Mathematics - 2015-03-04 (page 2 of 5)

6:00 AM

And you do so by studying the space of solutions to a certain PDE on your manifold.

Ah, excellent. I'd heard before that PDEs have a deep connection to the study of manifolds in differential geometry, but I didn't know why. This seems like a good place to start.

Mike Miller

This is distinctly different from their place in differential geometry (and in particular Riemannian geometry). I know zip about that.

Like, studying the spectrum of the Laplacian and stuff.

Alex Wertheim

Oh? I must have misunderstood, I'm sorry. What did you mean by studying 4-manifolds up to diffeomorphism?

Mike Miller

I mean to say that I think when people say that PDE has a deep connection to the study of manifolds in differential geometry they aren't referring to gauge theory. I think it's two different stories, both of which involve PDE.

Alex Wertheim

Ah, I see. Gotcha.

Mike Miller

6:06 AM

(When I said that I meant that this provides a tool via which you can define an invariant of smooth 4-manifolds that's not invariant under homeomorphism. i.e., you can distinguish smooth structures with it)

(also if you want to know about what this does for us in the theory of 4-manifolds the wikipedia page on gauge theory is not the place to go)

Alex Wertheim

Neat. Am I making misguided analogies, or is this a kind of "inverse" problem to Milnor's work exhibiting different differential structures on the 7-sphere (i.e. structure which is variant under diffeomorphism but invariant under homeomorphism?) I'm probably way off base here.

David Wheeler

I have what might seem a silly question: why do groups have kernels?

Alex Wertheim

Lol. I did have a look at the "gauge theory" Wikipedia page. It was indeed unhelpful (to me, anyway).

Mike Miller

@AlexWertheim I don't quite grasp your (i.e.) but there; I guess you're just saying that he showed that there are exotic smooth structures on $S^7$. The point of gauge theory is certainly not to show that there are not exotic smooth structures on 4-manifolds; indeed there are usually lots.

The point is that you want to be able to actually distinguish them.

For $n>4$ you can use what's called surgery theory to study this sort of thing algebraically; but that doesn't work so well here, for reasons of four is not bigger than four.

Kaj Hansen

@MikeMiller, Pete uses the term "isometric embedding" $i:X \rightarrow Y$. I cannot remember the precise definition he used in class. Is such an embedding one where $d_X(x, y) = d_Y(i(x), i(y))$.

Mike Miller

6:17 AM

Aye

Kaj Hansen

Thanks :)

Alex Wertheim

Hrm. My parenthetical remark was almost certainly gibberish, unfortunately. I'll have to read a bit more before I have anything meaningful to say.

LOL. Best reason ever.

Alex Wertheim

6:29 AM

Well, anyway. Thanks for indulging me Mike. Off to bed.

Mike Miller

Glad to. Night!

deostroll

6:56 AM

Can we draw "trees" in this site?

Balarka Sen

7:10 AM

@Kaj!

Kaj Hansen

Hey there @BalarkaSen

Trying to get homework done for tomorrow :/

Balarka Sen

[Your definition of isometric embedding is correct]

Thanks!

Hey @Kaj

Hey @JulianRachman

7:13 AM

@BalarkaSen You!

Julian Rachman

I got 100% on my linear algebra exam!

@Kaj how's top?

Kaj Hansen

That's great @JulianRachman :D

David Wheeler

Ok, but what was your score? :P

Kaj Hansen

I'm trying to get my problems done for tomorrow

Balarka Sen

To slip in geometric group theory, again, there is something called quasi-isometric embedding, $i : X \to Y$ such that $1/A d_X(x, y) - B \leq d_Y(i(x), i(y)) \leq A d_X(x, y) + B$ for some fixed $A \geq 1, B > 0$.

Julian Rachman

7:15 AM

@David talking to me?

@Kaj Oh. what problem set?

Balarka Sen

You can imagine that as equivalence of $X$ and $Y$ obtained from "stretching" and "enlarging"

Kaj Hansen

That "no more lulz" set I linked before.

What is "Ad" @BalarkaSen ?

Balarka Sen

What's particularly interesting is classification of groups upto quasi-isometries of the Cayley graphs (with usual metric).

Kaj Hansen

Oh never mind!

Julian Rachman

oh ok

@Kaj do you have to do all of them?

