How important is linear algebra?

[Anonymous No.11401118]

Do I really need to learn this shit to progress in physics and math?

[Anonymous No.11401124]

>>11401118

[Anonymous No.11401127]

It's extremely useful and applicable in many fields.

Basic shit like row ops and determinants will make your life much easier when analyzing systems.

In the grand scheme of things the more rigorous aspects are a stepping stone on the path to mathematical maturity.

[Anonymous No.11401152]

>>11401118
Literally the most valuable thing you will ever learn. But ignore it, whatever.

[Anonymous No.11401267]

>>11401118
the most important math i know, with out a doubt

[Anonymous No.11401356]

>>11401118
Everything makes sense once you master it. It's also very hard to explain the importance of a subject to someone who doesn't understand such subject.
What I mean by that is that you should suck it up and learn linear algebra before asking stupid questions.

[Anonymous No.11401362]

>>11401118
Yes. 100% of quantum and 30% of GR is linear algebra.

[Anonymous No.11401373]

Combinatorics and Linear Algebra are the ultimate pleb filter.

[Anonymous No.11401375]

Is Wildberger WildLinAlg playlist on YouTube a good way to learn linear algebra?

[Anonymous No.11401405]

>>11401118
If you're frustrated enough with it to ask /sci/ this question, you're probably in the wrong program.

[Anonymous No.11401407]

>>11401124
this. cant do quantum without lin alg

[Anonymous No.11401410]

>>11401375
Use a book nigger. youtube is for brainlets.

[Anonymous No.11401411]

>>11401410
What book would you recommend?

[Anonymous No.11401540]

>>11401362
90% of GR is linear algebra. You can have a topological manifold but you can't do shit on it without the structure of linear spaces. You don't get tangent spaces, tensor fields, a differentiable structure, the LC connection (hence metric), etc. without linalg.

[Anonymous No.11401634]

>>11401118
yes, it's not just "important". it's absolutely fucking essential, don't think even for a little bit that you can be knowledgeable in math or physics without mastering linear algebra.

[Anonymous No.11401654]

>>11401127
What is mathematical maturity? Like try to define it

[Anonymous No.11401657]

>>11401654
you don't start autistically screeching on sci whenever you encounter "proof is left as an exercise"

[Anonymous No.11401817]

>>11401118
I've always maintained that linear algebra is the most important, the most useful and the easiest to learn area of mathematics for non-mathematicians.

[Anonymous No.11401819]

>>11401411
M. Artin, Algebra.

[Anonymous No.11401820]

Quantum mechanics == linear algebra

[Anonymous No.11402086]

>>11401654
It's when you come across material you once found challenging and you breeze over it as it has become an instinctive part of your intuition, you no longer need to think about it because the results have been internalised and you can focus your effort on something more difficult/important.

Basically this
>>11401820

[Anonymous No.11402302]

Linear algebra is the easiest shit. You basically just need to know about row operations, invertibility, and determinants. It's probably the easiest math class you'll ever take.

The only thing you shouldn't be expected to understand is the proof for determinants. I've gone through it, and it's fucking brutal. Just accept on faith that a dterminant is what they say it is and you'll be golden

[Anonymous No.11402312]

>>11401654
When you find analytical proofs as easy as geometrical ones.

[Anonymous No.11402318]

>>11401118
vectors, systems of equations, tensors, high dimensional spaces, inverse matrices, etc come up very frequently in physics

[Anonymous No.11402324]

>>11401375
no

[Anonymous No.11402504]

>>11401118
>How important is linear algebra?
Every time you use a matrix you use linear algebra.

[Anonymous No.11402869]

>>11401407
you can do quantum without linear algebra. That said most people (me too) are heavily reliant on linear algebra

[Anonymous No.11403289]

>>11401118
>How important is math?
>Do I really need to learn this shit to progress in physics and math?

[Anonymous No.11403292]

[Anonymous No.11404708]

>>11401819
Shit tier. Dummit and Foote.

[Anonymous No.11404712]

>>11401657
Nail on the head.

[Anonymous No.11404716]

>>11401118
If you're having issues with linear algebra, just leave physics. If you're bored, pick up the more subtle details.

[Anonymous No.11404718]

>>11403292
Are you retarded?
I'm genuinely asking. OP is asking about the importance of a particular area of maths to maths and physics in general, that's exactly the kind of thread this board was made for. He isn't asking "where can I learn linear algebra", though that would also be completely acceptable, since it's still a question about maths.

[Anonymous No.11404720]

>>11402869
How do you handle probabilities of states in a multi state system?

[Anonymous No.11406235]

>>11401654
It's hard to define, but here's an example:
>we know pi is irrational, and sq-root(pi) is obviously irrational, but what about pi^2?
The mathematically mature answer:
>I don't know, I must investigate and then prove my conclusion
The mathematically immature answer:
>of course it's irrational because pi is irrational!

