
http://en.wikipedia.org/wiki/Gaussian_integral

>>7022905
A proper calculation is a proof. It certainly doesn't mean "Write down the formula I just gave you"

>>7022928
Well pulling e^-y^2 into the other integral is haram without proof

>>7022934
No idea what you're even saying.

When a math exercise says "Show ___" it is asking for a proof.

>>7022939
see the careful version >>7022926

>>7022637

use an injective mapping from another set of uncountable numbers.

Or prove that the set of natural numbers (which is uncountable) is a subset of the real numbers which proves that the real numbers are uncountable.

>>7022940
I see, boring analysis stuff. I suppose the exercise in Rudin lets you skip over that stuff. It's been a while since I've seen it, so I don't remember if it mentions it or not.

>>7022941
>Or prove that the set of natural numbers (which is uncountable)
lol

>>7022945

number 14 is trivial.

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>>7022723

Fine, here's the applied major version

I've had to do all but 11 and 12

>>7021248
Those are the ones you should be able to do, you fuckwit.

>>7021403
>you need a valid government ID to enter 4chan

>>7021458
Formalities are really unnecessary, but you should come up with a clear, logical way to demonstrate that they are true.

>>7021555
9. So, let's look at a general 1st order equation. These are of the form y' + p(t) * y = q(t), and we want to find an equation y(t) that satisfies this equation.. We're looking to reduce this to a function we can simply integrate. So keep in mind the product rule, d(f(x) * g(x)) = f(x) * g'(x) + g(x) * f'(x), we want to reduce the left side of the equation to this. If you look, the left side of the equation already has y' on one term and y on another, so y can act as our g. Therefore, our p is currently f = 1 and f' = p. This is impossible in and of itself, but we can multiply both by a common factor to make these two equations true. Remember that the derivative of the exponential function, exp(x) is itself. Further, by the chain rule, the derivative of exp(u(x)) is u'(x) * exp(u(x)). If we take p to be our u'(x), and P(t) is the definite integral of p(t), then we have exp(P(t)) is p(t) * exp(P(t)). It should be clear now that multiplying the two equations I pointed out earlier (f = 1 and f' = p) by exp(P(t)), we get f = exp(P(t)) and f' = p(t) * exp(P(t)).
Multiplying the entire equation by this function, now called our integrating factor, will give us exp(P(t)) * y' + p(t) * exp(P(t)) * y = exp(P(t)) * q(t). The left side can be reduced to exp(P(t)) * y' + (exp(P(t)))' * y, which can be reduced by the product rule to (y * exp(P(t)))'. So now we have (exp(P(t)) * y)' = exp(P(t)) * q(t). Now we can simply integrate to get exp(P(t)) * y = Int(exp(P(t)) * q(t)). Divide by your integrating factor, exp(P(t)) to get your solution.

tldr, multiply by exp(Int(p(t))) (integrating factor), left side reduces to (Int(p(t)) * y)'. Integrate both sides and divide by integrating factor.

>>702155510. I specifically want to discuss, very informally, why the geometric series converges or diverges for certain numbers. So remember that the geometric series is the infinite series over n of r^n. The sum, when it converges, is 1 \ (1 – r). This series only converges for |r| < 1, and diverges for everything else.

So let's look at where it converges first, when r is a fraction. r being less than one, multiplying by itself multiple times will result in a smaller number. As n approaches infinity, r^n approaches 0. So the terms of the series eventually begin to contribute nothing to the overall sum. Therefore, the sum does not increase without bound and the sum converges.

Now let's consider why the sum doesn't converge at r = 1. This is obvious from the convergence formula since the denominator is 1 – r. When r is one, of course you have a division by zero. Look at the sum, though. One to any power is one. Now you are adding together an infinite number of ones. This, of course, leads to a sum that grows without bounds.

This is precisely why the series diverges for any r > 1. Any r > 1 to any power greater than 1 is a larger number than r itself. Again, your sum will grow without bounds, and the sum diverges.

The derivation of 1 \ (1 – r) is left as an exercise.

>>7021874
It elegantly relates essential constants in analysis, geometry, and algebra to one another. It has no major impact in higher mathematics, but it is such an interesting thing.

>>7021925
Good luck doing any banking at all. Good luck using your computer securely. Good luck living in the fucking modern age, you defensive asshat.

>>7020939
MOAR like this please, it is good refreshen my memory and this is better than crosswords.

>>7022229
>OP picture is just a circlejerk of Austimo asshats who don't know what real maths is in real life
The picture is literally a collection of legitimate mathematical principles anyone studying real math (or any technical material) should understand, presented as would be seen in any fairly rigorous mathematical setting.

>a lot of people can't do this, but are scientists
Aside from the abstract proofs given (4, 5, 14), every competent scientist and engineer will be able to do this. Even then, anyone in a technical field should at least understand the statement being proved in 4, 5, and 14.

You are functionally retarded and cannot handle people on an anonymous image board telling you this.

>>7022127
What engineering program doesn't require a probability course? My school requires a probability course to graduate any major, even things like English and Theatre.

>>7022484
I remember that thread. So much autism and circlejerking.

>>7022344
>I can know plenty of advanced physics and astrophysics without ever picking up a calculator.
Absolutely true, because calculators and machines lack the creativity and ingenuity required to do the math required to develop and understand anything beyond high school physics. And so do you.

