/sci/ - Science & Math

>we keep first order terms only

>For the purposes of this text, "group" will refer to "Abelian group"

its a pure lazyness. I alwayse rage when on lectures the teacher asks: "do you understand?" and when someone says "no" he answers "Ok this will be your homework exercise".
Seriously, why is it so hard to explain?

Throughout this text we will use the classical notion of probability that relies on repeated experiments and it's accompanying terminology.

>introductory complex analysis
>fubinis theorem, dominated convergence theorem everywhere

>>6097732
Ok you're probably just stupid if you don't know why this is sound in some contexts.

>"this next concept is tricky, so I'll use an analogy"
>proceeds to complicate everything with shitty "fun" analogies

>And this is obviously just <name of something obscure from 3 chapters ago> that we used earlier. Therefore by a similar process we deduce that <bunch of totally non-trivial shit>

>>6098170

>>6097852

>It can be shown that..

>>6098185

>>6097844
Because the lecturer isn't there to spoon feed you.
Working on proofs and other problems yourself is immensely rewarding.

>>6098170
I generally hate analogies when it comes to maths
>The problem is familiar to anyone who has tried to walk a dog on a leash in a big city. If the pair encounters a lamppost and the leash is long, the canine will inevitably tangle the leash around the post. But if the human continually adjusts the length of the leash as they walk so it never quite extends to the post, then both dog and human will wind around the post an equal number of times and avoid entanglement.
Let us interpret the origin in the w plane as the lamppost, the contour f(C) as the path of the human and g(C) as the dog's path. Then h(z) = g(z) - f(z) becomes the leash, and the condition that the leash never extends from the human to the lamppost--and thus f(c) and g(c) wind around the origin the same number of times--is expressed as |h(z)|<|f(z)|

>>6098170
I hate this so hard

>this is a little trick, but to properly do this you need quantum mechanics which will be covered in a later module

>>6097844
>waaah, work and learning is hard
>I'm not at school to do those things

Pick 0.

>>6098170
What is Brian Cox explaining anything?

>>6098246
Obviously they are going to use analogies in pop science.

>imagine space time being this sofa cushion.

>Looking through the book to figure out a problem
>Find the section that talks the concept behind that problem
>"You'll figure out how this works in exercise 4.13 at the end of this chapter."

>>6098234
>waaah, work and teaching is hard
>the students are putting themselves in serious debt so they can get told to figure it out themselves

>>6098268
Not him but can you seriously not see the benefit of finding things out for yourself rather than having a prof just tell you everything? It doesn't have to be laziness, he might be actually trying to teach your sorry ass.

>Theorem 4.2: We save the proof of for later.
>Proof of Theorem 4.2: As shown in 4.3 [...]
It's so confusing to see, if the author actually proved things in the right order, when they do this shit...

>>6098279
>can you seriously not see the benefit of finding things out for yourself rather than having a prof just tell you everything?
Sure, the main benefits being that you don't need to pay for school or follow some mediocre twerp's arbitrary curriculum.

It's awfully easy to hide laziness or incompetence behind some wise Yoda shit, especially when your real product isn't education, but status and employability certificates.

>>6098279
Why should we pay a dime to be told the title of a text book then "figure it out ur selflol"?

That isnt worth SHIT.

>>6098318
>paying for books
Don't you have libraries?

Also you could argue the converse:
A textbook that doesn't make you work is less effective in teaching.
And I'm sure SOMEONE publishes books that provide all the proofs.

>>6098326
A textbook should "make you work" by offering exercises where you can apply the information given by the explanatory and reference portions, it shouldn't make you work by leaving gaps in these and telling you to fill them in yourself.

>>6098170
le Charlie Epps faec

>>6098307
>Yoda shit
If you say so. I imagine we would have many more brilliant mathematicians if all they did in uni was copy proofs the professor wrote down.

>>6098335
>it shouldn't make you work by leaving gaps in these and telling you to fill them in yourself.
Why not? Those types of exercises are really valuable, if you really don't know how to start on one you know you really don't get whatever was on the chapter. If you did get it they're generally not very hard.

>>6098335
>apply the information
I'm not sure what you are studying, but for example in maths there is no "application".
Most exercises I had were small proofs.

Similar in physics: Every idiot can calculate the Lagrangian equations, but you need to do proofs and derivations (not in the calculus sense) to properly understand the matter.

