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nabla blah
nabla blah
12:20 AM
Does anyone have a good reference for a proof on how to define functions recursively
 
 
1 hour later…
Ted Shifrin
Ted Shifrin
1:33 AM
Hi skull, @Pedro, @nabla
 
Mike Miller
Mike Miller
Mystical greetings, @TedShifrin
(I'm changing up my hello)
 
nabla blah
nabla blah
Hi @TedShifrin @MikeMiller
Variety is the spice of life, is it?
 
Mike Miller
Mike Miller
aye
actually, not quite
a good cup of coffee is the spice of life
 
Alexander Gruber
Alexander Gruber
What's up homies.
 
nabla blah
nabla blah
Hi @AlexanderGruber
 
Mike Miller
Mike Miller
1:38 AM
hello
 
Alexander Gruber
Alexander Gruber
@nabla. How's it going?
@MikeMiller are you teaching calc this semester?
 
Mike Miller
Mike Miller
yup
 
Alexander Gruber
Alexander Gruber
how are you liking it?
 
nabla blah
nabla blah
How are your students so far
 
Mike Miller
Mike Miller
I'm not and they're not, we start on oct 2
 
nabla blah
nabla blah
1:39 AM
Oh
 
Mike Miller
Mike Miller
but I expect I'll like it quite a lot
I enjoy teaching
 
nabla blah
nabla blah
What if they ask you if -12 was an irrational number
 
Mike Miller
Mike Miller
As in, the entire class is confused about that for some reason? Then I'll be sad
 
nabla blah
nabla blah
Yes
lol
My friend's calculus class is like that..
She is very depressed about it
 
Alexander Gruber
Alexander Gruber
@MikeMiller teaching is a lot of fun
@MikeMiller I'd be shocked if they knew or cared. (assuming they aren't math majors)
 
Mike Miller
Mike Miller
1:45 AM
it's the cared part I'd be surprised about
 
Alexander Gruber
Alexander Gruber
You'll have to let me know how it goes... freshmen at UCLA might be a lot smarter than at UF
 
Mike Miller
Mike Miller
ehhh
 
nabla blah
nabla blah
lol
 
Mike Miller
Mike Miller
freshmen math majors, maybe
but I think the freshman intelligence is pretty universally constant
 
Alexander Gruber
Alexander Gruber
most of mine think that rational numbers are "all real numbers" or something like that
I got about 2 correct definitions on my last quiz out of a class of 95
it's a good sign, though. More material to learn 'em => more amazement at the end of the semester
 
nabla blah
nabla blah
1:49 AM
They think $\mathbb{Q} = \mathbb{R}$
 
Alexander Gruber
Alexander Gruber
@nablablah i mean, most of them are bio or psych majors
 
nabla blah
nabla blah
I think I thought that too when I took calculus
 
Alexander Gruber
Alexander Gruber
I don't know wtf a ribosome is, I can't really expect them to be like "$\mathbb{Q}$ must be proper because it is countable!"
 
Ted Shifrin
Ted Shifrin
Hi @Alex ... Hope your back is better ...
 
nabla blah
nabla blah
I didn't get a chance to take pre-calc because I accidentally tested out of it
 
Alexander Gruber
Alexander Gruber
1:51 AM
@TedShifrin there is actually progress
neurologist put me on some kind of pill that is fixing the headaches
 
Ted Shifrin
Ted Shifrin
Great!
 
Alexander Gruber
Alexander Gruber
i am pretty excited about it- that was the main problem.
@nablablah Yeah I never took past algebra 2 in HS
and went into calc when I was 24
 
Ted Shifrin
Ted Shifrin
Does he have therapy in kind to fix things gradually?
 
Alexander Gruber
Alexander Gruber
there wasn't really any testing out or whatever involved, i just belligerantly refused to leave the class and eventually they gave up.
 
Ted Shifrin
Ted Shifrin
Mind, not kind
 
nabla blah
nabla blah
1:53 AM
lol wow
 
Alexander Gruber
Alexander Gruber
@TedShifrin I'm going to be starting water therapy soon
which I don't know too much about
 
nabla blah
nabla blah
I'm not sure if it was a good idea for me to skip it because I feel like my foundations in proofs are a bit rocky and for some reason I feel like they taught everyone how to write proofs during pre-calc and I missed it all
 
Ted Shifrin
Ted Shifrin
Cool ... I hope things improve for you! Imagine you belligerent :)
 
Alexander Gruber
Alexander Gruber
@nablablah i'm pretty sure they didn't teach them any proofs during pre-calc. :p
@TedShifrin it's more common than you might think. :p
 
Ted Shifrin
Ted Shifrin
No, @nabla, no proofs of any sort in precalc!
 