David Wheeler

7:17 AM

@JulianRachman yes, you

Balarka Sen

@KajHansen A \cdot d.

Kaj Hansen

Not all @JulianRachman. 14 of them

Balarka Sen

@DavidWheeler Hullo!

David Wheeler

Your friend Sayjay, or whatever, was still working on that fixed-point theorem, and I had to deal with it.

Balarka Sen

Sayan?

Did he solve it then?

Julian Rachman

7:18 AM

@David Oh. The test had 25 questions with each bullet within the questions be 4 points so I guess 100

David Wheeler

After some wrong turns. He's not good with explaining his thoughts.

@JulianRachman My humor fails. Again.

Julian Rachman

@Kaj oh. DO you get to pick?

Kaj Hansen

Indeed @JulianRachman. Our problem sets are all about self-discovery, and we can choose whatever problems interest us.

Julian Rachman

@David haha. lol. Please explain.

It's not you, it's me... :/

@Kaj nice.

due tomorrow?

Kaj Hansen

Indeed

Julian Rachman

7:20 AM

and how many more do you need?

I need 3 more.

Oh. gg

Do the Banach one.

You said "I got 100%" which I deliberately mis-interpreted to mean : "I understood 100%".

Balarka Sen

Function spaces are some good example of topological vector spaces.

Kaj Hansen

7:21 AM

We can do challenge problems whenever, so I'll save them for Spring break.

@BalarkaSen, I've written up some of that one already. I'm planning on it.

Julian Rachman

@David oh!

lol

now laughing

Kaj Hansen

@BalarkaSen, is Ted's starred comment true? :)

Balarka Sen

Not particularly.

Kaj Hansen

:P

Your schoolteachers, on the other hand,..... ;)

David Wheeler

Balarka has no parents. He was created by mitosis. He killed his twin.

Kaj Hansen

7:23 AM

What are you covering in your actual high school (middle school?) math course @BalarkaSen ?

Balarka Sen

Close guess : I am a computer-generated program

David Wheeler

Gah! I really shouldn't be so mean to people. I might need charity one day.

Balarka Sen

@KajHansen Bunch of rubbish. Some funny word problems (banking, stupid), a bit of algebra (quadratic equations) and coordinate geometry.

Oh and we got some trig this time.

Kaj Hansen

LOL

"Find the zeros of x^2 + 4x + 4 by factoring"

Radicals in your denominator?! Tsk, tsk. Points off.

David Wheeler

I don't see any 0's in it-oh wait-it's a trick question: the coefficient of $x^3$ is 0.

Balarka Sen

7:26 AM

I've started encouraging my classmates to do minimizing quadratic expression by differentiating, or at least verifying by doing so.

@KajHansen lol

that happens so often

Kaj Hansen

Oh god, I'm laughing so hard right now. I can just imagine how rebellious you are.

Julian Rachman

lol im in Alg 2 and i have to fight with the dean to do calc AP next year

David Wheeler

Just shift the vertical coordinate axis to the vertex. Voila! EZ factoring!

Balarka Sen

@KajHansen pulls out the usual innocent face We got calculus in 11th grade, and we are in 10th right now, so it doesn't hurt to study a bit of calculus already evilgrin

Julian Rachman

today we learned the rational function f(x) 1/x

David Wheeler

7:28 AM

It's an isometry, so the number of roots is preserved-that's the main thing. Who cares what they are, really?

Kaj Hansen

2 EZ 4 me

Julian Rachman

and I got to teach the class what a limit is and how it is motivated by asymptotes

David Wheeler

What's a limit?

Balarka Sen

Direct or inverse?

David Wheeler

No seriously, I want to hear Julian's explanation.

I'm 15, never heard of it, and I wanna know.

Julian Rachman

7:31 AM

it is what a graph approaches to as x gets infinitely big

that was as simple as I went

Balarka Sen

you're thinking of $\lim_{x \to \infty}$

Julian Rachman

yes

that is what my teacher wanted to emphasis

Balarka Sen

what about $\lim_{x \to a}$ for finite $a$?

David Wheeler

are all limits "big"?

Kaj Hansen

@DavidWheeler, you're asking questions about Galois extensions without hearing of limits? ;)

I kid, I kid

Julian Rachman

7:33 AM

it was only specific to f(x)=1/x that is all I taught

Balarka Sen

@KajHansen there's no apparent connection

David Wheeler

I mean, come on, I'm not even convinced this "infinity" thing is real....

