/sci/ - Science & Math » Thread #11864068

47KiB, 1146x618, algebraic_anal.jpg

View Same Google iqdb SauceNAO

Fuck Calculus

Anonymous Fri 03 Jul 19:29:05 2020 No.11864068 View Reply Original Report

Quoted By: >>11864085 >>11864266 >>11864272 >>11864579 >>11865708 >>11865838 >>11866803

All my homies hate calculus

Anonymous

Anonymous Fri 03 Jul 2020 19:30:51 No.11864073 Report

Quoted By: >>11866948

>broke and woke
Those two say different things tho.

Anonymous

Anonymous Fri 03 Jul 2020 19:36:55 No.11864085 Report

Quoted By: >>11864108

>>11864068
Imagine picking a side. Both analysis and algebra are beautiful.

Anonymous

Anonymous Fri 03 Jul 2020 19:48:47 No.11864108 Report

Quoted By: >>11864111 >>11864592

>>11864085
I'm not picking sides. Both fields are fascinating on their own. I get algebra much better than analysis. Just a personal thing. I have nightmares about epsilon-delta proofs and Cauchy sequences.

Anonymous

Anonymous Fri 03 Jul 2020 19:50:47 No.11864111 Report

Quoted By: >>11864114

>>11864108
>epsilon-delta proofs and Cauchy sequences
Probably because you don't understand them. The idea behind them is actually very simple and once you catch the gist of it it becomes a pleasure to work with.

Anonymous

Anonymous Fri 03 Jul 2020 19:53:50 No.11864114 Report

Quoted By: >>11864215 >>11864262 >>11864943

>>11864111
exactly the opposite for me. I understand the concepts well and can visualize them, but when it comes to applying it in proofs I'm lost. Never happens to me in algebra. Concepts might be hard to grasp, but proof techniques seem more "natural" (just use the most obvious morphism lol, works 90% of the time).

Anonymous

Anonymous Fri 03 Jul 2020 20:46:17 No.11864215 Report

Quoted By: >>11864242 >>11864943

>>11864114
That's because algebra is trivial until two or three years in whereas you can ask challenging analysis questions with virtually no background

Anonymous

Anonymous Fri 03 Jul 2020 20:58:22 No.11864242 Report

Quoted By:

>>11864215
That's a fair point. Grad-level algebra looks like elvish to me.
>with virtually no background
Every undergrad analysis student implicitly learns basic field theory and topology just to grasp what a real number is. The questions are challenging exactly because you have so much shit dumped on you in the beginning.

Anonymous

Anonymous Fri 03 Jul 2020 21:03:58 No.11864262 Report

Quoted By: >>11864269

>>11864114
>I understand the concepts well and can visualize them
>when it comes to applying it in proofs I'm lost
one of these statements is a lie

Anonymous

Anonymous Fri 03 Jul 2020 21:05:33 No.11864266 Report

Quoted By:

>>11864068

> A Banach algebra
> e^a for a \in A

Anonymous

Anonymous Fri 03 Jul 2020 21:05:52 No.11864269 Report

Quoted By: >>11864538 >>11864715

>>11864262
You can visualize having sex all you want but you're still an incel

Anonymous

Anonymous Fri 03 Jul 2020 21:06:18 No.11864272 Report

Quoted By: >>11864579

>>11864068
The first definition gives one unique number, while the second isn't unique to one base.