Alexander Gruber
Alexander Gruber
1:55 AM
thanks though, always appreciate the support from here. not many people at my uni know about my injury (due to pride and paranoia) so I don't hear much about it.
 
Ted Shifrin
Ted Shifrin
Sometimes bottling things up hurts more than helps, @Alex ...
 
Alexander Gruber
Alexander Gruber
@TedShifrin letting people in charge of me know about vulnerabilities just hasn't worked out for me in the past. force of habit.
 
Ted Shifrin
Ted Shifrin
I understand ...
 
Alexander Gruber
Alexander Gruber
anyway, did you hear that this winter is supposed to be crazy?
i guess we're going to get snow down here in the south
 
Ted Shifrin
Ted Shifrin
Oh great ... A canceled week ... Wonderful.
 
 
2 hours later…
Gustavo Montano
Gustavo Montano
4:11 AM
Haha, down here in Australia our spring/summer is coming! I can't wait. Today was amazing. Nothing but sun ^_^. The last few weeks have been crazy rain :(.
 
r9m
r9m
4:58 AM
 
Gustavo Montano
Gustavo Montano
sigh. There are cleaner ways to kill people.
 
 
1 hour later…
anon
anon
6:05 AM
fuuuuuu I let a mosquito in
 
Anthony
Anthony
6:25 AM
@anon Are you there?
 
anon
anon
yeah
 
Anthony
Anthony
What's an example of two metric spaces that are homeomorphic but not Lipschitz equivalent?
 
anon
anon
doesn't remember what Lipshitz means, has to google it
 
Anthony
Anthony
Sorry :(
 
anon
anon
how about the complex plane with its normal metric versus the one induced from stereographic projection from the Riemann sphere
 
Anthony
Anthony
6:29 AM
Oh god
 
anon
anon
what?
 
Anthony
Anthony
When I think of metric spaces all I can think of are R with the discrete metric and R with the euclidean metric, lol.
What's the one induced from the sphere?
 
anon
anon
basically, given two points on the plane, unproject them back to get two points on the sphere, then take their distance from each other on the sphere
similar idea: the upper half plane with its usual metric, versus the hyperbolic metric
 
Anthony
Anthony
What's the measure of distance on sphere though?
 
anon
anon
make a circular arc between two points and take its length
 
Anthony
Anthony
6:35 AM
Yeah I just realized.
Herp.
Thanks.
 
anon
anon
mmhmm
 
Anthony
Anthony
Are you a student?
 
Alex Youcis
Alex Youcis
Hey
 
anon
anon
I am a student and a teacher
 
Alex Youcis
Alex Youcis
everyone
 
anon
anon
6:39 AM
hello
 
Anthony
Anthony
Yo.
@AlexYoucis You're at Berkeley, yah?
 
Alex Youcis
Alex Youcis
@Anthony That's right.
 
Anthony
Anthony
How scared should I be of Rieffel's 202a?
 
Alex Youcis
Alex Youcis
Uh
 
Anthony
Anthony
I have a pretty heavy courseload, but I don't want to drop it...
 
Alex Youcis
Alex Youcis
6:41 AM
Prob(I know what 202a is)=0
 
Anthony
Anthony
Oh really?
 
Alex Youcis
Alex Youcis
True fact
 
Anthony
Anthony
Grads don't even know which grad courses are which?
D:
 
anon
anon
I highlighted it, right-clicked, googled, clicked a result and found what it is in <5 seconds.
 
Alex Youcis
Alex Youcis
@Anthony Grads don't know what undergrad courses masquerading as grad courses are.
:)
 
Anthony
Anthony
6:42 AM
!
I like that answer.
@anon What'chu mean?
 
anon
anon
intro top/anal is a grad course at berkely?
 
Anthony
Anthony
For some reason, yeah.
 
Alex Youcis
Alex Youcis
@anon It's generally stuff not covered in every undergrad course. Mostly undergrads take it though.
 
anon
anon
I see
 
Alex Youcis
Alex Youcis
I think only one person in my year took it
and I think he knew most of the stuff
@Anthony I don't really know Rieffel either
@Anthony What year are you?
 
Anthony
Anthony
6:45 AM
I'mma junior.
 
Alex Youcis
Alex Youcis
@Anthony Are you doing DRP?
 