Julian Rachman

lim_{x\to\infty} 1/x=0

Kaj Hansen

You're quite right @BalarkaSen. I guess I just think it's weird if someone's gone that far in algebra without seeing any calc.

Julian Rachman

@Kaj are you refering to me?

David Wheeler

7:34 AM

@KajHansen I have some milk in the fridge-does that count?

Kaj Hansen

No no @JulianRachman

lol'd @DavidWheeler

Julian Rachman

ok. good.

:)

Balarka Sen

I'd explain stuff by graphing.

Julian Rachman

we have common core things

Balarka Sen

Graph whatever function you have.

You have some big singularity or missing chunk at $x = a$

David Wheeler

7:35 AM

Ok, graph the "circle function" for me.

Balarka Sen

look sideways.

if you trace the graph at $x = a$ from sideways and find something that makes sense, you have your limit.

David Wheeler

My point is, you can graph stuff that isn't functions.

Balarka Sen

@DavidWheeler What's the "circle function"?

David Wheeler

That's...kind of a problem.

Balarka Sen

@DavidWheeler Yeah, well, you need to graph something nice, of course.

David Wheeler

7:38 AM

More pointedly, I think confusing functions and graphs can lead to some problems.

Your typical conic section isn't usually a function, but...well there's some kind of similar something going on, there.

Balarka Sen

Well, you can always graph a function.

David Wheeler

OK, graph me the Weierstrauss function

Balarka Sen

If you have a function $f : \Bbb R \to \Bbb R$, your graph is $g(x) = (x, f(x)) \in \Bbb R^2$. That's all, really.

David Wheeler

Or the dirichlet function. that'll be easier.

Balarka Sen

I am not talking about practical plots. Just what a graph is.

Technically, you can always graph any function.

David Wheeler

7:42 AM

you mean every function has a graph (set)

Julian Rachman

Ok. Well, I am going to take a nap now so g-night @David and @Balarka. @Kaj good luck on finishing your problem sets.

Kaj Hansen

Thanks! Have a good night

Balarka Sen

A graph is a subset of the cartesian product of it's domain and codomain, so yeah.

David Wheeler

but this isn't what we mean when we "graph something"

Balarka Sen

We draw the subset, that's all what we do.

David Wheeler

7:43 AM

what I am trying to get at, is there's some confusion over two things with the same name

one is an "illustrative procedure", one is a formal construct.

Balarka Sen

I don't see your point at all.

David Wheeler

a high-school instructor will wave hands and act as if they are the same

Boni Tea

Is there a need to distinguish them at that level?

David Wheeler

it's perhaps understandable in the name of expediency, but it doesn't highlight the special nature of the simple smooth curves chosen to illustrate difficult concepts

Balarka Sen

A graph is just a way to visualize a subset of domain \times codomain, what more could be there to it?

I don't know what nature of simple smooth curves you are talking about.

David Wheeler

7:47 AM

@BoniTea well, that's kind of my point "at that level" means students of math are often mis-lead as to the true nature of what they are studying

let's say you're learning "pre-calculus"

in order to get an "intuitive feel", limits are presented rather vaguely

Boni Tea

@BalarkaSen I'm guessing he meant the conditions a function needs to satisfy to even define a limit.

Balarka Sen

or rather, if you prefer, a graph is a section of some trivial vector bundle. [cheek]

David Wheeler

6 years later, finding limit points in "weird topoloiges" is then hard, because they were over-simplified, and never really learned

Balarka Sen

@BoniTea Oh, I see.

Boni Tea

@DavidWheeler At that point, most of them could barely solve a quadratic. There's no room for appreciating the "true nature".

David Wheeler

7:51 AM

And yet, they can probably factor an integer into primes. There's no real conceptual difference.

Balarka Sen

I don't agree with you @David. I think intuition is needed before a formal construction.

You'll get lost inside a bunch of huge symbols before even understanding what this stuff is about.

Boni Tea

@DavidWheeler I had no problem learning sequences in topologies. It's just using a different but related definition in a different "domain" of Mathematics.

David Wheeler

@BalarkaSen Not really my point. Intuition is fine, and some details are too arcane to go into at "first look"

The trouble is, often, one is just "told things", but never why.

The "why" is often the most interesting part-and there's no room for exploration.

