Mathematics - 2011-10-28 (page 1 of 5)

Matt

00:00

Howdy

t.b.

Sorry, but what do you mean by "the" direct complement?

Asaf Karagila

Assume the axiom of choice :-)

I mean, simply the dimension of U+W cannot be \kappa, so the direct complement has to have a large dimension.

@Matt Hello there.

t.b.

@Matt: witness a set theorist ask an analyst something about characteristic two... If the blind leads the blind, both shall fall into a ditch

2

Asaf Karagila

This is general vector space right now...

I am even willing to assume the axiom of choice for this (well, and for the rest of the construction... but only thus far and no further!)

t.b.

Well, I agree with your dimension argument and I guess I agree that you can't play too many tricks with choosing a complement, so I guess your hunch is okay.

Asaf Karagila

00:05

phew

Matt

haha

t.b.

@Asaf: but remember, it's just a guess, I don't see how to prove that.

Asaf Karagila

I think that the cardinality game in the dimensions is enough.

Matt

Do you guys have any recommendations for other online chatrooms to discuss math and receive help in solving problems?

Besides here of course

And #math irc, or openstudy.com

Asaf Karagila

When you say #math irc, which IRC network are you talking about?

Matt

00:11

These 3 are my goto, im curious if there are other sites similar

Hmm, not sure, I just goto this site

webchat.freenode.net

and type #math in the channel

Asaf Karagila

Freenode. I need to get there sometime for some linux questions. Oh well.

t.b.

No, sorry, I can't help. I only lost my chat-virginity about a week ago.

Asaf Karagila

Wait, what?

You never been to a chat before?

t.b.

Nope.

Asaf Karagila

I remember chats back in 1997.

t.b.

00:13

I grew up without the internet, you know...

Asaf Karagila

And I was BBS-free as a child, I skipped that and got straight on the internet.

To your question, @Matt, no idea.

I am mostly here and on non-mathy chats on some other IRC network.

@tb Did you at least grow up with whiskey?

t.b.

woow that was quick, Zev!

@AsafKaragila Oh, yes... but mostly wine, actually

Asaf Karagila

I am not a big fan of wine. I only started drinking a bit of wine when I started dating my current girlfriend (you can't have romantic dinners with arak... :-))

I find most of it distasteful, although I am certain that with time this will change. I can't stand much other than Cabernet Sauvignon so far.

t.b.

I'm open to pretty much any wine. Stronger stuff, less so.

noooooooo!!!!!!!

Asaf Karagila

@tb Haha.

It's funny, and a bit sad.

The semester starts on Sunday, so we had a meeting of all the staff in the course I'm TA'ing this semester. Somehow I feel that exactly all the things we said about students not really trying to push through the course is embodied in today's happenings on math.SE

Srivatsan Narayanan

00:32

Please do elaborate, Asaf.

Asaf Karagila

We spoke about how somehow students don't really try to sit through their homework, they don't come to office hours, they do very little to follow the material in class and they expect to pass the exam by memorizing some theorems. This is an introductory course in logic and set theory, and I think that while it is possible to pass it without too much effort it is a lot easier to try and understand the material during the semester.

Srivatsan Narayanan

I was more interested in the "embodied in today's happenings on math.SE" bit. :)

Asaf Karagila

It became customary that there are marathons being given before the exams in which all the material is covered. It's often futile, a waste of money, and last year they were taught a completely wrong proof that was spread like wildfire in the exam. I think about 30% of the students gave it and lost good points on an easy proof otherwise.

Oh, that :-)

There are just a few questions by impatient folks that want their homework to be solved already. I do not like that one bit.

Srivatsan Narayanan

Specifically, today?

Asaf Karagila

I notice that specifically today, perhaps I'm just not paying enough attention during other days :-)

Srivatsan Narayanan

00:36

(reading through the chat log)

Asaf Karagila

Probably the upcoming weekend that sends pressure to finish the homework assignments fast.

t.b.