>>6097831
The theory of non-abelian groups is very different to that of abelian ones. There are many techniques that work only in the abelian case; abelian groups form an abelian category, and hence appear in homological algebra. As homology underpins a huge amount of modern mathematics (Wikipedia lists commutative algebra, algebraic geometry, algebraic number theory, representation theory, mathematical physics, operator algebras, complex analysis, and the theory of partial differential equations) one does get the feeling that abelian groups are very separate from the nonabelian ones.
The same goes for rings. Non-commutative rings are nothing like commutative, unital ones and one would save a great deal of paper by omitting the words "commutative" and "unital" in texts on algebraic geometry and related fields.

>>6098179
Textbooks usually accompany lectures, which might put more emphasis on the particular concept, either through discussion or example sheets.
Likewise make sure you do the problems in the book.
If this doesn't help then yeah, it's probably a shitty book.

>>6098255
Its time to stop posting, Brian.

>>6097730
There isn't infinite time in lectures, you can't explain everything. The proofs are trivial to the professors just like showing <span class="math">(a+b)^2\neqa^2+b^2)[/spoiler] is to you. If you still have troubles, try asking other people or tutors, you need to get over the school/babysit mentality.

>>6098370
>you need to get over the school/babysit mentality.
This, goddamn. I'd rather have lectures focus on what's important rather than a bunch of trivial proofs most students can do in 10 min

>>6098170
Why do people like you hate metaphors and analogies? They help so much, it's how I learn things and explain things.

Relating a concept to tangible real life examples that many can understand easily shows intelligence.

>>6098206
So why are we paying them? To be told the title of a book?

I'm sure I am capable of googling "Textbooks for <google classes required for degree in desired field and insert here>" and then torrenting a .pdf or even buying it with out paying some tenured faggot authority loving spineless nerds suck up to $25,000 a year to tell me the same titles.

Your argument fails.

>>6098326
I'm talking about tuition, asshole. It's free now? Why is it worth 10-30k a year if all the guy does is tell us a book to read then "do it urself"

>>6098405
So don't pay them, I get the impression you won't get very far with or without uni.

>>6098338
>>6098344
If you need to be taught to get through this stuff, you're not going to amount to much as a mathematician or scientist anyway, so why go through this farce of raising up real geniuses who walked through the snow to school uphill both ways?

Doing proofs and derivations with predetermined outcomes sure as hell doesn't teach you anything about creatively advancing the state of the art. It's something classroom instruction focuses on because it's easy to test, not because it's valuable.

It's like when they're teaching practical mathematics for engineers, and things like that. Instead of teaching you to build a mathematical model for novel real-world applications, they teach you how to solve equations by hand, which is something that gives a definite right or wrong answer, is easily taught and tested, and is entirely useless in practice because you can just have computers do it for you whenever you're doing real work.

I'm pointing this out because proofs by hand are very much the same thing and calculations by hand. It's not important, it doesn't signify genuine understanding, it's just easy to teach and test and rationalize as relevant.

>>6098419
and then there's this faggot

>>6098413
Im completely satisfied with my life and learn things I enjoy because I want to know about them. I'm not going through the motions to get a paper signifying im suitable to be a wage slave to some CEO. A mindless follower.


Your post is not an argument. You're attacking me, for god knows why instead of considering the fact there is no reason they deserve to be paid any where remotely close to what they currently get, for the service they provide.

And you don't want to admit you're a drone/grunt/worker bee/wage slave in training.


Tell me a rational, logical reason as to why they deserve to be paid for telling us the name of a book and giving us a fucking list of chapters to read? And they get 100-150k a year, tons of time off, flexible hours, tenure, status, respect, and authority.

If we're meant to figure it out ourselves why do professors exist? Nice try, you conniving kike. You take many forms but I can see through your stupid little veil.

You're defending your own laziness as you're a professor, support the creativity dulling structure of university like the sodomy loving semite you are, or are a student who wants to take advantage of this cushy disonest job later and reap the rewards by manipulating young, naive, impressionable kids trying to secure a foundation for their future.


Never trust a jew.

>>6098434
I don't see how their wages are relevant. They have a set amount of hours to teach the course material and they need to cram in as much important info as possible in that time.

You're not supposed to figure out everything yourself, idiot.

>assuming readers are well familar with [complex concept], it follows that [explanation of new complex concept]
Fuck, I'm not asking you to teach me addition again but don't just reference some post-grad application of a math term I learned last chapter to teach me this new term.