Balarka Sen

Also, limit of sequences aren't that hard to understand, if you're spaces are nice enough (<--- never been able to cope up with nonhausdorffness)

Mew

Hello

Can anyone help with this question?

0

Q: How can I solve this recurrence relation?

Suppose $A_n = n + nA_{n-1}$, How can I figure out an equation for $A_n$ in terms of $n$? Let the base case $A_0 = 0$.

recurrence-relations

David Wheeler

7:55 AM

If I was teaching limits, I would ask: "how can we tell if two points in space are near each other?"

Boni Tea

@DavidWheeler That's really not possible in most classroom settings.

David Wheeler

Why not?

Balarka Sen

Some "why"s might lead to overly complicated stuff.

David Wheeler

It takes 2, maybe 3 seconds to ask...not a long time.

Mew

Because near is subjective

Balarka Sen

7:56 AM

For example, say you're teaching imaginary numbers to a 5th grader.

Boni Tea

@DavidWheeler Takes notes Interview in a few hours. Going to be asked to "teach" my interviewer.

David Wheeler

If I was teaching imaginary numbers to a 5th grader, I would NOT call them imaginary.

Mew

What would you call them?

Boni Tea

@DavidWheeler It's a classroom full of teenagers. They have exam targets. They have other subjects. They have.. their "social lives". Most of them don't care about Maths.

Mew

Boni, irrelevant

David Wheeler

7:57 AM

I would draw a number line-they've probably seen those.

Mew

You must teach the subject in the fullest way possible

And let the students take from it as they wish

David Wheeler

"Right" as positive side, "left" as negative, not so uncommon.

Boni Tea

@Mew It is relevant. You can't leave half the class not knowing what you are talking about.

Balarka Sen

And he asks you "taking the square root operator on -1 gives you something that is not real. how d'you know taking some other operation on some complex number won't give you something that is not complex?"

David Wheeler

I would call imaginary numbers "up" and "down".

Boni Tea

7:59 AM

@Mew Exactly. Teach them the "intuition". And let them look into it if they wish.

Balarka Sen

you can't answer that question, as it leads you to fundamental theorem of algebra.

[personal experience]

David Wheeler

Not all questions a 5th grader asks can be answered, I grant that. I was merely answering Mew's question.

Mew

I would teach complex numbers by just leaving them in their sqrt form

e.g. sqrt of -1 is simply sqrt(-1), which we can figure out. But we know that sqrt(-1)*sqrt(-1) = -1

David Wheeler

Well, 5th graders might not have seen a square root sign.

Mew

Then as they get more comfortable let i = sqrt(-1)

True

Assuming they have met this operation

David Wheeler

8:01 AM

9th graders might have, now we can take a different approach.

Mew

If not, I woudl teach this symbol in the lessons prior

Can anyone do this: math.stackexchange.com/questions/1174789/…

1

Q: How can I solve this recurrence relation?

Suppose $A_n = n + nA_{n-1}$, How can I figure out an equation for $A_n$ in terms of $n$? Let the base case $A_0 = 0$.

recurrence-relations

David Wheeler

There are, even in "sophisticated" mathematics, competing ways to view the complex numbers. $\Bbb R[x]/(x^2 + 1)$, the Argand plane. $\Bbb R^2$ with special operations.

Balarka Sen

@Mike I was wondering if I can prove the hairy ball theorem with the machinaries I have.

Kaj Hansen

@BalarkaSen, I was presented a proof of the hairy ball theorem in Ted's course. Surely you have everything required.

Balarka Sen

Really? Without homology?!

Kaj Hansen

8:09 AM

Indeed.

I can look back tomorrow when I have access to the book

Balarka Sen

Interesting. But that must involve a lot of multivariable hotchpotch, if it was Ted's course.

:P

Kaj Hansen

mhmm

Committing to a challenge

Every Math class I feel worse at math :P. The fellow students seem to know more than me

I suppose it may just be that I only notice the ones that do know their stuff

David Wheeler

Long ago, I remember using Sperner labeling to prove that.

Boni Tea

@Committingtoachallenge They do tend to stand out.

@Committingtoachallenge It just means they are better prepared, for now. Leech off of their knowledge.

Committing to a challenge

8:20 AM

@BoniTea They are usually unpleasant to be around haha. But yes, I am trying to find the nicer ones

@BoniTea Wow in my tired state I thought you were Robjohn

(probably due to the colour of your picture)

Boni Tea

@Committingtoachallenge I cannot tell if that is a good or bad thing. Getting late?