@Srivatsan: this for example

Srivatsan Narayanan

I was actually clicking through the links you mentioned

Was looking at the "Hurry guys" question ;)

Asaf Karagila

At least he didn't write "Hairy gays" instead... :-P

Srivatsan Narayanan

That didn't quite make sense.

Asaf Karagila

00:39

Hurry -> Hairy; Guys -> Gays.

Srivatsan Narayanan

And to quote joriki: Impatience seems to be in the air today.

Asaf Karagila

If you have a Mediterranean accent these words sound similar.

t.b.

Well, this norm question comes up since almost a year in various guises. Always the same style, and I can't imagine why anybody would want to know, and if you really want to know, why it takes you a year to figure it out.

Srivatsan Narayanan

Is it the same person asking this question?

t.b.

Well, I'm pretty sure it is. I couldn't imagine several people ask the same thing over and over and over again and always in the same manner of presenting the problem.

Srivatsan Narayanan

00:48

Who knows? Perhaps the question is that popular that tons of people are always looking for the answer. And always failing, it seems. (Not that I am surprised by the failing part: I can barely motivate myself to read the 3-line question completely.)

Asaf Karagila

Srivatsan, if you have any remarks about the linear subspaces conversation me and tb had, feel free to add them :-)

Srivatsan Narayanan

Er, I hope I am not distracting you guys from the topic. I am not really sure I follow the conversation.

The closest I usually get to infinity is to imagine n and let n go to infinity.

Asaf Karagila

No, it's fine.

I'm just gonna assume I'm correct for the time being.

Worst case scenario, later on Jack will come back and tell me I am wrong again.

It's not that I have other ideas at the moment :-)

t.b.

oh boy

Asaf Karagila

?

t.b.

00:55

see here and here

Srivatsan Narayanan

Another of the expectation questions? How come? The coincidence seems uncanny.

t.b.

@Srivatsan: this time it was the same person for sure.

Asaf Karagila

What the...

t.b.

And hilarity continues...

Asaf Karagila

Awww.. I didn't get to vote closure :(

Let's reopen it so I can vote to close!

:-)

Srivatsan Narayanan

01:01

@tb But why? Surely we have nothing against any of the posters? We closed the first expectation question as a duplicate. Why creating another account to ask another question?

t.b.

Austin has one of his witty days today (and why was I so sure that someone would react to your comment, exactly that way?

Asaf Karagila

See my reply to joriki :-)

t.b.

@Srivatsan: I was talking about this user

Srivatsan Narayanan

Er, sorry, I am a little confused with all the links and tabs.

t.b.

Concerning that love question: what does
(Take, for example, 72.)

mean?

Srivatsan Narayanan

01:10

S/He says that "x < 3" implies "x < 3333", but not the other way round. For e.g., 72 >= 3, but still 72 < 3333.

Although 42 would've been a more satisfying counterexample.

t.b.

Ah, I was trying to interpret 72 as a kind of would-be-heart that didn't quite manage to become one...

Srivatsan Narayanan

01:23

Do you follow this question: math.stackexchange.com/questions/76526/… ?

t.b.

I stared hard at the second paragraph, but I couldn't make head or tails of it.

Asaf Karagila

Okay, that's it. I'm going to sleep.

Tomorrow I'll have better idea on how to solve this. I can't make up my mind if I want big support/small spaces or small support/small spaces.

Srivatsan Narayanan

I don't get it. Is the time really 3.30 there? Do you sleep so late?

Asaf Karagila

I sleep very little in general, and I prefer to divide my sleep between night and afternoon.

Ideally I would sleep four hours at each part.

Srivatsan Narayanan

Interesting.

Would like to know more details, but I don't want to detain you here.

Asaf Karagila

01:33

Oh it's fine.

As long as I am not gonna do any math, I can stay awake for a bit longer.

t.b.

Haha, I'm not the only one!

Srivatsan Narayanan

For how long have you been following this 4+4 thing?

Asaf Karagila

I don't really follow that. It's just the ideal. Most of my freshman year was 5+3, though, and it was great.

