Mathematics - 2022-01-14 (page 2 of 2)

Odestheory12

19:05

Uhm @TedShifrin the last result we used about sequences isn't true if we only have $\lim(a_n+b_n) = m$ right?

I mean without knowing any info of $a_n$ and $b_n$

Ted Shifrin

Of course. You can add two divergent sequences and get a convergent one.

Odestheory12

Yeah, if $a_n = n+m$ for fixed $m$ and $b_n = -n$ then both $a_n$ and $b_n$ aren't convergent but the sum is.

Ted Shifrin

Right.

Odestheory12

And if we know $a_n\to L$ the only way is that $b_n$ goes to $m-L$ or we get a contradiction.

Interesting, didn't notice that. Is a strong result.

Ted Shifrin

That's what you figured out a while ago, yes :)

Odestheory12

19:09

Yeah but I am trying to digest it :P

Ted Shifrin

Don't get indigestion.

leslie townes

ted you seem good at this, have you considered a career in mathematics instruction

Odestheory12

Kekw

Guys do you know the book "Calculus" of Robert Adams?

leslie townes

i don't

Odestheory12

It looks like Apostol's one but more applied.

(Calculus, not mathematical analysis)

Ted Shifrin

19:14

I taught out of his multivariable calculus once. It had some interesting mistakes.

Odestheory12

Oh I learnt multivariable from there, I liked the vector field calculus section.

Ted Shifrin

He had a false proof of the max/min test in several variables with even a counterexample as an exercise. (Some authors do such things on purpose and make a remark ... I think his was inadvertent.)

It was an ok book, but obviously I wrote my own :P

Odestheory12

I remember having problems at that proof in particular.

And I remember blaming it to my poor algebra formation at that time (zero knowledge of quadratic forms)

Ted Shifrin

Well, I don't know if he fixed the proof. I taught out of that book back in the 1990s. As I recall, he basically argued that if a function has a local max at the origin when restricted to each line through the origin, then it has a local max at the origin. This is very false.

Funny the things I remember ...

Now where did I leave my car keys? ....

leslie townes

one time i lost my keys and it turned out that i had put them in the freezer.

Ted Shifrin

19:19

That's the typical Alzheimers move.

leslie townes

i guess i'd dropped them while adjusting something else in the freezer. i don't know. this was about 15 years ago, so i've been operating in the world for a while after that.

Ted Shifrin

Not worth panicking just yet.

leslie townes

in my family dementia tends not to hit until the 70s at a minimum, and sometimes 80s.

so i have 50 more years.

Ted Shifrin

I'm not sure how many I have. 70 is around the corner.

leslie townes

one of my grandparents did die at 49, which is alarming, because i am at least 20 years away from that age.

Ted Shifrin

19:23

Uh huh. Sure.

leslie townes

for those just joining us, i am 41 and spend an unusual amount of time trying to sound younger than that.

Semiclassical

last time i saw my maternal grandmother you could see the onset of dementia

Odestheory12

This looks like a cool project: math.libretexts.org/Bookshelves/Calculus/…

Semiclassical

which was...oof

Ted Shifrin

Why, Odes?

leslie townes

19:26

semi: my grandmother's dementia was a tiny bit funny. she'd see cars on TV and think that the people driving them had stolen her car.

and we laughed about it even when she was alive.

Odestheory12

@TedShifrin It has pretty good pics

Ted Shifrin

I have lots of good multivariable integral problems in my book :)

Odestheory12

(keep in mind i am used to robert adams pics :P)

@TedShifrin What's your book name?

Semiclassical

the main thing i remember is her not being aware that i'd graduated college

Ted Shifrin

Don't say that, @leslie. I suffered almost 20 years with my mom's.

Odestheory12

19:27

Ah, found it :P

leslie townes

ted: i am sorry, i wouldn't want it to last that long.

Ted Shifrin

See my profile, @Odes. Also the 112 YouTube lectures.

Odestheory12

Wow that's really huge.