Committing to a challenge

@BoniTea It's 6:22pm but I had to get up at 4:30am and I have had 7 hours of lectures

And my girlfriend has the car, so I am at uni until 10pm, with a 5am start again tomorrow, overloading semester = no life :S

Balarka Sen

@Kaj So essentially we want to prove that there is no nonzero tangent vector field on S^n.

Well, isn't it kind of trivial? For every nonzero vector field on S^n, there is a point such that the attached vector points diametrically outwards and a point with vector pointing diametrically inwards, and a tangent vector field has none...

Boni Tea

@Committingtoachallenge Nap in the library and hope no one draws on your face? Five hours of sleep isn't good for learning Maths.

Committing to a challenge

@BoniTea We have a page at my uni called 'stalker space'[on facebook, with 10k members] and it's a very very popular joke that anyone who doesn't get atleast one picture of someone sleeping in their years at the uni isn't allowed to graduate(solely a joke), so people will always take a photo if they see you haha

[and they put the picture up on stalkerspace averaging 2k likes]

@BoniTea But yeah. I really want to start trying to get more sleep

Boni Tea

8:29 AM

@Committingtoachallenge Do you have to get up that early?

Committing to a challenge

@BoniTea Sadly yes, otherwise I can't get to uni in time for lectures, due to living ~1.4hr away with zero traffic or >2.5hrs with

Boni Tea

@Committingtoachallenge That means your girlfriend will be in the car for 6 hours today?

Commuting can be extremely time-consuming, yea..

Committing to a challenge

@BoniTea She goes to the same uni as me fortunately xD. She needed to leave to some event graduate work related

@BoniTea Normally we just go in early and leave late to avoid all traffic and get work done, since we can't seem to work at home due to distractions

Boni Tea

@Committingtoachallenge Cough Each other.

But yes, I leave early as well.

I sleep early though.

Committing to a challenge

If we were doing the same degree we would probably not distract eachother xD. She is doing mining engineering.

I am bad at sleeping[which seems impossible to most] - Hence I don't sleep early, even though I wish I could. Normally if I go to sleep at a good time, I can't get to sleep for 1-2 hours, and if I go to sleep when I am really tired I fall asleep instantly[really tired is usually 1-2hours after a good time] so I end up with some weird weighing up the options.

So what do you do @Boni? Career or study-wise. I haven't seen you talk here before I am fairly sure

Boni Tea

8:39 AM

@Committingtoachallenge Flaky sleeping habit can be self-perpetuating : S

@Committingtoachallenge Doing MSc. Maths.

And you?

Committing to a challenge

@BoniTea B.sc in pure taking all the requirements for analysis and algebra and for applied because I have no idea where I am going xD

hence the overloaded semester

@BoniTea Does Msc mean a thesis?

Boni Tea

@Committingtoachallenge It's good experience if you can handle it. Having the option to drop some of them can be nice, I suppose.

@Committingtoachallenge My MSc is a taught course. No original work.

Committing to a challenge

They are all really fun, and if I drop any I have do do another year, so I don't want to drop any if I am doing bad

@BoniTea Oh okay, have you done hono[u]rs year already? Most people in Australia do B.sc -> hono[u]rs -> M.sc -> PHD(as far as I know)

And honours is a thesis[in australia]

Oh masters here can be thesis aswell

Boni Tea

@Committingtoachallenge Really? So they are all compulsary?

Committing to a challenge

@BoniTea I believe so in Math, but I might be wrong

Boni Tea

8:47 AM

@Committingtoachallenge My BA came with honours. There wasn't anything extra to do.

deostroll

Can we draw trees with the mathjax we have for this website?

Balarka Sen

What kind of mathematics are you interested in, @BoniTea?

Committing to a challenge

@BoniTea Ahhh, was it a 4 year? Australia is weird and the B.sc has only three years

@deostroll Apparently not sorry.

@deostroll You can with some overly difficult means, but honestly it isn't worth it

You can with general LaTeX though

Boris_yo

"It needs 48 days for one person to finish one needle, but if we divide it into 48 procedures, each conducted by one person, then 48 persons can finish 1000 needles within one day, with average 20 needles for each person."

Just wanted to know the formula guys.