Anthony
Anthony
DRP?
DIRECTED READING PROGRAM
No.
 
Alex Youcis
Alex Youcis
Bums
(=bummer)
 
Anthony
Anthony
Why?
 
Alex Youcis
Alex Youcis
I was just curious.
 
Anthony
Anthony
6:46 AM
Oh.
I considered it.
But I had too much stuff already.
 
Alex Youcis
Alex Youcis
Should do it next term :)
 
Anthony
Anthony
Roger.
Anyway, I'm gonna go to bed.
 
Alex Youcis
Alex Youcis
@Anthony See ya.
 
Anthony
Anthony
Hasta.
 
Alex Youcis
Alex Youcis
7:01 AM
@anon How are things going with you?
 
anon
anon
pretty good
fun fun fun
 
Alex Youcis
Alex Youcis
@anon That's always good to hear. :)
@anon Learning anything fun right now?
 
anon
anon
mmm, thinking about the trace formula for schur functors (I can now prove it myself), how species relate to combinatorial proofs, and the problem of tiling a 70x70 square with 1x1, 2x2, .... 24x24 squares (which has been solved by computer but not by hand: not possible).
( recall that 1+2^2+...+24^2=70^2 is the only solution to 1+...+m^2=n^2)
 
Alex Youcis
Alex Youcis
@anon I have no idea what half of those things mean, kind of. I know schur functors are related to schur polynomials in alg comb. I know species are the thing that Bruno's dad used to be in to, and I don't know what the sig. of the tiling is.
Sounds fun though!
 
anon
anon
sig?
 
Alex Youcis
Alex Youcis
7:05 AM
significance
 
anon
anon
there isn't really any I don't think, it's just an exotic and unique finite problem that emerges from an exotic and unique fact
 
Alex Youcis
Alex Youcis
Fair enough haha
 
anon
anon
(the 1+...+24^2=70^2 thing is related to lattices and number theory and string theory and some other stuff)
 
Alex Youcis
Alex Youcis
@anon Like leech lattice words?
 
anon
anon
mmhmm
 
Alex Youcis
Alex Youcis
7:07 AM
Well, that's interesting. Borcherds would probably be all over that
 
anon
anon
he is
as I recall
 
Alex Youcis
Alex Youcis
I know he used to be
He probably still is
 
anon
anon
did you see the arxiv joke I pinned for an entire month?
 
Alex Youcis
Alex Youcis
Nope
 
anon
anon
I lol'd when this first came out on arxiv: arxiv.org/abs/1408.2083
 
Alex Youcis
Alex Youcis
7:09 AM
Oh yeah, I saw this
Numerology at its finest :)
 
Chris's sis
Chris's sis
7:27 AM
Greetings
 
 
1 hour later…
Ice Boy
Ice Boy
8:36 AM
Greetings
 
Manish
Manish
8:54 AM
any bpdy ?
*body
 
Sawarnik
Sawarnik
9:19 AM
@Manish Yes.
 
 
2 hours later…
Balarka Sen
Balarka Sen
11:37 AM
@anon you're suspected in the charge of killing @blue
 
Ice Boy
Ice Boy
@blue you're suspected in the charge of killing @anon
 
Chris's sis
Chris's sis
Let's consider $\displaystyle f(x)=\frac{1}{1+x^2}$. Compute $$\sum_{n=0}^{\infty} \left(\frac{f^{(4n)}(1)}{(4n)!}+\frac{f^{(2n)}(1)}{(2n)!}\right)$$ This is a question by Furdui.
 
Balarka Sen
Balarka Sen
@IceBoy that's a priceless comment!
 
Ice Boy
Ice Boy
:D
@BalarkaSen I could have commented "and vice versa" but I don't think it would have sounded as good.
 
Balarka Sen
Balarka Sen
haha, yeah, it wouldn't.
 
Ice Boy
Ice Boy
11:49 AM
Plus he wouldn't get the pings };-)
 
Chris's sis
Chris's sis
12:13 PM
I think you'd also like to know both you, @PedroTamaroff, and those that starred your message that before going to the place you called "proper analysis" you might like to know to compute some elementary series like the one above or more elementary ones.
 
Sush
Sush
What is $0\times 0$? Is it undefined?
 
Balarka Sen
Balarka Sen
@Sush Nope, it's not.
@Chris'ssis Computing series have nothing to do with analysis.
 
Sush
Sush
@BalarkaSen, you mean $0\times 0=0$?
 