The thing is that I hardly ever sleep well.

So if I sleep a lot it's usually a waste of time. I prefer to sleep a bit twice instead.

Srivatsan Narayanan

Couldn't resist posting this.

KRAMER: No, no, no, no. (comes in) This is evolutionary. I been reading this
book, on Leonardo da Vinci. See, that means 'from Vinci', d'you know that?

JERRY: (deadpan) That must be some book.

KRAMER: Yeah, well, turns out that the master slept only twenty minutes every
three hours. Now, that works out to two and a half extra days, that I'm awake
per week, every week. Which means, if I live to be eighty, I will have lived
the equivalent of a hundred and five years.

Asaf Karagila

Haha :-)

Srivatsan Narayanan

01:38

The thing I am interested in is, does it work? :)

I mean, do you feel fresh the remaining parts of the day?

Asaf Karagila

No, it's the other way around.

I hardly ever feel "fresh".

I have a constant headache for about 12.5 years now, my sleep is a mess, etc etc.

It's sometimes makes me wonder why I even do relatively okay in mathematics, but I guess it's just one of those things.

Srivatsan Narayanan

(Oh, of course, that excerpt is from Seinfeld, episode: The Friars Club.)

I have my concerns about my sleep pattern.

Asaf Karagila

What do you mean similar concerns?

What is it at the moment?

Srivatsan Narayanan

Sorry, edited that one.

Irregular, and I feel, not that efficient. I don't feel like fresh most hours of the day.

Asaf Karagila

Well. I can't really offer much there. I do think that some people are just not meant to sleep long periods. I know I work better around 1am in general.

If I have serious work I would usually run it through the nights rather than days.

t.b.

01:44

Have the two of you ever considered consulting an insomnia clinic/specialist? They can work wonders.

Srivatsan Narayanan

That's why I was interested when you mentioned 4+4. Wasn't really looking for help with my situation. More like, curious; that's all.

Asaf Karagila

I have gone through a nihilistic stage in life after which I hardly care about these things anymore.

t.b.

I know that from my own experience. It's not that the amount of sleep increased a lot, but the quality of sleep changed drastically.

Asaf Karagila

At some stage the headache was too much to deal with and nothing the doctor gave me helped. I went through this sort of nihilistic catharsis and eventually I rose from the flames of pain, still burning but flying instead of hurdled on the ground.

Srivatsan Narayanan

@tb Ah, good to hear that.

tb: Isn't it kinda late for you too?

t.b.

01:47

Yes, it is.

Asaf Karagila

Anyway, time to doze off for a while. Let's see what sort of madness my dreams are preparing for me this time! :-)

Goodnight @tb, @Srivatsan.

t.b.

Good night, Asaf!

@Srivatsan: I'm currently a bit out of my rhythm. Has to do with the winter beginning, not exactly my favorite time of year.

Srivatsan Narayanan

Good night, Asaf.

I kind of enjoy the winter here actually. At least more than summer.

t.b.

The problem of winter is that days are just too short for my taste. If you work you leave your house when it's dark and you leave the office when its dark again and you're lucky if you catch half an hour or an hour of sunlight each day.

Srivatsan Narayanan

Um, I almost always leave home after it's dark, so that makes little difference to me. :)

I like the winter perhaps for the snowfall.

t.b.

01:56

And I don't really like the cold. When I lived in the mountains it was different, there was snow, I could go to the slopes, etc. But now, winter has become kind of pointless.

Srivatsan Narayanan

(envious =)) Which mountains?

t.b.

Yes, the snowfall is nice, and it is beautiful to walk through a snowy forest when the sun shines. Everything seems so calm, the air is fresh, and you look forward to a hot chocolate.

Well I'm Swiss, so I lived in the Alps, in Davos, more precisely. South eastern Switzerland.

Srivatsan Narayanan

I guess the south Indian version of the hot chocolate would be masala tea with bajji (some snack). Nice experience, I agree.

t.b.

Yes, Masala Chai is quite popular around here, so it is comparable.