Anonymous

Anonymous Fri 03 Jul 2020 23:05:40 No.11864534 Report

Quoted By:

>not combining both into the exponential map of a Lie algebra

Anonymous

View Same Google iqdb SauceNAO 1587631940657.jpg, 41KiB, 511x671

Anonymous Fri 03 Jul 2020 23:06:57 No.11864538 Report

Quoted By:

>>11864269

Anonymous

Anonymous Fri 03 Jul 2020 23:18:23 No.11864579 Report

Quoted By:

>>11864068
>>11864272
ding ding ding

Anonymous

Anonymous Fri 03 Jul 2020 23:21:12 No.11864592 Report

Quoted By: >>11864596

>>11864108
>Just a personal thing. I have nightmares about epsilon-delta proofs and Cauchy sequences.
this is how you know that you're low iq, imagine being afraid of retard analysis

Anonymous

Anonymous Fri 03 Jul 2020 23:23:30 No.11864596 Report

Quoted By: >>11864620

>>11864592
got an A in my first semester analysis
C O P E
O P E
P E
E

Anonymous

Anonymous Fri 03 Jul 2020 23:28:53 No.11864620 Report

Quoted By: >>11864646

>>11864596
>I have nightmares about delta-epsilon proofs and cauchy sequences
You're a faggot

Anonymous

Anonymous Fri 03 Jul 2020 23:34:41 No.11864646 Report

Quoted By: >>11864665

>>11864620
at least I'm not a retard who can't copypaste and types it all up

Anonymous

Anonymous Fri 03 Jul 2020 23:44:08 No.11864665 Report

Quoted By:

>>11864646
have a good day anon :^)

Anonymous

View Same Google iqdb SauceNAO y-9tCKYsmgcTmkVy-OAQ3QoAe-0qcYmO (...).jpg, 90KiB, 500x1200

Anonymous Sat 04 Jul 2020 00:03:24 No.11864715 Report

Quoted By: >>11864722

>>11864269

Anonymous

Anonymous Sat 04 Jul 2020 00:09:24 No.11864722 Report

Quoted By: >>11864726

>>11864715
>no argument
I accept your concession

Anonymous

View Same Google iqdb SauceNAO 1564958812342.jpg, 142KiB, 1050x741

Anonymous Sat 04 Jul 2020 00:11:25 No.11864726 Report

Quoted By:

>>11864722
You have to go back.

Anonymous

Anonymous Sat 04 Jul 2020 02:02:55 No.11864943 Report

Quoted By:

>>11864114
Sounds like you're not being asked hard questions in your algebra course.

>>11864215
You can make any math course arbitrarily hard or easy.

Anonymous

Anonymous Sat 04 Jul 2020 09:27:02 No.11865708 Report

Quoted By:

>>11864068
you're the guy who forgets '+ c' aren't you...

Anonymous

Anonymous Sat 04 Jul 2020 10:33:49 No.11865838 Report

Quoted By: >>11866276 >>11866839 >>11866846

>>11864068
Can anyone recommend a good calculus book. I wanna learn it back from the very basics

Anonymous

Anonymous Sat 04 Jul 2020 13:57:28 No.11866276 Report

Quoted By:

>>11865838
Fuck Calculus

Anonymous

View Same Google iqdb SauceNAO 1579406770998.png, 369KiB, 750x750

Anonymous Sat 04 Jul 2020 16:54:10 No.11866803 Report

Quoted By: >>11866820 >>11866827 >>11866829

>>11864068
retard here, can someone explain the second definition?

Anonymous

Anonymous Sat 04 Jul 2020 16:59:43 No.11866820 Report

Quoted By: >>11866844

>>11866803
That's not a definition. It's simply a property that the function e^x and generally a^x for any a >0 has that
a^(x+y)=(a^x)(a^y)
In a way, it transforms addition to multiplication.
There are actually much more such functions
f(x+y)=f(x)f(y)
taking logs of both sides and letting g=log(f), we find
g(x+y)=g(x) + g(y)
this is the well-known Cauchy functional equation that has many solutions (not just linear functions, although assuming that g is continuous forces g to be linear).

Anonymous

View Same Google iqdb SauceNAO braingrl.jpg, 230KiB, 1080x1350

Anonymous Sat 04 Jul 2020 17:00:48 No.11866827 Report

Quoted By:

>>11866803
${\mathrm e}^{x+y} = {\mathrm e}^{y} \cdot {\mathrm e}$

acts, on the right domains, as homomorphism, defined as

$\phi(X \box Y) = \phi(X) \bullet \phi(Y)$

And in this case, it's for the two operations of addition and multiplication of the reals.

