/sci/ - Science & Math

[Anonymous No.15637433]

>be me reading textbook
>understand concepts with little effort
>No difficulty with example exercises, usually do them without having to read demonstration
>get to end of chapter exercises
>am too fucking retarded to do all exercises, have to turn to solutions for at least one every time

What the fuck. Every time I find a good textbook I get filtered by at least one of the exercises per section.

[Anonymous No.15637447]

you sure do seem to like talking about yourself on social media

[Anonymous No.15637537]

>>15637433
That's exactly why theory isn't enough.

[Anonymous No.15637588]

theyre designed to challenge you, hence the challenge

[Anonymous No.15637754]

>>15637433
Textbooks with exercises are retarded. The exercises are either 1. trivial or 2. they author being too lazy to write out the details of his proofs or 3. random bullshit that cannot be solved with only the knowledge from the chapter. Putting exercises at the end of a chapter is poor style. You want to present an enlightening example? Put it in the main text. You want to omit part of the proof? Just give a footnote referencing the source of the full proof. You want to demoralize readers with exercises that take several pages of paper and a bunch of other textbooks to solve? Just fuck this shit. Useless NPC trash shouldn't be allowed to write textbooks. If the exercises aren't trivial after reading the chapter then your choice of exercise doesn't match your skills of explaining the content and you should lose your professor license.

[Anonymous No.15637759]

>>15637754
If the problems are trivial you won't learn anything.

[Anonymous No.15637763]

>>15637759
You're supposed to learn from reading the book. Exercises are not a method of learning. In fact it is epistemologically impossible to learn from exercises. They are merely a test of what you learned so far. Either your knowledge is sufficient to solve them or it isn't. In the latter case only the author is to blame.

[Anonymous No.15638853]

>nooooooooooo don't do exercises its stupid
This guy is mentally disabled

[Anonymous No.15638882]

>Unofficially wasting time with end of chapter exercises
Keks if you know you know, you know, if you don't then reread the chapter until you know you know

[Anonymous No.15639064]

>>15638882
OP here. Usually when I complete the exercises it gives me a deeper understanding of the subject. All I'm complaining about in this post is the exercises that I'm just not able to solve, and then checking the solutions to see that it was fucking obvious. I know that my IQ isn't low, so I think it's my autism which prevents me from thinking creatively. I still try to complete every important exercise

[Anonymous No.15639128]

>>15637754
You are absolutely retarded, the best kind of math books are those with only the bare essential theory-wise that let you develop the rest on your own through exercises.

[Anonymous No.15639134]

>just read the book because it makes you feel high IQ
>don't do the exercises or try to apply the knowledge because it makes you feel low IQ
>t. /sci/

[Anonymous No.15639188]

>>15639128
What a waste of time. You don't learn shit from doing exercises you already know how to solve. You don't learn shit from failing to solve an exercise either. In conclusion, you don't learn shit from exercises.

[Anonymous No.15639432]

>>15637433
No shit, this is why you should have multiple textbooks for a topic. Each text author writes completely differently. No single text rules all.

[Anonymous No.15639437]

>>15637433
try thinking about them

[Anonymous No.15640173]

>>15639188
Actually doing the exercise and applying knowledge is a way of reenforcing the knowledge you have by forcing you to apply it. This becomes less necessary the smarter you are, so you shouldn't be doing every exercise in the book, but it never becomes unnecessary.

[Anonymous No.15641010]

>>15637433
yes, passive consumption is not studying, actual thinking is the big filter. Now you know that being smart isn't about reading many books

[Anonymous No.15641289]

>>15637763
Retard spotted. Doing maths succesfully relies on being able to put together the right bits of knowledge quickly. Doing exercises simply allows for this to occur faster. You already know everything you use to solve it, yes, but you become more experienced at piecing together the solution, and thus are able to come up with a more complex solution to a similar problem more quickly, in the future.

[Anonymous No.15641741]

>>15637433
That's normal for grad-level textbooks. Often you'll find there are no solution guides to turn to, or at least not any that are close to complete.
Why pic related? Because a paper I was reading cited an -exercise block- in this book.

[Anonymous No.15641886]

>>15639188
I guess it is a waste of time if your sole objective is to know the theory, but if you plan on actually producing some results of your own some day knowing the theory alone is gonna be worth shit.
You need to know how to use it, and that's what exercises and problems is there for.
If your book has good exercises they can also let you gain a deeper understanding of the theory which in turns make you better at "knowing" .