(at least the version we have here is comparable)

But I don't think I know bajji

So you grew up in south India?

Srivatsan Narayanan

Well, bajji is simply batter (with stuffings like potato, onion, or chilly) fried in oil.

Yes, this city. Heard of Madras before?

t.b.

02:03

Oh, I see, then I tasted a version of that, too, for sure.

Oh of course!

Srivatsan Narayanan

Goes well with the cold, and of course, the tea.

t.b.

But does it really get cold around there?

Srivatsan Narayanan

The same city, renamed to Chennai which is more Tamil.

No, it rarely does. It's extremely pleasant weather in the winters (compared to here or I guess, Zurich).

I was talking about the colder places, like say, hill stations.

t.b.

@SrivatsanNarayanan Well, I knew even that. I heard a lot about it when Viswanathan Anand was in the news around here.

Srivatsan Narayanan

Cool :).

Another claim to fame for our state (not the city) was S. Ramanujan.

t.b.

02:09

Oh, yes. And then there are some cricket players, I presume...

But for some reason, that sport isn't that popular here. Hardly ever in the news.

Srivatsan Narayanan

Well, most of them are from Bombay or north India.

t.b.

You still write Bombay?

Srivatsan Narayanan

There are franchises for cricket in India now. Modeled after football in Europe.

Oh well, I am in the process of switching.

t.b.

When I was in Cambridge, we went to Parker's Piece to watch the cricketers train there. Somebody tried to explain the rules to me but it was even further above my head than baseball. :)

Srivatsan Narayanan

At some stage I liked the Anglicised version better, but then I decided it was pretentious ;). I somehow find it hard to write Kolkata though.

Kolkata=Calcutta, Mumbai=Bombay.

t.b.

02:12

Got it!

So how did you end up at CMU?

Srivatsan Narayanan

In fact, they recently changed West Bengal to Paschimbanga (Bengali for West Bengal) ;). Probably doesn't sound that funny to you, but to me, it sounds a bit hilarious. Hence the smiley.

t.b.

Well, that I would never have guessed. It sounds hilarious to me, too! :)

Srivatsan Narayanan

Well, short story is that I went to IIT Madras, CS.

Like many people do over there, I applied in my final year, and took the best of the places that I got admitted in. :)

t.b.

I see. Sorry for being so curious.

But sounds like quite the change.

Srivatsan Narayanan

To explain the final sentence, it is somewhat common for IIT students to apply (but these numbers are fast decreasing; the "appers" are an endangered species now). But since the options in India aren't that great, we are forced to apply abroad.

Not at all, tb. Hopefully my previous comment clarifies a bit better.

Few people apply to Europe for some reason. (I feel proud for even considering applying to couple of Israeli universities ;). I never did though...)

t.b.

02:19

I understood. We had a few Indians in grad school, too.

I never really left Europe, so far. Hardly ever Switzerland. I worked in Germany for about a year, but that wasn't so great.

Srivatsan Narayanan

But I guess it's understandable. For instance, I have been meaning to ask this to someone across the Atlantic. How easy would it be for a vegetarian to live there?

t.b.

Here in Europe, you mean?

Srivatsan Narayanan

Yes. Or at least Switzerland specifically.

(You mentioned you were in Cambridge sometime. Were you just visiting?)

t.b.

I think it isn't that hard, especially in Switzerland. Vegetables are very good here and you get a choice of vegetarian food everywhere (and not just salads).

Srivatsan Narayanan

Hmmm, ok.

Because Europe is an option in my mind after grad school. Let's see.

t.b.

02:26

I really don't think there's any problem.

I was in Cambridge just three or for times, each time for one or two weeks. I had a good friend who studied over there.

Srivatsan Narayanan

And where did you do your Ph.D.?

t.b.

In Zurich.

At ETH. I studied there and did my Ph.D. there.

I lived in Zurich on and off almost half my life, now :)

Srivatsan Narayanan

Nice.

t.b.