Boni Tea

@Committingtoachallenge I think most Bachelors in the UK takes three years.

Boris_yo

8:49 AM

48x48=2034 needles per day its for me but seems I am wrong...

Committing to a challenge

@Boris_yo What is the question? I can't see it

deostroll

anywhere online where I can fiddle with latex?

Boris_yo

1 min ago, by Boris_yo

"It needs 48 days for one person to finish one needle, but if we divide it into 48 procedures, each conducted by one person, then 48 persons can finish 1000 needles within one day, with average 20 needles for each person."

Committing to a challenge

There is no question there Boris

Boris_yo

Do you want link to website?

Committing to a challenge

8:51 AM

@Boris_yo Me? Sure

Boris_yo

co-logistics.com/ceo.html

It's about manufacturing efficiency I think.

Boni Tea

@Committingtoachallenge I'm off. Do find a place to rest your eyes. Tata.

Committing to a challenge

@BoniTea Talk later hopefully :)

@Boris_yo What is your question?[not trying to be rude if it seems that way(text and all)]

Balarka Sen

@Committingtoachallenge So, have you been studying Simmons, then?

Committing to a challenge

@BalarkaSen Simmons hmmm, was that the alternative to rudin?

(sorry I am really tired, much more so than normal)

Balarka Sen

8:53 AM

Yeah, alternative to chapter 2.

No problem. Get some rest.

Committing to a challenge

@BalarkaSen Yeah I was using it periodically and it was great. Right now I am doing fine in rudin though(chapter 3)

But I haven't finished all the exercises for Chapter 2, since I needed to recover convergence and cauchy sequences for functional and complex analysis

Wait what, Cambridge is a city or state or something?

Balarka Sen

Good. You can also use Simmons to do topology, if you plan to study it at some point.

Committing to a challenge

@BalarkaSen I believe topology is very important in functional analysis?

It has munkres as a required text. So I suppose that confirms it

Balarka Sen

Ugh. I guess I need to stop digressing and focus on this maddeningly complicated proof of excision theorem.

@Committingtoachallenge Yeah, I guess. I never studied functional analysis.

Committing to a challenge

Homological algebra^^ ?

Balarka Sen

8:57 AM

I plan to study it at some point though.

@Committingtoachallenge No, just homology ;)

But the proof uses quite a few concepts from homological algebra, which is a nightmare. It's as non-visualizable as it can get.

Committing to a challenge

That is sad. Visualizable seems to be important for me (atleast in regards to some of this intro stuff)

[e.g. Metric space concepts]

Balarka Sen

Yep, try to visualize everything you do. Draw a lot of pictures when you study.

Committing to a challenge

I carry around an A3 art book for this purpose

Balarka Sen

Metric spaces are pretty easily visualizable. It's great stuff.

Committing to a challenge

What about banach spaces?

Balarka Sen

9:00 AM

Topological vector spaces are not that ill-behaving.

Committing to a challenge

Well I won't distract you any longer(tonight), I will go and try to study in this state now until I can go home in three hours :S

Balarka Sen

Well, try to get some rest if possible. Good luck!

ys wong

9:40 AM

Hey guys

Committing to a challenge

hi

ys wong

I am a self learner in mathmatics and i wanted to learn mathematics online

Committing to a challenge

Get some textbooks :)?

libgen.org has pdfs for every textbook I have ever looked for

ys wong

Do u know which websites have the best resources for it?

Committing to a challenge

@yswong What subjects are you wanting to study?

ys wong

9:42 AM

I wanted to start from the basic level and then slowly move my way upwards

Committing to a challenge

What have you done already? Highschool mathematics?

ys wong

Mostly mathematics

Committing to a challenge

?

ys wong

I just completed Calculus and now im starting on Linear Algebra

Committing to a challenge

Linear algebra done right - Axler is pretty good in my opinion(and my abstract algebra II teacher agrees and he is very impressive)

And everyone loves Rudin's - Principles of mathematical analysis

Do those two and you will not regret it

ys wong

9:45 AM

Rudin books is on which topic?

Committing to a challenge

Introduction to Topology and Modern Analysis: George Simmons is also awesome - For real analysis & topo

Rudin is Real analysis[one of the most important subjects you will take, arguably the most.]

ys wong

I see

Is the textbook for Linear Algebra done right freely available online?

Or do i have to purchase it?