>>7022127
Your are a massive faggot and probably 29yo and learning FOIL at the local juco. ME/AE/Civil/ChemE all take a course called Statistics & Probability for Engineers. At a large school each department might teacher their own, and at a small school they will shares a course. EE people take two classes, a probability course and then a random process course. Stop shit posting and go practice First-Outside-Inside-Last.

UCLA Mechanical Engineering
174. Probability and Its Applications to Risk, Reliability, and Quality Control
Introduction to probability theory; random variables, distributions, functions of random variables, models of failure of components, reliability, redundancy, complex systems, stress-strength models, fault tree analysis, statistical quality control by variables and by attributes, acceptance sampling.

C175A. Probability and Stochastic Processes in Dynamical Systems
Probability spaces, random variables, stochastic sequences and processes, expectation, conditional expectation, Gauss/Markov sequences, and minimum variance estimator (Kalman filter) with applications.


UCLA Electrical Engineering

131A. Probability and Statistics
Introduction to basic concepts of probability, including random variables and vectors, distributions and densities, moments, characteristic functions, and limit theorems. Applications to communication, control, and signal processing. Introduction to computer simulation and generation of random events.

131B. Introduction to Stochastic Processes
Introduction to concepts of stochastic processes, emphasizing continuous- and discrete-time stationary processes, correlation function and spectral density, linear transformation, and mean-square estimation. Applications to communication, control, and signal processing. Introduction to computer simulation and analysis of stochastic processes.

The stuff posted by OP and the other questions later on are all first year stuff and some are set at 16-18 yos.
However everyone should be allowed to take part in a discussion about /sci/ however I do feel that if we had entrance requires for this board we'd get less pseudointellectualism shit like
>but what if time was a cake
Basically if you can't do this shit the only questions you shouldn't be allowed to create threads.

>>7023068
>makes sense
I shouldnt multitask

Threads like these remind me of just how fragile all of your precious egos are. Thanks for the laugh!

>>7022614
I didn't give a reason to stop smoking weed. You're making false assumptions.
I still use drugs, I only do mdma and lsd (every few months). Studying civil engineering atm, I pas all my analysis classes cuz I'm fucking good at math. Studying vector analysis atm. Proved Greens theorem by myself without opening my book/using internet.

It is possible to use drugs w/o fucking up your intelligence.
My exams end in 10 days, then I go dancing with these two hot chicks. I will probably take drugs because it makes dancing so much fun. You jelly?

>>7022904
That's just evaluating an integral where you know what the answer should be.

>>7020948
someone should post a solution to this already, or at least some links that will help us get to the solution.

>>7020939
I can do 14 of these but for a real maths major, the 6, 8, 11 are useless and even counter productive for 11 (you don't find euler formula, you define trig functions with euler formula)...

>>7020939

If you are Anonymous, you can belong anywhere and everywhere, nowhere and somewhere all at the same time. Anonymous is a unit of measure, not a real person.

>Can't do any of this
>STILL make more money than you dick stroking autists
fucking stemfags, why are you all so smug when most of you won't achieve anything?
>inb4 muh safe and insignificant research article is an achievement

After BC and MV calc in high school, where is the best route to continue in college?

>>7023463
Jaden Smith laddies and gentleman.

>>7023686
What the fuck is MV calc? Multivariate? It's certainly not standardized so you will never be able to find an accredited university that accepts it as calc 3 credit, basically your only options are to start out in calc 3 and diff eq, or be a lazy piece of shit and take calc 1 and/or calc 2 over again.

There is some merit to retaking that sequence if you're at a top tier university, like seriously Harvard it's not even worth it at UCLA that's not top 5-10 worldwide, otherwise calc 1 is a complete waste of time and calc 2 is as well unless you didn't learn it that well in high school and need more practice.

>>7023686
Assuming you got college credit or tested out of vector calc:

ODEs, Proofs, and Matrix Algebra in the fall followed by Linear Algebra/Vector Spaces, (Complex Variables or Topology or Differential Geometry of Curves and Surfaces), and PDEs in the spring. Then brace your ass for 2 semesters each of Real Analysis and Abstract Algebra the follow year.

>>7023505
some loser wrote this post because was jealous of people that are good at math

how sad

>>7023857
>It's certainly not standardized

Different schools name their courses differently. The problem is whether he did it as a joint community college class and can get credit for it or needs to convince the math department/adviser/chair he knows it and can skip it for something else.

>>7022212
>It asks for wishy-washy "interpretations"
>it asks for shitty graphical illustrations.

>not caring about geometric interpretations
>Not understanding the power of graphical illustrations

A advice for you chav: stop studying math right now. It's not a field for you.

Also

>misunderstanding the whole point of the OP

Okay you should actually stop living. It isn't a field for you either.

>>7023857
UCLA student here. We get rated in the top ten occasionally, but that's mostly for grad school. We also have "honors" courses in the math department, which pull some of their homework problems from the Ivy league and even graduate level courses of other schools. They can be pretty damn tough. Lots of students who go through the honors sequences sign up for grad courses, too.

>>7023861
What the hell is "Matrix Algebra" and "Proofs"? Certainly you don't have entire courses dedicated to those topics.