I like it a lot and ETH is a great place to be, even if it pushes the elitism button a bit too much for my taste...

Srivatsan Narayanan

Oh.

Oh wait, you graduated in 2008? I imagined you to be much older :).

t.b.

02:32

Well, I am much older. It took me a long time to graduate...

You know, we go to high school until 20 then roughly 5 years to the diploma and again 5 years to the Ph.D.

Srivatsan Narayanan

Not that much older (you have no idea what I imagined ;)). You're like 10 years older. (The DoB is mentioned in the dissertation abstract.)

t.b.

(I figured that). In fact, on Sunday I'll be exactly 10 years older than you :)

Srivatsan Narayanan

Yes, I was going to surprise you with a birthday wish, you know.

t.b.

Oh, that's nice!

You can still surprise me!

But I'm curious: how old did you imagine I was?

And why?

Srivatsan Narayanan

Not really sure. What I imagined was a jolly old man, a Santa Claus. ;)

t.b.

02:38

Heh?

An old man! So childish?

Srivatsan Narayanan

Don't ask me why. No, of course, not.

I think it's because you're just friendly to me.

No, wait, you're saying I am childish?

t.b.

No, I meant to say: An old man who behaves as childishly as me?

Oh, I try to be friendly. Sometimes I lose my temper, but usually I manage to contain myself.

Srivatsan Narayanan

Well, actually, I have a similar image in my mind for Gerry as well.

I don't know why. (But Arturo looks very different to me.)

Now I am curious how old is each of these guys...

t.b.

maths.mq.edu.au/staff/gerry.html

louisiana.edu/Academic/Sciences/MATH/faculty/arturo.html

Srivatsan Narayanan

It seems I am wrong on each count. Very wrong.

t.b.

02:46

Well, Gerry has his outbursts as well...

:)

Srivatsan Narayanan

Well, for Gerry, it's just something about the name. I am reminded of Jerry Seinfeld.

t.b.

It is fun to try and find pictures of some of the contributors here. They rarely match what I expected...

Here's another example

Srivatsan Narayanan

Ah ah, now I see what you meant about the outburst. :)

Oh my god, I never could've guessed that.

t.b.

Not quite the Cheshire cat...

yayu

@Srivastan an IITian which batch?

Srivatsan Narayanan

02:51

Hi yayu

yayu

(Gu 2010)

t.b.

Hi yayu

yayu

*wahati

process91

@tb Hey t.b. - I found out that the problem you chimed in on earlier was an uncharacteristic lapse on the part of the author, I believe.

yayu

hi t.b.

Srivatsan Narayanan

02:52

That will still not be clear for poor tb. yayu meant IIT Guwahati, 2010 batch.

yayu

yeah... it took me quite some time to figure it out

batch and which campus?

Srivatsan Narayanan

IIT Madras. 2009, I think.

yayu

you think ;)

Srivatsan Narayanan

Yes, it's 2009. Hey, give me a break; my memory has rusted with the many months that have gone by ;)

I had a question, yayu. Are you the same as kuch nahi?

yayu

hmm. From your profile... I guess it must be CS

t.b.

02:54

@process91 I saw your edits. I looked at the spanish version of the book you linked to and it seems to me that he wouldn't have intended otherwise because he didn't consider any other situations. That's what I tried to tell you earlier.

Thus, I wouldn't go as far as to call that a lapse, but I agree, the terminology is a bit loose.

Srivatsan Narayanan

@yayu CS is right. But what about my profile suggests that?

yayu

number theory, combinatorics, discrete...

process91

@tb Yes, I've gotten used to his rigorous style. The fact that I've gotten this far into the book and this is the first instance which has caused this sort of confusion is, in a way, an accolade to his prose

yayu

etc. Plus, fact that pure math is rarity, the ones with msot exposure to it outside math departments are CS

*rare in India

process91

@tb thanks again for your input.

t.b.

02:57

@process91: I see, as long as you don't take that too negatively everything is fine with me.

Srivatsan Narayanan

@yayu Your deduction is correct ;). So which department were you in? And what are you doing currently?

t.b.