[Anonymous No.15641939]

>>15637447
kill yourself bot
>>/sci/?task=search&ghost=false&search_text=+you+sure+do+seem+to+like+talking+about+yourself+on+social+media

[Anonymous No.15642624]

>>15641289
>>15641886
>t. had to solve hundreds of "compute the derivative of ..." exercises and still didn't get an A in calculus
Sorry to hear your IQ is too low to learn from only reading a text.

[Anonymous No.15642771]

>>15642624
"ah shit I don't know how to respond better make something up about the people who replied"

[Anonymous No.15642778]

>>15637754
Mathematics isn't a spectator sport you dumb fuck.

[Anonymous No.15642835]

>>15642778
Math isn't a sport at all. The goal is not to become the fastest derivative calculator. We have computers for that kind of shit. The goal is to understand more and more abstract stuff. Understanding is gained by reading good explanations. As explained above, learning from exercises is epistemologically impossible.

[Anonymous No.15642861]

I make up my own exercises after reading each chapter.

[Anonymous No.15642893]

>>15642835
Exercises let you see if you truly understood the subject, and not simply had the illusion of understooding. Also being able to go through a proof of a theorem doesn't necessarily mean you understand it well or have any intuition at all. Being able to apply that theorem, tinkering with its presuppositions and observing the effects of the tinkering thereby seeing why the presuppositions are necessary as they are, doing all that actually helps you to develop intuition of the theorem in question and being able to prove it without looking anywhere.
>>15637754
>learning from exercises is epistemologically impossible
By the same reasoning it's epistemologically impossible to learn from anything which doesn't introduce new axioms, as all the theorems in the text are just their consequences.

[Anonymous No.15642900]

>>15637433
It really depends on the author's intentions. Maybe the exercises are supposed to be a "you should be able to complete all of these easily now" checkpoint, but maybe there's a mix of easy and hard ones with the reader not necessarily being expected to find all of them a breeze.
Generally, if I can answer most of them and understand the solutions for the ones I miss, I'm comfortable moving on.

>>15637763
>>15642835
>learning from exercises is epistemologically impossible
I don't know what to say to this because it's so different from both my own lived experience and that of everyone I've talked to about learning maths that it almost feels alien. If you genuinely found that you could become proficient in mathematics from reading alone then you're extremely unusual.

Personally, I found that simply reading about a maths topic was basically a waste of time. I would read it and feel like I understood it- and then be completely unable to apply or remember it. The only purpose of reading was to enable me to make notes, and the only purposes of making notes was to prepare for attempting the exercises. Only successful completion of exercises (often followed by writing more notes) actually indicated successful learning.

[Anonymous No.15642907]

>>15642893
>Exercises let you see if you truly understood the subject, and not simply had the illusion of understooding.
If the reader is too dumb to learn from the text then exercises won't make a difference.

>Also being able to go through a proof of a theorem doesn't necessarily mean you understand it well or have any intuition at all.
Sorry, I never experienced it from your low IQ perspective. To an intelligent reader the intuition comes naturally when reading the heckin text.

>By the same reasoning it's epistemologically impossible to learn from anything which doesn't introduce new axioms, as all the theorems in the text are just their consequences.
Good thing that a proper math textbook does indeed introduce new definitions and helps gain intuition with theorems and examples. Only shit tier books need exercises.

[Anonymous No.15642941]

>>15642835
>Understanding is gained by reading good explanations
That's completely wrong and you obviously have never learned math. "Good explanations" are what satisfies the midwit who is immediately convinced he understands the topic, then finds himself totally dumbfounded before the simplest exercise. You can't encode the tacit knowledge that mathematics really consist of in a verbal explanation, just like you can't teach swimming via a textbook. And "fastest derivative calculator" is a strawman, good math exercises are proofs and derivations, not applying algorithms.
Yes, a proper textbook will be clearer and more to the point than others, but the intellectual work starts with thinking those explanations through in your own way while tackling an actual problem.
>As explained above, learning from exercises is epistemologically impossible.
Wrong. Whatever you learn, you always start with your inherent faculty of logic and apply that to whatever new concepts that are introduced. An exercise can give you a definition, then ask you to prove some statement about it. It's a ver effective method of learning, in fact the actually talented students will learn much faster via the motivation to solve interesting puzzles than via rote consumption of information.

[Anonymous No.15642944]

>>15642835
who said learning from exercises is epistemologically impossible, despite you and other anon? in math and science we learn though making exercises

[Anonymous No.15642946]

Gonna piggyback off of this

I have an extremely easy time learning from reading and observing, but find myself struggling with exercises when I'm first introduced to something. It's almost always because I overlooked something small while trying to work my my to the answer. Typically if I see a worked solution of a similar problem I will remember and retain the information extremely well and have no trouble using it in the future. However, it seems like using this approach offends people. Why?