Semiclassical

the betty white exit is about as good as one can hope for: dying in your sleep, just in time to screw up a major publication's plans

Ted Shifrin

Yes, Betty did it just right. So did the mother of one of my good friends here; she just fell asleep with her tablet on her lap and never woke up.

Semiclassical

19:31

on one hand it is sad she didn't make it to 100, but the fact that she died just in time to make the People magazine cover incorrect is just funny

Ted Shifrin

I'm sure she planned it that way.

Odestheory12

@TedShifrin how much time does it take to teach all the contents of that book/videos?

1 year?

There is a lot of content. Here, in spain, that content usually takes 18 ects (idk the equivalence in the US)

Ted Shifrin

Yes, I covered pretty much the whole book in one year (4 lectures a week).

Odestheory12

Ah it seems its 2 ects : 1 american credit, so 9 american credits

Ted Shifrin

Credits depend on the university. But usually numbers of almost-hours of class per week.

Odestheory12

19:38

Uhm interesting. I've never seen the concept of differential forms in the uni. Only when I studied diff geo by my own.

Ted Shifrin

I'm a huge fan of differential forms. Most of my research used them to a great extent.

Koro

19:55

Odestheory12: Alternatively, take ordered sets $A=\{k\in \mathbb N: k\ne 3n \text{ for any } n\in \mathbb N\}$ and $B=\{3n: n\in \mathbb N\}$. Assuming the result that I wrote [earlier](https://chat.stackexchange.com/transcript/message/60153064#60153064) to be true, consider the sequences $(x_a), a\in \mathbb A$ and note that it converges to some L by the use of the linked result and the given condition. $(x_b)$ converges to L, is given.
So by the linked result, since $A\cup B=\mathbb N$ and that $A\cap B=\emptyset$, the sequence $(x_n)$ also converges.

Odestheory12

Yeah, when I said that $\{S_{3n}\}, \{S_{3n-1}\} ,\{S_{3n-2}\}$ describe the whole sequence $\{S_n\}$, i meant $A\cap B \cap C =\emptyset$

It looks cool described like that

Wait can you use induction to prove that statement @Koro

Ah nah, $A$ and $B$ aren't finite sets

is not inductive either

Cauchy sequences are a pretty good tool for this kind of proofs.

Koro

20:11

Or using contradiction.

Odestheory12

I need to practice a bit more proofs using the negation of limit definition

copper.hat

21:24

i use contranegative myself.

curious why the mad rush to close seems to hit a hiatus. not complaining.

364539917

madness comes in waves?

copper.hat

some strange second order human group dynamic

always found it strange that waves should be dampened

364539917

21:42

hmmm...most herd mentality involves the boom, bust, and echo sequence. sorta like the business cycle

copper.hat

yeah, but how does the '2nd order' effect come about?

364539917

21:57

don't know; but, group dynamics may turn into gang mentality very quickly

PM 2Ring

Here's a traditional song you may enjoy, @copper.hat. Aoife O'Donovan and Sarah Jarosz do some beautiful harmonies on Some Tyrant. Sarah's playing an octave mandolin.

Some delta blues. Robert Johnson's Crossroads, by one of my favourite young performers, Chiara Kilchling & her friend Diletta. Chiara is a multi-instrumentalist and a painter. She lives in Germany, but mostly sings in English, although she has recorded a couple of songs in Hungarian.

copper.hat

22:17

nice!

am i being rude? math.stackexchange.com/questions/4357091/given-the-subspace-x-0-x-1-x-n-c-and-a-vector-v-in-mathbbrn?noredirect=1#comment9096948_4357091

PM 2Ring

They all play & sing a diverse range of styles. Here's Aiofe doing Joni Mitchell's Coyote, in celebration of Joni's birthday, on Live From Here (the show formerly known as Prarie Home Companion).

copper.hat

oh wow, i thought from the first that Sarah Jarosz was Aoife O'Donovan based on the way she sang.

Ted Shifrin

Slightly brusque, yes. But presumably this was assigned as homework after projection was defined and discussed. In my classes I used to make people to projection onto hyperplanes two ways (one, projecting onto the normal; the other, using the projection formula for projecting on a subspace).