Balarka Sen
Balarka Sen
Yes.
 
Chris's sis
Chris's sis
@BalarkaSen Mathematical analysis is a branch of mathematics that includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions.
Mathematical analysis
Mathematical analysis is a branch of mathematics that includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). == History == ...
 
Balarka Sen
Balarka Sen
12:18 PM
@Chris'ssis Don't trust wiki.
 
Chris's sis
Chris's sis
@BalarkaSen I don't trust you.
 
Balarka Sen
Balarka Sen
Try peeking at Rudin before commenting on what analysis is.
 
Gustavo Montano
Gustavo Montano
Analysis is beautiful.
Incredibly hard, but beautiful.
 
Balarka Sen
Balarka Sen
@GustavoMontano Hard though.
Haha, jinx.
 
Gustavo Montano
Gustavo Montano
It's where abstraction meets imagination.
Wait, did I describe it right.
Some abstractions are so incredibly hard to "imagine", that's why its so difficult.
 
Balarka Sen
Balarka Sen
12:20 PM
Well, @Chris'ssis, you don't have to, but it's better to look at well-recognized textbooks before copying what wiki says. Have you ever tried Rudin?
 
Chris's sis
Chris's sis
 
Balarka Sen
Balarka Sen
Rudin, Rudin, not flim-flam sites.
 
Chris's sis
Chris's sis
@BalarkaSen You say a lot of stuff out there (it easy to say anything you want to).
 
Gustavo Montano
Gustavo Montano
I think Analysis as a word touches on many branches of mathematics.
"Hard Bloody Analysis" = Rudin.
 
Balarka Sen
Balarka Sen
It's soft analysis.
 
Gustavo Montano
Gustavo Montano
12:21 PM
Really
 
Balarka Sen
Balarka Sen
@Chris'ssis Well, if it's quotes we are doing, let's quote mathematicians : terrytao.wordpress.com/2007/05/23/…
 
Gustavo Montano
Gustavo Montano
Terry Tao is Australian :).
 
Sush
Sush
@BalarkaSen, then when we solve quadratic $x^2-3x+2=0$, we get $(x-1)(x-2)=0$, that is $x-1=0 or x-2=0$ but if $0\times 0=0$, then $x=1=2$, right?
 
Balarka Sen
Balarka Sen
@Sush Nah.
$0 \times x$ for any $x \in \Bbb R$ is $0$.
 
Gustavo Montano
Gustavo Montano
Anything times $0$ is $0$ Sush.
 
Balarka Sen
Balarka Sen
12:23 PM
Since $1 \neq 2$, either $(x - 1)$ or $(x - 2)$ is $0$.
 
Chris's sis
Chris's sis
@BalarkaSen You should read first what you give me to read. Did you even read that?
 
Gustavo Montano
Gustavo Montano
Hmmm, that's a good question.
 
Sush
Sush
@BalarkaSen, OK! So, it is other way around!!
 
Balarka Sen
Balarka Sen
@Chris'ssis Yes, I did.
 
Gustavo Montano
Gustavo Montano
Well, yes it's OR, because $x$ can only take one value at a time.
 
Sush
Sush
12:24 PM
@BalarkaSen, many many thanks, Sir!
 
Gustavo Montano
Gustavo Montano
$x$ can not be $1$ and $2$ at the same time.
Mutually exclusive.
I realised today why we can use minutes and seconds when talking about angles.
It just HIT me. I never thought about it.
 
Balarka Sen
Balarka Sen
Latitude-Longitude.
 
Chris's sis
Chris's sis
@BalarkaSen And reading that you have concluded that the series and integrals are not part of analysis?
 
Gustavo Montano
Gustavo Montano
A minute is an angle. A second is an angle.
 
Balarka Sen
Balarka Sen
@Chris'ssis Reading that I have concluded that series and integrals are not part of soft analysis
 
Sush
Sush
12:26 PM
@GustavoMontano, I am economics student. Glad to meet a finance student.
 
Gustavo Montano
Gustavo Montano
Yes! I do Finance, Pure Mathematics and Computer Science :).
Economics is a great subject.
 
Sush
Sush
:D
 
Chris's sis
Chris's sis
@BalarkaSen “Hard analysis” is mostly concerned with finite quantities (e.g. the cardinality of finite sets, the measure of bounded sets, the value of convergent integrals, the norm of finite-dimensional vectors, etc.) and their quantitative properties (in particular, upper and lower bounds).
 