>>6098216
My insides turned at that. Fuck I see that so much, esp in physics.

>>6098419
Agreed. You my friend are not a mindless idiot.
>>6098428
sup fuccboi, you mad that someone called you out? You're incapable of creative innovative thought and think blindly following laws and rules and sucking the jew cock of authority is the definition of intelligence. University is not a place that fosters creativity or unique ideas now a days given how society is and how the job market is compared to the past.

It WAS years ago. There's a reason there haven't been many great geniuses like there was before world war 2.

Men being raised to never question authority like effeminate submissive fuckboys such as yourself, hopelessly dedicating his life to please society by gaining the respect of women. Go against society and you're seen as odd, weird, and a loser. Creative thought puts yourself at risk of being wrong more often than being right, and often does make you 'odd/weird' (But only idiots think thats bad. drones. followers).

And if you're not financially successful, you dont get that hot wife you were planning on after you hit 30 and she looks for a provider.

So you go with what works, what's safe, what everyone else does to get good grades, to get the certificate that shows you have status and would make a good moderately skilled but unremarkable employee.

>Fun Fact: Anyone not mentally handicapped could do most jobs you go to school for, with a few months of on the job training if University wasn't required

There will be no Eletronic Devices allowed during the lecture, including laptops and tablets.

If you finish the test early, you must stay seated until the end of the testing period.

>>6098442
Are you blind?

Why are you ignoring the fact we pay for tuition that funds their salary and the school in general? We pay to be TAUGHT. Not to be told to figure it out ourselves.

Why is wanting to receive the service you paid for so bad? You make the professor work? You have to stand up for yourself and not be a pussy and ask him to do a better job?


>Justify the cost of going to college with out attacking my character or self in any way when all they do is tell
you to figure it out yourself in many cases. And deny help if office hours are full, or make some TA help you.

>Justify the cost of going to college with out attacking my character or self in any way when all they do is tell you to figure it out yourself in many cases. And deny help if office hours are full, or make some TA help you.

>Justify the cost of going to college with out attacking my character or self in any way when all they do is tell you to figure it out yourself in many cases. And deny help if office hours are full, or make some TA help you

>Justify the cost of going to college with out attacking my character or self in any way when all they do is tell you to figure it out yourself in many cases. And deny help if office hours are full, or make some TA help you.

>>6098356
>homology

LEL Math majors are GAY LMAO

>>6098463
Feels like I'm arguing an extreme I don't actually agree with here so I'll make myself clearer.

No anon, I am not fine with a professor refusing to answer any questions not in his lecture plan because "lel look it up yourself". Sometimes more explaining is required for a lot of students and then it's warranted.
However if you can increase your understanding a lot by just giving it a go yourself why shouldn't he encourage it? You are being paid to be taught, not to have absolutely everything served on a silver platter because that way of teaching is pretty shit.

If you still can't figure it out on your own after sitting with it, go ahead and ask again. If the prof still refuses to answer or guide you in the right direction he's just a cunt, I'm sure those exist but I've never had one.

>This lecture is my intellectual property and any notes you make are derivative works.

Related

http://theproofistrivial.com/

>>6098481
I fully agree you should try to learn things yourself. But.

The professor should be eager to help and base his lectures on, trying to explain it as effectively as possible. The student should want to learn naturally about it and try to figure it out himself.

You know, you can be spoonfed all the information, and then have exercises that challenge you to think critically and creatively apply the spoon fed information right?


We don't have to reinvent the wheel when learning how to design new vehicles. We're taught, STEP BY STEP how things are built, via spoon feeding us every bit of information. Then we use all the previous knowledge to form new ideas, unique ideas and things that involve applying that knowledge.

Making people "Re invent the wheel" so to speak, at college as part of the 'process' is fucking retrarded. Teach them everything possible, as easily as possible and fill their brain with information. SPOON FEED EM THAT SHIT.

Information/knowledge are like tools. Brain = Toolbox.

The more tools you have, the more ways you can McGuiyber a situation and find a clever solution that is new in it's self as an idea. A new way to use the tools.

Instead of getting the people to re invent existing tools since it teaches them how to 'think'.

No, it doesn't. Everyone thinks their own way. Trying to pigeonhole people into reaching a certain outcome that another guy did, years ago using the "amass tools until you find a combo that fixes the problem" by leaving out information and making them think in abstract rather than practical natural ways is just stupid IMO.