[Anonymous No.15642963]

>>15642941
>That's completely wrong and you obviously have never learned math.
I have a math degree.

>"Good explanations" are what satisfies the midwit who is immediately convinced he understands the topic, then finds himself totally dumbfounded before the simplest exercise.
Thanks for admitting that exercises are bullshit. If a reader is "dumbfounded" by exercises then obviously he can't learn from them.

>You can't encode the tacit knowledge that mathematics really consist of in a verbal explanation
Uhm, just write it down explicitly? Why do NPCs hate verbal IQ so much?

[Anonymous No.15642970]

>>15642944
>who said learning from exercises is epistemologically impossible, despite you and other anon?
Our arguments should be more than enough to convince you. Or are you that intellectually immature that you need to hear it from an authority before believing it?

>in math and science we learn though making exercises
"We" don't. Only midwits suffer from the illusion that wasting time on exercises made a difference. Smart people learn from reading explanations.

[Anonymous No.15643015]

>>15642907
>If the reader is too dumb to learn from the text then exercises won't make a difference.
Right, the exercises are for those who are smart enough to learn from the text and are apply to apply that knowledge.
>To an intelligent reader the intuition comes naturally when reading the heckin text.
So by your reasoning proving something on your own is as easy as reading a proof from a text which was once published in a paper. You must have a lot of publications in Q1 journals then. What is your h-index?
If intuition comes so naturally to you, would you at least be able to come up with proofs of something like the inverse function theorem, change of variables of integrals on a general manifold, Fubini theorem? Those are pretty simple results, and going through their proofs usually doesn't present many difficulties. However were you able to prove them without looking anywhere after you learnt them first? Can you prove them now on your own?
>gain intuition with theorems and examples
From which accroding to you, it's epistemologically impossible to learn anything, were your IQ as high as you claim, you'd see that contradiction in your reasoning.
If an example is presented as an exercise, why do you think it makes the book shitty? If you're able to understand everything on the fly anyway, what difference does it make if an example is not completely elucidated and includes an exercise? Assuming the exercise is obvious to you.
Also can you name 10 good math study books for students which don't have any exercises? And compare some of those books to other books with exercises on the same topic, explaining what makes your choice better.

[Anonymous No.15643025]

>>15642963
>If a reader is "dumbfounded" by exercises then obviously he can't learn from them.
Doesn't follow at all. You obviously are low in verbal IQ yourself. One learns by starting to think, when one finds it's not enough to regurgitate.
You also seem to have some awkward confusion about intelligence. Why would a smart person be so pissed about exercises? Should be a piece of cake if you're high-IQ. In fact it's "explanations and examples" you should not need as a smart person, you can go straight to application. And do you think those good explanations you enjoy fell from heaven? Legend has it that they were worked out in independent intellectual effort by other mathematicians, something you should easily be able to repeat as a high-IQ chad.

[Anonymous No.15643026]

>>15642624
LEARN FROM ONLY READING A TEXT HAHAHAHAHAHHA IN MATH

[Anonymous No.15643067]

>>15642970
I would say that the problem is about your arguments, but it isn't the problem. It's your hypothesis. I would pay more attention if some important authority said some like this because it's a filter, but this is bullshit

[Anonymous No.15643069]

>>15642963
>I have a math degree.
That only shows how dumb you are. If you got math degree in a decent place, you should have had uni mates who were on IMO level of intelligence or a bit below, and those mates surely liked exercises.
To complete a math degree you had to write a thesis which is essentially a big exercise. Do you think writing thesis then makes no sense as it doesn't help you to learn the topic and the educational system should change? Also accroding to you publishing a previously unknown result is as easy as reading the paper about the unkown result, and anyone who's read and understood the paper would be familiar with it as well as the author.

[Anonymous No.15643082]

>>15643015
>Right, the exercises are for those who are smart enough to learn from the text and are apply to apply that knowledge.
There is no need to apply that knowledge. Either the exercise is trivial or it's bullshit that requires additional knowledge not presented in the text. Either way it's a waste of time.

>So by your reasoning proving something on your own is as easy as reading a proof
Strawtranny fallacy. I never said this.

>You must have a lot of publications in Q1 journals then. What is your h-index?
I don't give a shit about social credit score "What color is your Bugatti?" bullshit for acadummic soibois.