PM 2Ring

Sarah's of Polish extraction, but grew up in Texas.

Ted Shifrin

Are Poles allowed in Texas?

(no math humo(u)r to follow)

copper.hat

22:25

only on the right half plane

Ted Shifrin

I'm of Polish and Russian extraction, but I had the decency to grow up in CA and MA.

PM 2Ring

@copper.hat The OP doesn't seem to mind. That question's likely to get closed if the OP doesn't show some attempt & explain where they're stuck.

UnderMathUate

I just ran into my computer science professor from last semester. He said he was shocked I did well on the final since I'm a math major. I'm going to take it as a compliment.

PM 2Ring

:)

UnderMathUate

:D

For real though, that class was probably the hardest I've taken in my academic career. I was dreaming about binary search trees in the days leading up to the exam.

PM 2Ring

22:31

Some playful young Russian ladies, Beloe Zlato, who usually sing in Russian, doing California Dreaming

364539917

coolio

PM 2Ring

I've sometimes dreamed I'm coding, but it's really hard to read in dreams, and computers don't work very well.

UnderMathUate

I know what you mean. I get the feeling that what I'm seeing is almost correct, but then when I wake up, it seems like nonsense.

Except one time I actually did dream the solution to a proof.

It was a really simple one, though.

364539917

proof by nightmare

UnderMathUate

Lol

PM 2Ring

22:40

I think your subconscious can come up with good precursor material while your dreaming, but you need to actually be conscious to make the final synthesis. I've often fallen asleep after working on a mathematical proof or coding problem, and then 5 minutes after I wake up I know exactly what to do.

364539917

they should allow 5 minute naps during the putnam

UnderMathUate

@364539917 I second this.

PM 2Ring

Chiara's also done a nice version of California Dreaming, but here she is with her friend Jesse doing Going To California by Led Zeppelin. I almost like her version better than the original. :)

copper.hat

22:56

@TedShifrin my advisor was Polish

@PM2Ring my few good ideas all came after some meditation (longer story there)

oh my, the answer is sooo sledgehammer than i may need to answer

PM 2Ring

Polish mathematicians cracked the original version of the Enigma code. The work at Bletchley Park by Turing et al was a direct development of the Polish technique. Without that original Polish work, it would've taken a lot more time to crack the more advanced versions of Enigma, and England would probably have fallen at the end of 1942 or early 43.

copper.hat

i suspect my advisor's time in Poland was not the stuff of great memories.

Turing got his posthumous apology for his abominable treatment. not that it did him any good.

i had my daughter read Singh's The Code, she says it was what make CS interesting to her

This reminds me of one of Ted's starred comments about reducing a problem to something you know www.funnyjunksite.com/clean-jokes/mathematician-fireman/

PM 2Ring

23:30

Andrew Hodges wrote a good biography: Alan Turing: The Enigma, which is well worth reading, and a section of his website contains a lot of info about Turing. turing.org.uk/index.html The book has a lot of info about the Enigma machine and how it was cracked. Hodges is a mathematical physicist. His PhD advisor was Roger Penrose.

Ted Shifrin

Excellent book!

copper.hat

yeah, i read the enigma

leslie townes

i haven't read that. korner's pleasures of counting contains quite a bit about the enigma that is not in the code book (although i do like the code book)

copper.hat

23:52

im stuck at Korners discussion of internecine squabbles

leslie townes

i've never directly come up with anything in my sleep, but i did come up with a simplification of something that had already been written but not submitted yet. woke up and it was all there.

my coauthor asked where it came from and i had to tell him, a dream.

reminds me of the simpsons episode where one cop tells another, i think we should go investigate X. chief wiggum, who has just had a dream mimicking a scene from twin peaks that led him to the same conclusion, says "did you have the same backwards-talking dream with the flaming cards?" and after a pause the other cop says "... i'll drive."

copper.hat

:-)

i'm really running the psq gauntlet today

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$Mathematics$ Mathematics