Balarka Sen
Balarka Sen
That's hard analysis, yes
 
Chris's sis
Chris's sis
mostly
 
Balarka Sen
Balarka Sen
12:27 PM
Not soft analysis
1 min ago, by Balarka Sen
@Chris'ssis Reading that I have concluded that series and integrals are not part of soft analysis
 
Gustavo Montano
Gustavo Montano
No matter the case, soft analysis and hard analysis are subsets of analysis.
 
Balarka Sen
Balarka Sen
@GustavoMontano I am sure Pedro meant soft analysis while talking of "proper analysis"
 
Gustavo Montano
Gustavo Montano
Oh, is that what this is about.
Well you can ask him when he comes on xD.
 
Balarka Sen
Balarka Sen
Analysis is the official name for soft analysis, actually
 
Gustavo Montano
Gustavo Montano
What's your favourite branch of mathematics @BalarkaSen?
 
Balarka Sen
Balarka Sen
12:31 PM
Number theory.
So, naturally, I am more attached to hard analysis than soft.
 
Ice Boy
Ice Boy
both qualitative and quantitative understanding is needed in all areas of Science
 
Balarka Sen
Balarka Sen
@IceBoy that's just irrelevant
 
Ice Boy
Ice Boy
is it?
 
Balarka Sen
Balarka Sen
yes. we were talking of terminologies. =)
 
user101036
user101036
Of course computing integrals and series are a part of analysis. You don't maybe need to know how to compute stuff very fast, but it is extremely profitable to know how to compute things. Many things in analysis, inequalities to be proven rely on "tricks". A good way to get a good feeling of convergence for series is to actually try to compute them , or bound them by something
 
Balarka Sen
Balarka Sen
12:34 PM
@user101036 Convergence is definitely part of analysis
 
Ice Boy
Ice Boy
how do you assign numbers to something you can't describe qualitatively?
 
Balarka Sen
Balarka Sen
Extreme computations of extremely crazy integrals are just out of the blue sometimes
 
Gustavo Montano
Gustavo Montano
@IceBoy. Yes you are right.
 
Chris's sis
Chris's sis
@BalarkaSen I understood your point. What do you recommend me here? Maybe a simple hint (a tiny one) ...
 
user101036
user101036
I don't see any point in spending too much time on crazy integrals, but some mathematicians have made quite a lot out of being extremely good computers.
 
Chris's sis
Chris's sis
12:35 PM
Let's consider $\displaystyle f(x)=\frac{1}{1+x^2}$. Compute $$\sum_{n=0}^{\infty} \left(\frac{f^{(4n)}(1)}{(4n)!}+\frac{f^{(2n)}(1)}{(2n)!}\right)$$
 
Gustavo Montano
Gustavo Montano
I mean, a better observation are the quantities we make from qualitative analysis.
Turning ideas into mathematics.
 
Balarka Sen
Balarka Sen
@Chris'ssis I am recommending nothing to you. I am just pointing out that I agree with Pedro's comment. Well, not quite, I agree with your correction of Pedro's comment.
 
Gustavo Montano
Gustavo Montano
That's the BEST part of mathematics in my opinion ^_^.
 
Balarka Sen
Balarka Sen
Integrals are surely part of mathematics. But there is more to it =)
 
user101036
user101036
That sum that @Chris'ssis gave might be useful to know in some actual theoretical argument, or something similar. To practice on such things are not a waste of time and many of the absolute best hard analysists I know are very good computers.
 
Chris's sis
Chris's sis
12:37 PM
@BalarkaSen When someone says "Math is not about computing crazy integrals." you'd expect that someone else said before "Math is about computing crazy integrals." No one said that! Is that a part of the cooking? (in case it's not a part of math)
 
Gustavo Montano
Gustavo Montano
Pure mathematics is the applied mathematics of tomorrow.
3
What do we think about that quote?
My statistics lecturer mentioned it.
 
Ice Boy
Ice Boy
nice^
 
user101036
user101036
So a tip is not to be so categorical about things @BalarkaSen .
 
Gustavo Montano
Gustavo Montano
I thought it was great too! In fact, I tried to imagine a time when a well known concept that is applied today was a "pure mathematical" abstraction.
 
user101036
user101036
When you say that "series have nothing to do with analysis" that is a very strong statement . Some tenured mathematicians have made careers out of computing series and integrals. I wouldn't say that it is an integral part of analysis , but it is of a part of analysis at least.
 