[Anonymous No.11406245]

>>11401118
Brehs, I dropped out of eng to do a md degree. Miss the simple days of lin alg

[Anonymous No.11406250]

>>11401118
For physics multivariable calculus (vector calc), linear algebra, functional analysis and probability are absolutely essential for almost all fields. You literally cannot understand QM, ED, GR without linear algebra.

[Anonymous No.11406727]

>>11406235

hmm

it is possible for a number to be rational yet its square root is irrational, i must investigate

[Anonymous No.11406769]

>>11406727
>>11406235

okay so if pi^2 = a/b, then pi^2 - a/b = 0, so pi would be a solution to a polynomial with rational coefficients, but pi is transcendental, so pi^2 must be irrational

[Anonymous No.11406841]

>>11406769
>pi is transcendental
That's a neat factoid, but mathematical maturity requires you to prove things from mathematical foundations. Here is a sketch of what I mean:
>construct a consistent mathematical system capable of supporting circles (pi), rationals, and polynomials and their roots
>prove, using no more than what you have constructed, that pi^2 is irrational
You don't get to just say pi^2 is irrational because pi is transcendental. At the very least you have to prove that fact, and mathematical maturity means you have to understand every step of the proof (and why the writer chose each step of the proof, as there could be many proofs that pi is transcendental). Mathematical maturity is a slippery slope argument. If you don't get to use pi is transcendental, do we get to use pi is irrational (ignoring the original question)? Do we get to use a Taylor series definition for pi? Do we get to define pi in terms of radians? What is pi? Do we get to assume that C/d is pi for every circle? And so on the rabbit hole goes, until we are left applying ZFC to geometric objects. Of course, you will never see professional mathematicians starting a proof from scratch. Mathematical maturity also means knowing what you can build, given nothing, and then filling in the details starting from there, so that your colleagues don't have to sift through a giant wall of symbolic text.

[Anonymous No.11406995]

>>11406841

I gotchu, not claiming to mathematically mature, I’m still in undergrad, I was just giving the question a go

[Impact NPC No.11407055]

>>11406841
Because we need basic communication to be THAT repetitive and peer-based instead of trust or common sense or wanting to get actual problems solved?

Is there anything in the English language and its sciences which isn't just satisfying daddy or paycheck?

[Anonymous No.11407074]

>>11401118
Yes. Algebra = hardcore math. Math is needed everywhere.

[Impact NPC No.11407089]

>>11407074
Even rapists need maths so they can count their victims.

>Predictive exhaustive audience

[Anonymous No.11407093]

is this bate

[Anonymous No.11407095]

>>11401411
don't listen to either of these idiots >>11401819 >>11404708, these books are for a general algebra course, not a linear algebra one (D&F is basically a fucking encyclopedia and Artin is too focused on matrix groups and other shit, he only has 2 chapters on actual LA). if you're a complete novice/brainlet, use Strang's LA books. if you're mathematically mature, as mentioned in the above posts, try Hoffman&Kunze's book. i won't recommend Axler's LADR, because it's essentially coordinate-free and, while i may be wrong, i think you need coordinate-based LA for physics

[Anonymous No.11407103]

Is Friedburg, Insel, and Spence a goon Lin Alg book. That's what my uni uses

[Anonymous No.11407110]

>>11407095
>you need coordinate-based LA for physics
Nope, although it is used often in classical mechanics.

[Anonymous No.11407290]

>>11407095
>>11407110
in that case Strange and Hoffman&Kunze for the high level books. for connections between LA and geometry go for Kaplansky, Gelfand, Shafarevich or Kostrikin/Manin

[Anonymous No.11407847]

>>11401118
linear algebra is essential, be it for physics, engineering, computer science

[Anonymous No.11408214]

>>11407103
It’s standard and has some good problems. Not great but not bad.

[Anonymous No.11408224]

>tfw got my CS degree in a meme uni that didn't have linear algebra
Is there like a short summary of it so I can self learn? Im sure Ill get lazy halfway through a book so whats the fastest way to learn it?

[Anonymous No.11408225]

>>11408224
You should learn it. Linear algebra is fundamental to computer science. You may not use it at your meme job but it’s important and widely used

[Anonymous No.11408231]

>>11406841
I don't think you understand what mathematical maturity is. There's no way research mathematicians can understand the entire body of work that their research is predicated upon. For some things you accept it and move on - for others you dig deeper. Lemme know when you're out of undergrad, kiddo

[Anonymous No.11408265]

>>11401654
>>11406841
Mathematical maturity refers to the acquisition of experience and intuition to the point where instead of tackling problems based on their form or pattern matching, you start tackling them with ideas and intuition while using rigor and technical details to thresh out leads and throw away misconception.

[Anonymous No.11408274]

>>11406841
>>11408265
Oh and: maturity isn’t remembering every line of every proof. It’s the ability to see “how the story plays out” and then walk through the steps of rigor without second thought. Most of early proof math is building form. The second part is building maturity, and then the third part (which is very late undergrad - early and mid grad) is learning how to produce novel leads

[Anonymous No.11408509]

>>11407103
>literally using incel's LA book

[Anonymous No.11408956]

>>11408231
>there's no way research mathematicians understand their own work
cope

[Anonymous No.11409356]

>>11406841
>foundations
lmao, you undergrad nigger. no working mathematician cares about that shit beyond knowing ZFC is self-consistent

[Anonymous No.11409485]

>>11409356
Depends on their field. Type theory is pretty big right now
Exactly what do you consider a “working mathematician” works on?

[Anonymous No.11409521]

>>11401118
Linear algebra is essential and sublime.

[Anonymous No.11409633]

>>11409356
The point is that they are capable of constructing math, and that they understand the hierarchy of knowledge. "Pi is transcendental" is an immature argument that pi^2 is irrational.

[Anonymous No.11409641]

>>11401118
You need it for your CS degree, which is the only subject worth studying

[Anonymous No.11409663]

>>11409641
>degree
>subject worth studying
The industry disagrees with you. They prefer someone who isn't a total computer nerd and got a degree in something applicable to reality, and then self studied CS. Even a math degree is superior to a CS degree, as broader mathematical skill is more broadly applicable than CS. Also you don't need real linear algebra for a CS degree, just that second-year undergrad shit that your uni bundles up with baby difeq. Or, god forbid, they just gloss over it in a "discrete math for CS" class. CS kiddos really are delusional.

[Anonymous No.11409695]

>>11407095
>Axler
Good if you don't want to learn algebra.

[Anonymous No.11409699]

>>11409695
Curtis intro is my pick tbhq

[Anonymous No.11409722]

>>11408956
>there's no way research mathematicians understand their own work
Why would one publish something they understand?

[Anonymous No.11409727]

>>11401118
Who gives a fuck, you’re an ape if you can’t appreciate pure mathematics.

[Anonymous No.11409737]

>>11409722
What you think modern mathematical research is:
>download metamath
>start with a known tautology of form P->Q
>use a random symbol generator to substitute increasingly complex formulas into each side of the implication
>occasionally reorder the symbols and partially simplify the tautology
>apply each tautology to a program that checks for certain "usefulness" criteria
>publish muh groundbreaking theorem without understanding a god damn thing
Believe it or not, there are actually people out there with IQ capable of understanding what you don't.

[Anonymous No.11410173]

>>11401118
>how important is arithmetic?
>do I really need addition and multiplication to progress in science and math?

[Anonymous No.11410573]

Really wish they offered AP linear algebra or something like that in high school. I guess people somehow find it more difficult than calc? Shame. Matrices are fun.

[Anonymous No.11410659]

>>11410573
>finish calc by the 11th grade
>while everyone else is doing that senioritis shit, I'm taking linear algebra at the local community college

[Anonymous No.11410723]

Can someone explain why dividing X by (1/2) is the same as multiplying it by (2/1)? I'm just having a hard time visualizing it.

[Anonymous No.11410864]

>>11410659
nice blog post.

[Anonymous No.11410871]

>>11409663
you sound like an undergrad who hasn't actually worked in the industry.

[Anonymous No.11410897]

>>11401118
Do you notice this two subscripts? Einstein famous equation for general relativity is basically an equation for 4x4 matrices. If you happen to know that these are not just matrices but tensors, well, change of basis in vector spaces is one of the fundamental notions in tensor definition. Source: Spacetime and Geometry, Sean M. Carroll.

[Anonymous No.11411213]

>>11410864
>>11410871
cope

[Anonymous No.11411225]

>>11410864
>waaaah the opportunities weren't served to me on a silver platter because I am soooo advanced in math my high school just couldn't keep up
Literal beta male mentality. Sometimes you have to work and go out of your way to advance yourself. Instead you just let society slow down your life trajectory.

[Anonymous No.11411239]

>>11411213
no, I just have perspective outside of /sci/. most hiring managers and mba chads filter for computer science and engineering degrees.

[Anonymous No.11411245]

>>11411225
okay. all I'm saying is nobody gives a fuck about what classes you're currently taking. it doesn't elevate the discussion.