It teaches people to be fucking drones and kills creativity.

>>6098405
You pay them to provide you introduction and guidance to the subject, to provide you with a framework of accomplishment, and to serve as an expert evaluator of your mastery of the topics. You can TRY to teach yourself from books all you want. Most people will fail miserable, because they only THINK they understand.

>2013
>needing this spelled out for you

Do we need any greater evidence of how stupid the modern student is?

>>6098452
>all this rationalization for being a weed smoking dropout

>>6098514
I see your angle, however I disagree in some respects. I think some reinventing helps in learning, even the smallest problems help.
A lot of these exercises, proofs, whatever, are essentially "use the tools you've been taught so far and finish the puzzle", completely agree. What it can accomplish (I know it does for me) is that I spend more time thinking about what I have, how they actually work and thus it simply sticks better. You figure out how you can use them better than you otherwise would.
Other times you actually have to apply the tools creatively, think outside the box so to speak. Obvious benefits to that. Thinking abstract helps with thinking abstract, and that's invaluable when mathematics becomes more abstract.

What it boils down to is what you want to get out of your maths courses and that's very dependent on your major. There's a reason books on analysis have very different exercises compared to regular calculus books after all.

>>6098521
>You pay them to provide you introduction and guidance to the subject, to provide you with a framework of accomplishment, and to serve as an expert evaluator of your mastery of the topics. You can TRY to teach yourself from books all you want. Most people will fail miserable, because they only THINK they understand.
This, my god.

If you can learn as well without lectures and uni mates to study as you can in uni there's obviously no "point" in going to uni for pure educational purposes.
From what I have seen this is very rare.

>>6098372
If it takes a student 10 minutes to do them, why can't the professor do it once in 5?

>>6098539
Because then you'd need to be in lecture twice as long, at least. And for the zillionth time: doing stuff on your own is part of the learning process you moronic twit.

>>6098539
To get on with the initial lecture? 5 minutes here, 5 minutes there.. it adds up.

>>6098535
You know, if you need an expert to validate your understanding, there's a pretty good chance that what you're learning isn't all that valid.

It's always better to test your understanding by applying it to things that will fail if your understanding is incorrect. There's a lot of opportunity for that these days with computers.

>>6098548
>I wanna be a surgeon!
>C'mere Timmy, I need to see if I understood that text on aortic dissections!

Sure, you probably use a cadaver or something like that, but the point remains: if you think you don't need an expert to help you figure out if you're a moron or not, then you are a moron. Randomly testing shit all on your own is impractical and foolhardy.

>>6098460
>You can use notes on the exam, but they won't help you

>>6098460
>If you finish the test early, you must stay seated until the end of the testing period.
Seriously?
Usually it's 'can't leave within first hour or last 30 mins'.

>>6098566
I have never heard that in my life.

Usually I tell my students to remain seated during the last 1/4 of the exam. I've never heard of "you can't leave until a certain amount of time has passed", though if enforceable I could see that as a way of going "haha, if you thought you were going to randomly pop up in here and start shit and run out, then you just wasted an hour of your day instead of a few minutes". There's no way you could really enforce it, though, at least not in the US (unless maybe you were in a ghetto school and had security officers in the classroom or something).

>>6097730
>The group is nilpotent by techniques from [3]
>
>
>[3] Kontsevich, Unpublished

>>6098577
lel

>>6098569
our uni had the 30 min time thing, the way it was enforced was that when you enter the exam you had to present your student card so that they know who you are, and if you leave before the time they will tell you not to, and if you leave anyway it would go on your academic record as disrupting exam

What's the purpose of the 30 min thing anyway? Not that I mind it because I always sit them out. If someone realizes he's completely fucked after 15 why can't he leave then?

>>6098668
They can't allow anyone to join after first person leaves. This way someone delayed will still be allowed to test.

>>6098577
That is admittedly kind of annoying. Assuming there is no arxiv or other online link.

>>6098703
Oh that makes sense.

>>6098356
Yeah, I agree, it's like, many texts on rings are going to just state on the first few pages that they'll just be dealing with rings under an abelian group.
>>6098509
>Just view the problem as an alternating topological space
That is indeed a very helpful website. Why doesn't Wolfram Alpha have a similar problemsolver?