>If intuition comes so naturally to you, would you at least be able to come up with proofs of something like the inverse function theorem, change of variables of integrals on a general manifold, Fubini theorem?
Sure, because ... I've read the proofs. They weren't exercises, they were presented in the text.

>Can you prove them now on your own?
Yes, every mathematician should be able to do prove trivial undergrad shit instantly.

>If an example is presented as an exercise, why do you think it makes the book shitty? If you're able to understand everything on the fly anyway, what difference does it make if an example is not completely elucidated and includes an exercise? Assuming the exercise is obvious to you.
Then why call it exercise? Makes it look like retard school crap. Just call it example and put it in the text.

[Anonymous No.15643083]

>>15642970
>smart people learn from reading explanations

sorry if the average student don't have your IQ, Newton

[Anonymous No.15643088]

>>15643025
lord you are insufferable, you read like an early 00s fedora neckbeard, you are reddit incarnate

[Anonymous No.15643105]

>>15643069
>uni mates who were on IMO level of intelligence or a bit below, and those mates surely liked exercises.
I had those classmates. They weren't smarter than me. IMO is just autistic puzzles and not relevant to actual math.

>To complete a math degree you had to write a thesis which is essentially a big exercise. Do you think writing thesis then makes no sense as it doesn't help you to learn the topic and the educational system should change?
Indeed, theses are bullshit. At the low level where you're supposed to write them they are essentially just regurgitation. Merely an acadummic humiliation ritual.

>Also accroding to you publishing a previously unknown result is as easy as reading the paper about the unkown result, and anyone who's read and understood the paper would be familiar with it as well as the author.
Strawtranny. I never said this.

[Anonymous No.15643112]

try making more basic exercises on the internet about the topic that you're studying. here in Brazil I like to make exercises from "todamateria" and similar sites

[Anonymous No.15643115]

>>15643088
Well I should have guessed you're just baiting, I suppose replying in earnest does make me a bit reddit...

[Anonymous No.15643125]

i love that mathematician that can't understand that applying math theorems and concepts to solve exercises and problems is bullshit

[Anonymous No.15643137]

>>15643115
>Well I should have guessed you're just baiting, I suppose replying in earnest does make me a bit reddit...

man it's strange how you people love to bait each other in this website

[Anonymous No.15643171]

>>15643082
>There is no need to apply that knowledge
Why learn it at all then?
>or it's bullshit that requires additional knowledge not presented in the text
And why is it always supposed to be bad? That knowledge could be in prerequisites. Books on topology can often assume familiarity with linear algebra, a bit of ring and group theory, manifolds and other stuff which you should learn in other books and then apply it to your knowledge of topology.
>Strawtranny fallacy. I never said this.
No, your reasoning is that exercises don't help you to gain a better understanding. That entails that you believe that if you're able to read a proof of a theorem, you undertsnad it as good as someone who's able to prove that theorem on their own.
>I don't give a shit about social credit score
Perhaps if you were able to go through the exercises, you'd end up as good as your peers. At least your honest and don't larp. But you not giving a fuck has nothing to do with the point, if you were able to prove important theorrems and publish them, your paper would be referenced by other mathematicians eitherway. There are plenty of accomplished mathematicians who also don't give a fuck.
>Sure, because ... I've read the proofs
Can you give an outline of a proof of change of variables for multiple integrals on a general manifold? Don't look anywhere.
>>15643105
>IMO is just autistic puzzles and not relevant to actual math.
Nevertheless IMO gold medalists usually go on to have a succesful mathematical career,
>Strawtranny. I never said this.
It's not a strawman, you're just not able to apply your own reasoning to that situation.

Also list 10 good books that don't have exercises,

[Anonymous No.15643277]

>>15643171
>Why learn it at all then?
For fun. To expand your knowledge.
>And why is it always supposed to be bad? That knowledge could be in prerequisites. Books on topology can often assume familiarity with linear algebra, a bit of ring and group theory, manifolds and other stuff which you should learn in other books and then apply it to your knowledge of topology.
You know very well that that's not what I was referring to.

>That entails that you believe that if you're able to read a proof of a theorem, you undertsnad it as good as someone who's able to prove that theorem on their own.
Either you understand the proof or you don't. Once you understood it you're just as qualified to present it as the guy who proved it the first time.

>if you were able to prove important theorrems and publish them, your paper would be referenced by other mathematicians eitherway.
I haven't yet proved any important new theorem. My IQ is too limited for that. No amount of exercises in shitty textbooks would change this.

