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/sci/ - Science & Math

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15520238 No.15520238 [Reply] [Original]

Why are math books harder than they need to be?

Pic related is Wikipedia's definition of sigma algebras. It's concise and easy to understand, and comes with short simple examples.

Wheras textbooks only list a clumsy definition with 0 simple examples

>> No.15520241

>>15520238
I find the opposite. I have an easier time understanding textbooks than wikipedia, desu.

>> No.15520244
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15520244

Wikipedia's example for the definition.

This example along with the definition makes it very CLEAR and EASY to understand what the concept is about.

Wheras textbooks will list a much clumsier definiton and won't give even a single example or exercise that helps you understand what the hell the definition is about.

>> No.15520250
File: 27 KB, 482x117, sigmaalgebra.png [View same] [iqdb] [saucenao] [google]
15520250

>>15520238
That definition is taken straight out of papa Rudin and the entire rest of the first chapter is dedicated to understanding what this concept is about in terms of measurable spaces, with plenty of exercises on the definition of a sigma algebra, such as the very first exercise: "Does there exist an infinite sigma-algebra which has only countably many members?" Lots of what you're asking for are things you are expected to be able to create for yourself in a process of active reading. It builds mathematical strength and maturity.

>> No.15520257
File: 261 KB, 468x294, math book CRT.png [View same] [iqdb] [saucenao] [google]
15520257

>>15520238
>be modern Zoomer student
>want to learn math
>live in Democrat district
>open math book, hoping to learn math
>math book: "Did you know that Republicans are racist???"
This is the world we live in

>> No.15520269

>>15520238
Read the preface of this book that some anon posted in the other thread
>>15518397

>> No.15520306

>>15520238
there is a lot more to math than just learning the definition. you need lots of examples to really connect the dots and apply the math in a useful way.

>> No.15520327

>>15520250
Maybe my uni just uses shit textbooks then.
I'm using a textbook they use in a second year undergrad class, and it teaches everything much shittier than what you linked (and it says it's written for first year graduate students). Your example could still be made clearer with the addition of one or two simple examples.

The book I use has no notes or explanations. Weird notation. Only one shitty exercise for the first 20 pages of the book. Etc.

>> No.15520351

>>15520238
Math:
>oops! you are incorrect because you didn't do a triple summersault backflip while preparing a steak dinner while trying to follow our convoluted process of answering these convoluted equations!
Science:
>thing happened because another thing happened
Fuck math.

>> No.15520357
File: 55 KB, 622x618, 1671698290998527.jpg [View same] [iqdb] [saucenao] [google]
15520357

>>15520238
>doesn't post the definition he's bitching about in the first place

>>15520351
Math:
>do the triple somersault
>your theorem is now true for all of eternity
Science:
>"EHHHH THIS LOOKS SORT OF RIGHT"
>50 years later everything you think you know has been proven wrong

>> No.15520438

I have the exact opposite problem, wikipedia makes me feel like a brainlet but most of my textbooks explanations are much more cohesive

>> No.15520632

>>15520238
is it worth gaining an intuition for this bullshit if i'm brushing up on probability? or is it all a bit of a wank? t. applied math brainlet

>> No.15520859

>>15520257
group 6 member here - moderately conservative, very racially prejudiced

>> No.15520897

>>15520632
As a biobrainlet into genomics and ML and stuff, I have determined it's mostly wank but knowing how to read set notation and theoretically being able to understand the more fundamental definitions at will is extremely useful for reading papers.

>> No.15520916

>>15520238
because there are people that need to be taught through beating around the bush, you ain't one of them, good for you

>> No.15520958

>>15520632
mathematicians can come up with weird scenarios that can break many seemingly ok definitions, so think of it as fucky-math-proof.
that being said, in your applications you won't come across fucky math.