And you're welcome, of course.

process91

@tb :) I haven't seen J.M. on yet, but when I do I will thank him also.

yayu

chem. currently im wokring

about to leave though

Srivatsan Narayanan

@process91 If I may be so curious, which question are you and tb talking about?

@yayu leave? As in?

yayu

02:59

quit my job

process91

@SrivatsanNarayanan math.stackexchange.com/questions/76193/…

Srivatsan Narayanan

Thank you, process91.

yayu: What are your plans going forward?

yayu

To get into a department, physics preferrably.

what are you doing?

Srivatsan Narayanan

Oh, cool. I am currently studying. At Carnegie Mellon Univ, Pittsburgh. (Again CS ;))

yayu

Ill probably look into tifr..

Srivatsan Narayanan

03:04

Good, all the best for that.

yayu

thanks :)

Srivatsan Narayanan

By the way, are you the same as the user kuch nahi?

yayu

by any chance, does aryabhata come from iitm?

yes... username's dont update on chat apparently

Srivatsan Narayanan

No idea who the user Aryabhata is.

@tb You have any inside information? :)

yayu

i was looking at some of his answers.. i just thought maybe he had an inmo background

t.b.

03:07

@Srivatsan: No I don't, I'm just glad he changed his handle...

Srivatsan Narayanan

yayu: Apparently, you are chatting not as the user kuch nahi from MSE, but as yayu from Physics.SE. Perhaps that explains the name displayed here.

@tb Do you celebrate Halloween over there? Some friend suggested that it's primarily a US thing...

t.b.

No we don't. Maybe it was me you have in mind, robjohn asked me about it.

Well, to be honest, people start celebrating it now, but 20 years ago there was no such thing.

So children start knocking on the doors in the evening and bars are full of spiderwebs phantoms and the like.

Not to mention all those pumpkins.

Srivatsan Narayanan

Not you, just a friend living in Pittsburgh.

t.b.

Ah, I interpreted "here" as "here on SE", or this chat, more specifically

Srivatsan Narayanan

Wonder when it'll be imported by India...

t.b.

03:17

I don't know. They also started with Valentine's day around the same time

So maybe that can be an indicator.

Srivatsan Narayanan

Oh yes, Valentine's day has caught on in India as well. Let's see...

t.b.

Well, to be honest, in catholic regions there is all hallows and all souls (?) which are just the days after and celebrated.

Valentine's day makes a bit more sense to me :)

Srivatsan Narayanan

Does your region (whatever that is: Europe, Zurich, Switzerland) count as Catholic?

Sorry, I have a near-zero knowledge of Europe, other than through our textbooks.

t.b.

Switzerland is around 50/50 protestant and catholic, maybe a bit more protestant (I haven't checked). Zurich (Zwingli) and Geneva (Calvin) are centers of protestantism (next to Leipzig with Luther).

Srivatsan Narayanan

Ah, ok.

t.b.

03:23

Italy, Portugal and Spain are almost exclusively catholic, as is Austria. In Germany there are regions of both, arch-catholic with Bavaria and Cologne, for example, then there are large regions of protestantism. France is complicated, I couldn't tell numbers, and Scandinavia is mostly protestant.

I'm not entirely sure about the other countries.

Srivatsan Narayanan

Ok. Not that I can keep track of all countries anyway.

t.b.

In Eastern Europe you have other forms of Christianism (Greek and Russian orthodox), but also Muslim and Jewish regions.

yayu

france has 27% atheists according to en.wikipedia.org/wiki/Demographics_of_France#Religion

surprising

Jack Schmidt

is probably oversimplistic, but seems roughly ok

t.b.

@yayu: don't forget about communism/socialism!

Srivatsan Narayanan

03:28

That's a high number. I think many of them should be really non-practicing atheists. ;)

t.b.