>Can you give an outline of a proof of change of variables for multiple integrals on a general manifold?
Follows directly from the definition of pullback of a differential form.

>Also list 10 good books that don't have exercises
Gotta look in my library when I'm at home. I doubt I'll find 10 though.

[Anonymous No.15643368]

>>15643277
> that's not what I was referring to
Then you're admitting that at least some exercisess are useful.
>Once you understood it
And the only way to confirm it is to prove it yourself and apply it, that is the goal of the exercises. How do you check your knowledge otherwise? Are exams useless?
>Follows directly from the definition of pullback of a differential form.
It's not an outline of the proof at all, as using pullback is just one of the steps here. So I am free to ask you why is the integral of that fullback the same as the original one? For example in one dimensional case it's simply a consequence of the fundamental theorem of calculus. Why does it hold in dimension n?
>Gotta look in my library when I'm at home. I doubt I'll find 10 though.
So in your view there are barely any good books? Why do you need to rerer to the library though, if you did your major well, you would at least come up with several good books.

[Anonymous No.15643450]

>>15643368
>Then you're admitting that at least some exercisess are useful.
Only the ones that should be better declared examples and put in the text instead of exercises.

>And the only way to confirm it is to prove it yourself and apply it, that is the goal of the exercises. How do you check your knowledge otherwise?
To whom do I need to prove my knowledge?

>Are exams useless?
They serve the purpose of filtering brainlets.

>So I am free to ask you why is the integral of that fullback the same as the original one?
Just work it out in local coordinates and observe that it coincides there with change of coordinate equation for Lebesgue integral.

>So in your view there are barely any good books?
Indeed.

>Why do you need to rerer to the library though, if you did your major well, you would at least come up with several good books.
Never needed books in university. Since exams are merely a brainlet filter it was easy to pass them with only the lecture notes.

[Anonymous No.15644135]

>>15637433
Should I even bother with textbooks without any sort of solutions? How can I know I understand the material correctly otherwise?

[Anonymous No.15644141]

>>15644135
With most problems you can just kinda intuitively know if your solution is correct, so don't worry, you'll still learn the material even if a few exercises are off.
If your using kino textbooks, there will be solutions online anyway

[Anonymous No.15644460]

>>15644135
Yes, typically you can put your answer back into start of the problem and see if its consistent

[Anonymous No.15644550]

>>15637433
I have a degree in math and have only completed half these books and it pains me

[Anonymous No.15644563]

>>15644550
I've a bachelor of science in Math and i never ever read Serge lang until recently where i started to collect lang books

[Anonymous No.15644575]

>>15637433
The way you study is highly inefficient and precisely the way brainlets study. This is what you should do: skip reading the chapters entirely, go straight to the exercises, and then go back through the text to find the theory you need for each exercises as you work through it.

[Anonymous No.15644595]

>>15639128
Any examples of such books?

[Anonymous No.15644606]

>>15644595
Rudin

[Anonymous No.15644636]

Imagine not being able to derive everything from first principles.

[Anonymous No.15644691]

>>15637433
anon...
exercises aren't supposed to be easy
you're addicted to instant gratification. lay off the porn.

[Anonymous No.15645696]

>>15637763
> epistemologically impossible
I've heard this word used one (1) other time in my life and it was used by a complete and utter fucking retard. I wonder if there's a causation here.

[Anonymous No.15645706]

>>15645696
Categorically

[Anonymous No.15645711]

>>15645706
> unironically using category theory

[Anonymous No.15646204]

>>15645706
Category theory is the ultimate midwit meme. It tells me you can not hack the more technical proofs in your undergrad classes, but to still gain a sense of superiority over your peers you decide to self-study category theory instead. Now you can draw fancy arrows and bury everything in needless layers of abstraction without having to do the actual hard, technical work of the proofs in your classes.

[Anonymous No.15646251]

>>15645696
>causation
Uh oh, it's correlation, sweaty.

[Anonymous No.15646253]

>>15646204
>oh no, those category trannies are writing more elegant and more abstract proofs than me
Cope harder

[Barkun's Cum Rag No.15646264]

>these textbooks
>cover anything smart

Use nature nerdfag

[Anonymous No.15646492]

>>15646253
t. undergrad

[Anonymous No.15646836]

>>15644636
Derive first principles from first principles

[Anonymous No.15647190]

>>15645711
>cat·e·gor·i·cal·ly
/kadəˈɡôriklē/
adverb
in a way that is unambiguously explicit and direct.
"the rules state categorically, “No violence.”"

???????