taylor and maclaurin series

[Anonymous No.10778378]

in high school AP BC calc my teacher continuously said that taylor and maclaurin series are just useless to learn (besides for the app test itself) because we have the tools to approximate and calculate exact answers. he believed that these series seem obsolete. do other people in the higher math fields feel this way as well? or is there some use for them that my teacher was too stupid to know about? should we just flat out ditch this content for (mainly high school) courses (or even drop them in higher education) ?

[Anonymous No.10778412]

>>10778378
>calculate exact answers
KEK

[Anonymous No.10778418]

Ever wonder how your calculator calculates sine and cosine values?

[Anonymous No.10778427]

>>10778378
Series are useful in advanced math, for example you can integrate any function if expressed in series form.

[Anonymous No.10778428]

>>10778378
your teacher is retarded, I bet he's an education major
taylor series are one of the most important tools in analysis and physics

[Anonymous No.10778436]

>>10778378
>do other people in the higher math fields feel this way as well?
No. The concept is EXCELLENT for use in proofs.

[Anonymous No.10778449]

I just approximate all transcendentals using repeated addition

[Anonymous No.10778479]

>>10778418
Yeah. It uses the CORDIC algorithm, not a Taylor series.

[Anonymous No.10778483]

>>10778378
.

[Anonymous No.10778749]

>>10778479
Fake and gay.

https://github.com/lattera/glibc/blob/master/sysdeps/ieee754/dbl-64/s_sin.c

[Anonymous No.10778766]

>>10778378
>is analysis useless???
Yes. Now start learning symbolic logic, set theory, and abstract algebra.

[Anonymous No.10778922]

This is bait

[Anonymous No.10778933]

>>10778378
Your teacher is a literal retard and probably never had to even solve something simple like the motion of a pendulum.

[Anonymous No.10778959]

>>10778378
>in high school AP BC calc my teacher continuously said that taylor and maclaurin series are just useless to learn

All of physics is just one big Taylor series (until you get to perturbation series which are Taylor series on drugs)

[Anonymous No.10779575]

This better be bait

[Anonymous No.10779799]

>>10778378
I had a similar experience where the AP teacher prefaced the section on permutations and combinations as “only useful for gamblers” and didn’t know why it was required curriculum.
It took me a few years of self study before I recovered from the damage the public education system inflicted.

[Anonymous No.10779912]

>>10779799
He was right, though.

[Anonymous No.10779918]

>>10778766
>symbolic "logic"
>False -> False and False -> True are True implication statements
No thanks lol

[Anonymous No.10779948]

>>10779918
based

[Anonymous No.10780058]

f(x) = f(a)/0! * (x-a)^0 + f´(a)/1! *(x-a)^1+....
f(x+a) = f(a)/0! * x^0 + f´(a)/1! *a^1 + ...
x=1
a=x
f(x+1) = f(x)/0! + f´(x)/1! +f´´(x)+.....
f(x+1) = (1+D/1! + D^2/2! +....)*f(x)
f(x+1) = f(x) * e^D
problem?

[Anonymous No.10780158]

>>10779918
>he doesn't understand that the material conditional is literally just (not A) or B
>he doesn't realize the material conditional is not the only conditional somebody could choose to use

[Anonymous No.10780173]

Your teachers an idiot. Series are an indispensable tool in mathematics.

I bet your teacher thinks sets and sequences are "useless".

[Anonymous No.10780588]

This is utter bait

[Anonymous No.10781508]

>>10779918
Implication does make sense tho, even from an intuitive point of view. If you know a statement is false, you dont know if it's consequences are wrong, for all you know they could be right or they could be wrong. 2=3 implies that 0=0, it also implies that 4=5. However, if you know something is true, its consequences also must be true.

[Anonymous No.10781521]

>>10781508
To add: i think the actual objectionable counterintuitive thing about formal logic is the way it treats OR statements. In natural language "or" usually means XOR and not OR. In this sense formal logic doesn't quite capture the way we think all the time. It is a trivial unimportant thing, but its still weird to me

[Anonymous No.10781610]

>>10779918
How much of a brainlet can you be? A false statement implies ANY statement at all, so it implies both true statements and false ones.

A retard like you once asked Bertrand Russell to prove that he was the pope under the assumption that 2 = 1. Russell then proved it by saying that he and the pope are two men, and since 2 = 1, they must be one and the same man, otherwise we would have 2 != 1.

So even in informal arguments conditional statements with false antecedents still behave as they do in symbolic logic.

The behavior of the material conditional is also determined a fortiori by the truth table of other connectives. If we counted "P implies Q" as false when P is false then (since "P implies Q" is also false when P is true and Q false) "P implies Q" would have the same truth table of "P and Q", which is absurd since informally we don't expect conditionals to behave like conjunctions.