I was pretty wrong about my numbers in Switzerland: 42% catholic, 36% protestant, 5% islam

yayu

@ t.b true didnt marx call religion "opiate of society" or some sort

but i think the number of non marxist/socialist atheists is high as well

surprising because i heard it had the highest density of churches

Srivatsan Narayanan

yayu: Actually, doesn't your first sentence explain the second?

t.b.

@yayu: yes. Religion ist Opium fürs Volk/religion is opiate for the people

Srivatsan Narayanan

Not that surprising if many of the churches were built before 1850s. Not to claim that this is the truth though.

yayu

03:33

kashmir is painted hindu on that map..

tibet is shown under chinese religions...

while mahayana buddhism is supposedly distinct from mainland chinese religions..

t.b.

Oh, I forgot: There was de-christianization during the french revolution, of course!

yayu

and what god did they then turn to?

Srivatsan Narayanan

I guess I will keep away from the sensitive questions yayu is pointing to. :)

t.b.

@yayu: Wikipedists can explain better than me

Srivatsan Narayanan

@robjohn, How was Nightfall?

robjohn

03:37

Hey guys!

t.b.

Hi robjohn!

robjohn

I am out on the telescope field using my iphone

Srivatsan Narayanan

@robjohn You are currently chatting from there? This deserves a special badge.

2

t.b.

*hands over the astrophotographer badge*

3

yayu

have to leave. see you all.

t.b.

03:52

See you, yayu!

Srivatsan Narayanan

So, tb, what's a diploma?

Is it the equivalent of a Bachelors or is it something to do after that?

t.b.

@Srivatsan: It's more like a Master

They introduced the Bachelor/Master system in Europe a few years ago, and the diploma is treated as equivalent to a master.

Srivatsan Narayanan

A five-year Masters? :) Sounds rigorous...

t.b.

Yes. You went to the university directly from high school and the diploma was the first and only thing that counted something.

Now they have 3 years of bachelor and about 2 years of master studies.

Srivatsan Narayanan

Ah, that's not so bad then, I suppose.

t.b.

04:01

I preferred the old system, actually. The first two years were quite stressful but after that you could take your time and actually think :)

Srivatsan Narayanan

Perhaps. Did you have to do non-math courses as well?

One of those questions: math.stackexchange.com/questions/76562/… .

"Why do mathematicians absolutely hate ravioli?"

t.b.

Well, ETH has a strong tradition of physics, so we had good foundations in classical physics during roughly the first three years which were mandatory. Then, in addition we had to visit a course per semester in so-called Geistes- und Sozialwissenschaften

Srivatsan Narayanan

Social sciences?

t.b.

(you just had me laugh out loud!)

Yes, social sciences and humanities

Srivatsan Narayanan

Oh, yes, my friend taught me those words. He took German elective in undergrad.

t.b.

04:08

Those were extremely interesting, however when I was in my fourth year, they started to control that more rigorously than they did before, which resulted in hundreds of non-motivated people sitting in those lectures, so it wasn't profitable anymore.

And you weren't allowed to elect language courses!

Srivatsan Narayanan

1

Q: How do I be like Arturo Magidin?

For Halloween I want to dress up as Arturo Magidin. I don't know much group theory. Any good group theory texts that are advanced. I want to act like a group theorist also.

soft-question

That one's made my day.

t.b.

The Chaz's reaction is great!

yunone

Heh, I wonder if Arturo is flattered, or just annoyed.

t.b.

A little bit of both, I presume.

yunone

I just saw that in Terry Jones' other question that he (Arturo) finds it perjorative.

Shoot, Terry James* (Monty Python was apparently on my mind)

Srivatsan Narayanan

04:13

The OP removed both the questions. :-/

t.b.

Zev did.

Correctly so.

Srivatsan Narayanan

Oh. Yes, indeed.

At least we seem to have a screenshot of the second question right before us ;).

Should I remove it as well?

t.b.

I don't think you can.

Srivatsan Narayanan

You're right, I can't. I can flag the mods, but I don't think that's necessary.

t.b.

I would just leave it.

(you have a 2 minutes grace period for editing and deleting here)

Srivatsan Narayanan

04:18

I know about the editing part. I thought I can always delete comments and I was wrong.

t.b.

Well, anyway, loads of good questions here today. How do I prove that without using a rectangle?

Srivatsan Narayanan

Rectangle?

Oh, tb, by the way, what about the English language? I suppose you did not use it as a medium of instruction in high school; is that right? How about diploma?

t.b.

I meant this, but Austin edited already

Srivatsan Narayanan

I loled on the rectangle question.

t.b.

Another guy in a hurry

yunone

04:26

Hey Theo, from which book(s) did you first learn measure theory/functional analysis?

t.b.

@yunone: measure theory: Royden (third edition) and functional analysis from a German book that isn't translated: Werner. Highly recommended if you read German.

(I'll expand in a second)

yunone

Thanks, I've skimmed parts of Royden's Real Analysis, but I've never heard of Werner. I've wanted to learn German for years, guess this is the time now...

t.b.

In order to really profit from Royden, I suppose you need the equivalent of "baby Rudin" as a prerequisite. I find Rudin's real and complex analysis a bit steep, but it is good as well. Another great book is Wheeden-Zygmund.

yunone

I have a copy of baby Rudin that I've wanted to go through, and Momma Rudin too eventually. Thanks for the roadmap!

t.b.

As for functional analysis, I think it is necessary to have at least the basics of Lebesgue theory handy before delving into it (otherwise it probably remains a bit shallow). The principal examples of spaces all stem from real analysis/measure theory and if you don't have the prerequisites for understanding these... In Momma Rudin you get the basics already, and much preparation is also done in the second part of Royden. I don't know what to recommend to you at the moment.

yunone

04:36

Oh that's fine. I probably won't get to that point any time soon. I would probably spend quite a while just trying to get comfortable with measure theory before even attempting to understand functional analysis.

t.b.

Maybe you can skim through Zimmer's excellent Essential Results of Functional Analysis to get an impression what it's all about.

It's a small little book, but the important stuff is there.

and it shouldn't be too expensive

yunone

That might be good. I just feel awfully lopsided when it comes to algebra vs. analysis. The answers you and others post concerning different analysis branches all seem very cool, I just wish I understood them better. All in all this should keep me occupied.

t.b.

Oh, thanks, nice to hear that! I guess the problem with analysis is that you need to put much more work into it in order to get to the interesting stuff (at least what I consider interesting), while group theory and algebra in general needs little prerequisites beyond a little bit of maturity. That's not to say that this makes it easier!

By the way, do you know a little bit of complex analysis? That's something I imagine you should like and you don't need much preparation for that. It's certainly less demanding in the basics than measure theory.

yunone

I don't really have any familiarity with complex analysis, but I would like to soon. Is real analysis usually a prerequisite? I thought of looking through Ahlfors at some point, but I hear some really dislike that book.

t.b.

Oh, Ahlfors is wonderful! But it is pretty demanding and not for the faint-hearted. Concise and to-the-point, but leaves most of the details to you. I wouldn't go for it right away. Some acquaintance with real analysis certainly helps, but if you know what a continuous function is and know how to differentiate and feel comfortable with the Riemann integral, you're well set. No need for anything fancy. Maybe Needham's book visual complex analysis might be a good start.

And my own personal favorite is Remmert, this book is pretty self-contained

yunone

04:52

Oh yes, people seem to really praise Needham's book, and I'll take a look at Remmert. I've been looking for a change of pace, since Lang's Algebra has gotten a little discouraging. I'll probably drop it for now and come back later.

t.b.

Well, Lang, there are more pleasant reads than that, I suppose :)

yunone

Definitely. The completionist in me really want to finish that book by at least 2025, but I think I may just be torturing myself now.

Anyway, I have to head out. But thanks for your suggestions. See you around.

Srivatsan Narayanan

I like this question: math.stackexchange.com/questions/76575/experiences-with-kumon.

Refreshing to see such a well-phrased question from a brand new user.

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$Mathematics$ Mathematics