Compare with linear maps between vector spaces $M: V\to W$ and two vectors $x,y\in V$ , which has
$M(x+y) = Mx +' My$
in a vector space, where + and +' are the two additions in V and W, respectively.

Anonymous

View Same Google iqdb SauceNAO braingrl.jpg, 230KiB, 1080x1350

Anonymous Sat 04 Jul 2020 17:02:10 No.11866829 Report

Quoted By: >>11866835 >>11866858

>>11866803
${\mathrm e}^{x+y} = {\mathrm e}^{y} \cdot {\mathrm e}$

acts, on the right domains, as homomorphism, defined as

$\phi(X \Box Y) = \phi(X) \bullet \phi(Y)$

where $\Box$ and $\bullet$ are the binary operation in domain and codomain.

And in this case, it's for the two operations of addition and multiplication of the reals.

Compare with linear maps between vector spaces $M: V\to W$ and two vectors $x,y\in V$ , which has
$M(x+y) = Mx +' My$
in a vector space, where + and +' are the two additions in V and W, respectively.

Anonymous

Anonymous Sat 04 Jul 2020 17:03:32 No.11866835 Report

Quoted By:

>>11866829
Hi Nikolaj.

Anonymous

Anonymous Sat 04 Jul 2020 17:04:43 No.11866838 Report

Quoted By:

${\mathrm e}^{x+y} = {\mathrm e}^x \cdot {\mathrm e}^y$

I shouldn't insist on rm'ing the "constant" e.

Anonymous

Anonymous Sat 04 Jul 2020 17:04:43 No.11866839 Report

Quoted By:

>>11865838
Please

Anonymous

Anonymous Sat 04 Jul 2020 17:06:30 No.11866844 Report

Quoted By:

>>11866820
thank you anon! I get it now, I didn't understand the notation

Anonymous

Anonymous Sat 04 Jul 2020 17:07:15 No.11866846 Report

Quoted By: >>11866893

>>11865838
Spivak, Calculus
Schlomo Sternberg, Advanced Calculus

Anonymous

Anonymous Sat 04 Jul 2020 17:08:33 No.11866858 Report

Quoted By: >>11866903

>>11866829
cool, I get it now

Anonymous

Anonymous Sat 04 Jul 2020 17:19:56 No.11866893 Report

Quoted By:

>>11866846
Thanks anon

Anonymous

View Same Google iqdb SauceNAO IMG_20200703_2145181492.jpg, 135KiB, 705x940

Anonymous Sat 04 Jul 2020 17:22:07 No.11866903 Report

Quoted By:

>>11866858
It breaks for non-commutative algebras over ${\mathbb R}$ , but in a controlled way. Namely with extra factors, as

$e^{X+Y} = e^{X} \cdot e^{Y} \cdot e^{-\frac{1}{2} [X,Y]} e^{\frac{1}{6}(2[Y,[X,Y]]+ [X,[X,Y]] )} \cdot e^{-\frac{1}{24}([[[X,Y],X],X] + 3[[[X,Y],X],Y] + 3[[[X,Y],Y],Y]) } \cdot e^{\cdots}\cdots$
(Zassenhaus formula)

Anonymous

Anonymous Sat 04 Jul 2020 17:34:47 No.11866948 Report

Quoted By: >>11866980

>>11864073
fpbp.
Even if the isomorphism in the second line is in ${\bf Diff}$ it still wouldn't imply the first line. It's like no one on here have even passed first year middle school

Anonymous

Anonymous Sat 04 Jul 2020 17:42:05 No.11866980 Report

Quoted By:

>>11866948
>is in Diff
Are there solutions to it (with the + corrected for *, obviously) that aren't C0?

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches