/sci/ - Science & Math

>>10579097
orthos is the ancient greek word for 90 degree angle

>>10579097
Google terms you don't understand, read wikipedia.
A lot of what people find "hard" about math is the terminology. You're learning a new language in which you can communicate and understand ideas.

>>10579101
Yeah, I know what it means geometrically, but I have no idea why we have to screw around taking double limits of products of functions.

>>10579117
I know what the word means, I just have no idea why it has significance in the solution of PDEs and shit.

>>10579123
You just want your paycheck, don't you?

>>10579127
>>10579123
orthogonality is kinda defined by the cross product and then the cross product is defined by orthogonality
linear algebra has all the proofs, basically it's a way to work with higher dimensions

>>10579097
orthogonal means maps to 0
0 cancels
0 doesnt add
0 is easy to use

>>10579147
*dot product

There are 3 types of engineers. Potentially 4.
>Average engineer
Got his degree. Does his work is mediocre and can possible be replaced as soon as someone else is willing to do the same thing but is cheaper.
>Average Engineer who became a manager
Pretty self explanatory.
>A good Engineer
Constantly learning and improving his base of knowledge. Potentially working as a research engineer at big companies.
>0.1x Engineer
You

>>10579097
Engineers learn connotation and inhibit it to means for general electives as a general mean for the length of time a bulb takes to light a new series in ots variable to prove that light is that using the major functions and the priors to it are a resistance for keeping the bulb lit long enpugh for it to seem to hold charge when it is in fact simply making all useful electricities in it be still long enough not to be radioactive. otherwise we would low light fusing and super bright candlesin houses ehere the candles were used to make a bread box seem higher than on the ground and the whole house seem lit. That is a joke and a pun and excuse me for aharing engineer in prospect rather than in te use of lighting for candles as the use of women holding up phones to be sen into naked instead of out of them so can actualy have fun.

>>10579502
Damn he ded

>>10579097
You ever going to put 300lbs on your back and squat up and down outside a gym? Probably not, but the strength it builds serves you in other ways. Math, and education in general, is the same way.

>>10579502
Damn son, don’t hold back on these shitters.

It allows you to find the coefficients' values in front of each basis function in a Fourier or Bessel series so you can actually solve for non trivial boundary conditions in PDEs. I. e. orthogonality allows the use of "Fourier's trick".

>>10579097
Watch the 3blue1Brown youtube series on linear algebra. Then try and attain that visual intuition you had no idea existed with anything else you learn, by yourself.

>>10581224
Visual intuition is useless, algebraic intuition > visual shiteuition

>>10581262
What is algebraic intuition? Please make a positive definition.

>>10581262
based

>>10579097
>pure math
>literally just vector calc and ODEs
>and 10th grade "orthogonality" algebra
If you can't do that then you have to share your job with any 3rd year math major.

>>10581588
We take PDEs too.

>>10581593
My point still stands. Maybe 3rd year applied.

>>10581601
How many fluid mechanics or thermo courses does the average math major take?

>>10579097
Can you please elaborate on what the average "pure" math test looks like in your engy program?

>>10579097
>pure math
lol what? We learn differentials, some optimization theory, some vector calculus, and some linear algebra. The rest is application specific. It's hardly "pure."

>>10579138
This. I can't stand this kind of thinking. If it doesn't result in immediate material gain it's of no interest to these peasants.

>>10581603
they're not pure
also, they're not super hard. People found fluid mechanics hard because they're not good at basic sink/source bullshit.
"Incompressible flow" is not nearly as hard as we make it out to be. It's just bitching to make ourselves feel good

>>10581603
The average math major also took AP physics in high school and can figure the rest out on his own. You don't honestly think memorizing all those formulas is going to be hard for someone who actually has to understand things? Anyway, if you can't do the low difficulty trivial math, somebody has to step in and do it. And then you will be sharing work and pay with a literal no degree intern. And that lowers the bar for all of us.

>>10581605
Here's an old final for our PDE course. When I took it, the questions were similar but our prof didn't give us a crib sheet.

http://pacific.math.ualberta.ca/gordon/teaching/300/2009/final.pdf

>>10581603
>03▶
>>>10581601
>How many fluid mechanics or thermo courses does the average math major take?
IDK how many IT database shitter courses does a cs major have to take? How many x for business majors courses does an operations research or industrial engineer have to take?

>>10581621
Knowing separation of variables, greens functions and fourier transform is in no way pure math. They are basic techniques in most scientific problems with mathematical basis.

>>10581621
I haven't taken PDE but it all looks very easy
>Use this technique to solve this equation
>all computations
>no proofs
>take TWO limits instead of one
All this is at the level of lower division math. All math majors have to take complex analysis, so I could probably figure out how to solve all these problems without even taking the class.
Just go to class, pay attention to how the examples are worked, and memorize the formulas. Easy.

>>10581621
>http://pacific.math.ualberta.ca/gordon/teaching/300/2009/final.pdf
this is not pure math. it's a good test for examining whether you can apply basic algorithms to solve these common forms that show up in science and engineering

There are no proofs. It's just symbolic solutions and crunching the computation. This is not a pure math exam

>>10581642
>formulas
You know how I know you're lying? In pure math we memorize theorems, not formulas.

>>10581621

thats actually really easy, its basically just solving initial value problems for known PDEs

>>10581674
>In pure math we memorize theorems, not formulas.
He's telling the engy to memorize formulas, not saying that he does it.

>>10581674
You must be the engineer
>shit tier
memorizing steps of procedure/computation
>bad tier
memorizing formulas
>meh tier
memorizing theorems and how to use them
>ok tier
memorizing proofs of theorems and proof techniques
>good tier
understanding all the proofs and proof techniques
>ascended god tier
understanding all the proofs, taking note of your thought process, then giving yourself temporary brain damage with drugs and fistfighting so you have to learn everything a different way, and then making an informed decision on which is the superior thought process.

>>10579097
>>10579123
>>10579127

Orthogonal is a linear algebra term more than a geometric one.

As far as I can tell, two basis vectors are orthogonal if they are mutually exclusive. In geometry, this manifests as right angles, but loses that meaning in higher dimensions typically associated with other branches of math. It kind of makes sense intuitively if you imagine a fourth dimension as color: changing the color of a vector does change this fourth dimension, but has no effect on the vector in the other 3 dimensions, thus the new unit vector (color direction) is orthogonal to the other three basis vectors

Dumbasses

>>10581674
...no we don't? By the time it came to the exam, I had already used/reviewed/derived so much with the theorems that they were just an extension of my understanding of the material. Take Analysis I for example: once you prove anything Bolzano showed, you immediately start to see the themes about how he recursively subdivides his intervals and derives a conclusion once he's constricted the size to something suitably small. He then demonstrates we're allowed to pick what we want once we've tunneled down towards relevant neighborhoods.

You could just memorize his results, or you could see how a lot of facts about the existence of set elements(aka, lots of proofs surrounding them too), compactness, etc., revolve around choosing what elements you want, considering small subsets, etc. Once you realize this, a lot of theorems become self evident as pretty obvious facts. Once you realize this, you can motivate exactly why this is relevant to your study.

>>10581621
>Did you go to class and do at least half of the homework: The exam

>>10581642
>formula

Fake

No math major worth their salt uses that lingo

>>10581712
You forgot
>god tier
having a chinese kid do all of the above for you

>>10579138
Not him, but yes. Why?

>>10579097
Engineering schools aren't solely focused in teaching you engineering. In reality, most of your classes (specially the math ones) will have the sole purpose of serving as the intellectual equivalent of a gym. You're not meant to use most of the movements you do while lifting in your day to day life, but these exercises make you stronger. In a similar way, most of what is taught during an engineering undergrad program is meant to make you big brained, and that's about it.
Also, if you want to work with cool shit like dynamic systems, you'll need to have some advanced math skills

>>10581612
If you're thinking you're on some sort of noble selfless quest of expanding humanity's limits or something, you're the delusional fool. Everyone's in it for themselves, even if it's just for the pleasure of discovering new things or getting recognition from one's peers. You're in no position to look down on others for pursuing their own happiness.

For the same reason you need to learn arithmetic even though calculators exist.
If all they do is teach you how to use the tools, you'll be able to do exactly what other people have done already.
By learning the underlying theory and the concepts behind the scenes, you can use your knowledge to apply concepts in new ways and synthesize your own new concepts. If all you're doing is plugging in inputs and getting out an answer, you don't truly understand it.

>>10579097
>this whole fucking thread
And you people say computer scientist don't learn enough math.
Yikes.