>>10781521
>In natural language "or" usually means XOR and not OR.
>In this sense formal logic doesn't quite capture the way we think all the time.

That's because you think in an inferior, barbarian language like English. In Latin "vel" means OR and "aut" means XOR; the distinction was very clear in the mind of the ancients.

[Anonymous No.10781640]

>>10781610
Take it easy, man, no need to be aggressive all the time. Its easy to get pissed off at people, but it doesn't serve to make people understand things better. I learned that the hard way.
> In Latin "vel" means OR and "aut" means XOR; the distinction was very clear in the mind of the ancients.
That's a cool feature of Latin tho, looks like it could be a bit more convenient to talk about some things in math in Latin or Greek than in English. I don't think most people are willing to learn Greek or Latin to talk about mathematics, especially considering how math people are often autists not that much interested in human things like natural language. I will start learning some Latin, I've got a lot of free time in my hands.
>That's because you think in an inferior, barbarian language like English.
Well, i only think in English half the time, the other half I think in a barbarian slavic language called Russian.

[Anonymous No.10781650]

>>10778378
Well you're HS teacher is lying to you or really stupid. Probably the latter. Power series' are really important in science fields of study.

[Anonymous No.10781702]

>>10781640
>I don't think most people are willing to learn Greek or Latin to talk about mathematics, especially considering how math people are often autists not that much interested in human things like natural language.
That's what pseuds do. Most successful mathematicians were very much interested in "human" things (von Neumann knew more about the Byzantine Empire than any historian).

The idea that there is a clear-cut distinction between "human" things and "natural" things is mistaken: humans are a product of Nature, and everything they do (included their language) is therefore natural in some ultimate sense. The great divide between the social "sciences" and the natural sciences is a matter of methodology and bias. Social scientists believe their theories are true because they want them to be true; natural scientists are usually much less biased towards their theories. Social scientists are more emotionally invested in proving their theories right because they wish to change society in a direction that is more in line with their ideology and their own self-interest; natural scientists usually have no desire (nor opportunity) to alter the laws of Nature. The issues facing social scientists are also enormously complicated and their methods are oversimplified and wholly inadequate to discrminate between truth and falsity (see the "Sokal affair", which also highlights the political bias of the editors who published Sokal's fake article).

At any rate the study of language is closely related to the study of logic, and anyone overly lax in his language will entertain lazy thoughts and he will be ultimately unable to pursue any scientific endeavor (since we use language to think and talk about any subject matter at all).

[Anonymous No.10781759]

>>10781702
>Most successful mathematicians were very much interested in "human" things (von Neumann knew more about the Byzantine Empire than any historian).
Depends, mathematicians can be very different people. There are many mathematicians who are interested in their field of study to the exclusion of everything else. From what i know about Perelman for example i can tell that he was doing math,playing classical music and living like a complete monk. Not everyone is like von Neumann or Feynman, even tho they should be.
>The great divide between the social "sciences" and the natural sciences is a matter of methodology and bias
I agree with that. The problem is that there is no rigorous methodology for studying quite a lot of things in areas like sociology and psychology, so many would inclined to not even bother with those topics

[Anonymous No.10781935]

>>10781610
>A false statement implies ANY statement at all, so it implies both true statements and false ones.
This is false.
>>10781508
>2=3 implies that 0=0, it also implies that 4=5.
So is this.

You've been brainwashed by shitty modern philosophers. Implication is defined the way it is so that we can have garbage mathematical proofs like (not(A) -> not(B)) IFF (B -> A)

[Anonymous No.10781941]

>>10781610
Results like this just prove that two-valued logical systems are ridiculous.

[Anonymous No.10782260]

>>10778427
>Series are useful in advanced math, for example you can integrate any function if expressed in series form.

This has saved my ass on exams several different times, especially dealing with messy trig functions.

[Anonymous No.10782271]

>just use a calculator lmao
Literally should be fired, what a faggot

[Anonymous No.10782277]

>>10782271
>just use a calculator lmao
God that shit pisses me off

[Anonymous No.10782817]

Explain to me why the derivative of the series for the exponential function is itself while its integral is different

[eqn]

\frac{d \sum_{n = 0}^{\infty} \frac{x^{n}}{n!}}{dx} = \sum_{n = 0}^{\infty} \frac{x^{n}}{n!} \\

\int_{0}^{x} e^{t} dt = \sum_{n = 0}^{\infty} \frac{x^{n+1}}{(n+1)!}

[/eqn]

[Anonymous No.10783038]

>>10782817
Because when you take the derivative of both sides of the second equation, you get the Taylor series for exp(x)