Committing to a challenge

They are easily obtained online in pdf form in all editions, whether it is legal is another story

Axler

Rudin

ys wong

Yup thanks for the linlk

I mainly want to learn mathmatics beacause i eventually want to go towads Quantum Mechanics

Thats why i need a strong math background for that

Committing to a challenge

I can't speak much for that sorry, but real analysis is still a prerequisite at my university.

And abstract algebra is recommended prerequisite for reasons unbeknownst to me(due to lack of experience and networks in that area apologies again)

ys wong

9:53 AM

Prerequisite for Quantum mechanics?

Committing to a challenge

Quantum physics in general

ys wong

Haha i see

Committing to a challenge

Dummit and foote is a great text for abstract algebra, but I promise you that it is intense and amazingly long

You definitely would not need to finish that book(but maybe[hopefully] you will want to ;) )

ys wong

Btw whats ur maths background?

Committing to a challenge

Third year math student + doing a personal challenge of getting through 15 textbooks in 2 years(all math related)

Axler and Rudin I am doing[for classes and challenge], Dummit and foote is for classes, but not the challenge

ys wong

9:57 AM

Oh im a physics student. Im studying maths mostly so that it can help me with my physics.

I enjoy math too

Committing to a challenge

Real analysis will change the way you think, it is a must

If you are only motivated enough in math to do one, it is must be rudins PMA in my opinion

Or some other real analysis text of course

ys wong

In ur school what is the pre requisite for real analysis?

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If you are going to a university or plan to( I don't know your background), I would be really surprised if you didn't have to do this as a requirement

@yswong None

But calculus is recommended strongly

(just so you have had enough exposure to math)

ys wong

In my school though besides calculus we still have to take a subject called Foundations of Mathematics before we can take real analysis.

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Well getting ahead is definitely good(especially in Real analysis)

ys wong

10:01 AM

I have to clear that first before i can take real analysis

Basically that subject teaches u how to write proofs simillar to real analysis but a lower level

Oh btw do u use OCW?

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@yswong What is OCW sorry?

ys wong

Open courseware

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@yswong No sorry, it is definitely good to test your ability, but for me it wasn't great for teaching the material

ys wong

Yup thats what i think too.

Do u all study physics subject?

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That was what caused me to look for textbooks, and a user(@AbeautifulMind) showed me a list of textbooks that all seemed great to do in order, and this caused me to start doing them, which worked out great

@yswong No physics subjects for me, I am doing pure math in Algebra and Analysis as well as applied(non physics) maths

Since I don't have any idea what I want to be doing

ys wong

10:11 AM

I see

This the the kind of physics that i will be doing

faculty.cord.edu/ulnessd/pchem/notes11-12.pdf

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It looks like a bunch of calculus to me, but you will need complex analysis to get around problems that can't be done in calculus(or so I have been lead to believe) and this will require real analysis

Boris_yo

10:43 AM

@Committingtoachallenge My question is how they came to such conclusion. If 1 person makes 1 needle in 48 days, then 48 people would make 48 needles?

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@Boris_yo You missed the point of the article. They are saying that piecewise tasks are better than doing the whole process. This is very common in optimization, since one person doing some task in a chain all the time causes them to master that stage

Meaning everyone is an expert in their part of the chain

Think of fast food, someone makes the burgers, someone serves, someone gets chips/nugget/popcorn chicken/etc done, and someone does the cooking

If one person served, and then went and put the chips on, walked over and made the burger then packed it all and grabbed the drink, he would be doing it much slower than if many people were all doing it piecewise(even with the same number of customers)

Here the resource that is not optimal in my example is time(due to increased walking distances and lower expertise)

Boris_yo

@Committingtoachallenge I didn't miss the point. It's about optimization of process. What I was lookng at were numbers. I assumed there was certain formula they used to calculate but it seems they just used them as an example to demonstrate the efficiency of piecewise tasks.

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No formula could generally solve such a problem

Boris_yo

10:58 AM

I assumed that if it takes 48 days for one person to make needle being invoilved in 48 processes then it would take 1 day 48 people being involved in each to make 48 needles in 48 days or 1 needle per day...

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Not the case in general, there are other parameters

Unknown parameters

Unknown constraints as well I imagine

In fact from the information given we can't make any non-trivial deductions

Imagine if parts of the process occurred in different buildings?