Balarka Sen
Balarka Sen
12:41 PM
@GustavoMontano I think it's a perfectly true comment.
 
Gustavo Montano
Gustavo Montano
Share it with the world :D.
 
Balarka Sen
Balarka Sen
@Chris'ssis Indeed, Pedro was incorrect to say that integrals are not part of mathematics. That is why I starred both of your comments.
 
Chris's sis
Chris's sis
@user101036 True.
 
Balarka Sen
Balarka Sen
@user101036 I understand analysis to be soft analysis, thus the comment.
 
user101036
user101036
Analysis is broad. It is not in general only soft analysis.
Carleson's theorem theorem is very much hard analysis, and I would call that analysis like nothing else.
 
Gustavo Montano
Gustavo Montano
12:45 PM
Yes, I would have to disagree with Pedro at a literal level. But I think we all know what he was trying to say.
 
Balarka Sen
Balarka Sen
@IceBoy You know Pedro =P
 
user101036
user101036
@BalarkaSen For example, consider the following:
 
Gustavo Montano
Gustavo Montano
Metaphor for "grow up and do some real maths :p" ?
 
Balarka Sen
Balarka Sen
@user101036 I have a lot of mental blocks about mathematics, I can't help not being categorical.
 
user101036
user101036
If f:[0,1]-> C is lebesgue measurable, then f \in L^\infty([0,1]) iff fg \in L^2([0,1]) for every g \in L^2([0,1]). One implication is trivial, the other is trickier. The easiest approach I know of uses hard analysis and the proof is about 4-5 sentences. The soft analysis approach takes almost over a page.
 
Balarka Sen
Balarka Sen
12:49 PM
The branch I like to think about is number theory and algebra (mostly ring-field-galois, not group) so I kinda super-hate analysis.
 
user101036
user101036
both proofs have merit
Well, I am not an analyst but if you are into number theory, analysis will become important there as well
 
Balarka Sen
Balarka Sen
I am ignorant. Meh.
 
user101036
user101036
you have for example Tate's thesis on harmonical analysis on adeles
 
Balarka Sen
Balarka Sen
I know, I know, but I am still ignorant =P
I am just a beginner. I hope to shift up this mental blocks if I learn more.
*these
 
Huy
Huy
@BalarkaSen: What exactly is soft analysis?
 
Balarka Sen
Balarka Sen
12:51 PM
The only kind of analysis I like is complex analysis =P
 
Chris's sis
Chris's sis
@BalarkaSen Then you shouldn't give any piece of advice to the others ... (frankly speaking). You say it clearly that you're ignorant.
 
Balarka Sen
Balarka Sen
@Huy Rudin-type analysis
 
Huy
Huy
@BalarkaSen: I'm sorry, I never read Rudin's books.
 
Balarka Sen
Balarka Sen
@Chris'ssis I haven't. you misunderstood me if you think I did
 
user101036
user101036
I don't mean to be mean or anything. Just give it some time and be open to all mathematics you find interesting. If you don't like some kind of mathematics the best thing is to just keep it to oneself. We all have a lot to learn and it is not unwise to be humble and thankful for all parts of mathematics (even if that part doesn't suit oneself)
3
 
Gustavo Montano
Gustavo Montano
12:55 PM
Complex analysis! By far my favourite course!
 
Balarka Sen
Balarka Sen
Indeed, @user101036. I just can't cope up with Rudin-type analysis.
 
Gustavo Montano
Gustavo Montano
Beautiful.
 
Balarka Sen
Balarka Sen
@GustavoMontano Excellent.
 
user101036
user101036
HAve you looked at Stein's books? I mean, Rudin's books are in general very terse
 
Balarka Sen
Balarka Sen
@user101036 nuh-huh.
 
user101036
user101036
12:56 PM
you might like it. It uses analysis to prove stuff in number theory and so on
 
Balarka Sen
Balarka Sen
I have read Apostol though, but I guess it's just hard analysis.
 
user101036
user101036
It ispart of the "Princeton series in analysis" or something
 
Balarka Sen
Balarka Sen
@user101036 Oh! Will definitely look.
I kind of like to stick to my algebra though.
 
user101036
user101036
If that is what you want to do, by all means. one shuld do the kind of math one likes
Regarding the books : Therearefour books, covering topics in graduate analysis but if you can read Rudin you can definitely read them.
I , who am very interested in number theory and algebraic geometry wish I actually knew more analysis.
 
00:00 - 13:0013:00 - 17:0017:00 - 22:0022:00 - 00:00

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