[Anonymous No.11411275]

>>11410871
>person A gets a CS degree
>takes out student loans or works menial jobs or has daddy pay for college
>lets school dictate his pace, gets a summer slaveternship, or goes to summer school, or works, or does jack shit. his "4 year degree" is at least 2 years of bullshit liberal arts and other assorted time wasting
>person B self studies CS, maybe his parents let him live in the basement rent free, maybe he supports himself through working the same jobs as person A
>within a year and a half, he has the knowledge required for an entry level position
>now his salary has jumped, and he is financially ahead of person A
>In the 3 year difference he can study the exact same knowledge person A will get in his college, while getting paid more and getting industry experience
Many such cases. A CS degree only counts if your employer has a government contract, and it'll come up in a (((background check))). There is literally no reason to get a CS degree. It's not so hard that you need somebody to hold your hand through Stanford's reading list. If you go to school for CS, you are literally a brainlet. I know, because I took some CS classes, and I could tell just by talking to classmates about assignments or tests what the IQ difference was.
>b-but those brainlets in your entry level CS all got filtered
That may be so, but they were all still able to land CS jobs after school with a different major. In the end, their stupidity was to their benefit, as they ended up getting degrees that actually counted for something. People with CS degrees are literally too smart for their own good, yet not actually smart.

[Anonymous No.11411279]

>>11411245
>currently
That was 8 years ago kiddo. My comment should inspire you to get off your lazy ass.

[Anonymous No.11411310]

>>11411275
>I know, bc I took some CS classes
>IQ
get a load of this guy, the all knowing. yeah of course it isn't difficult to self teach CS with the plethora of information available online. you can self teach anything if you're not clueless. it's just easier to land a high paying job right out of school with the degree as a safety net.

[Anonymous No.11411319]

>>11411279
>kiddo
I already graduated. thanks for the inspiration though.

[Anonymous No.11411329]

>>11411310
>it isn't difficult to self teach CS
>land a high paying job right out of school
Behold, the IQ of CS. Literally waste 4 years on school and probably go into debt to land a "high paying job" instead of self study for a year, get a decent paying job, and work yourself up to a high paying job in the remaining 3 years. Also
>easier
>safety net
that's beta mentality.

[Anonymous No.11411360]

>>11411329
you make a lot of assertions. for instance, believing your coursera credentials are going to impress some mba chad, or that you will get promoted in three years without a degree. it sounds like you are just coping to vindicate your major choice.

[Anonymous No.11411382]

>>11411360
>some mba chad
>job security
>high paying
There's no decent CS job to be found if the person in charge of the hiring policy doesn't understand that my coursera credentials are equivalent to your CS degree. Or maybe you're just looking for some idiot at the top who you can trick into paying you double.
>promoted in 3 years
That's how I know you're talking out your ass. Promotion is not pay raise. If you aren't getting your raise, you go out and apply for more jobs, and negotiate your higher rate with your higher bargaining position i.e. the experience you just gained from your current job. It can be done faster than 3 years plus paying off student loans plus however long it takes for your "higher rate" to catch up to my stead stream of income. But I wouldn't expect you to understand these concepts, because you studied CS, and dealing with rates is the study of calculus.

[Anonymous No.11411580]

>>11411382
when your job duties change from what you were hired to do, or you are given additional responsibilities as part of a promotion, the implication is you should earn a pay raise along with the promotion, or at least be in a better position to negotiate one. I have seen employers specify the educational requirements for various high-salaried positions such as executive level engineering roles, R&D, etc. within the company. for instance, they'll require x qualification to open up y salary / position. this does not imply you cannot finesse your way into these high-salaried positions with hard work, it's just harder to move up without the degree, especially early on in your career. if you want to talk about trade offs and if a college degree is worth it in the short term, that's a different discussion than long-term earning potential.

[Anonymous No.11411619]

>>11411580
>when your job duties change from what you were hired to do, or you are given additional responsibilities as part of a promotion, the implication is you should earn a pay raise along with the promotion
That's middle school tier delusion. Even a high schooler knows that working himself up from the deep fryer to the cash register doesn't earn a pay raise.
>or at least be in a better position to negotiate
Welcome to the real world kiddo.
>i've seen employers specify educational requirements
Even in such a rare case, they will literally pay you to go to school, which should be a cake walk.
>different discussion than long-term earning potential
All else equal, long term earning potential is better if the CS degree is replaced with literally any other technical degree. Replacing the CS degree with knowledge and experience makes earning potential equivalent.

[Anonymous No.11411634]

>>11411580
>hello, mr MBA Chad, I've been taking on a lot more responsibility since you promoted me and I would like my salary to reflect that, given median rates for somebody in my position
No.

[Anonymous No.11411660]

>>11401118
You mean, like space and time and shit? Nah, don't worry about it, you'll be fine.

[Anonymous No.11411670]

>>11411580
>>hello, mr Shekelberg, I've been taking on a lot more responsibility since you promoted me and I would like my salary to reflect that, given median rates for somebody in my position
Oy Vey, Goy! At least wait until the end of the fiscal quarter to ask me that! Our budget is tight right now and we wouldn't want to worry our shareholders, now would we? But just between you and me, I'm sure I can find the money for a nice fat 5% raise when the time comes. Oh, and I'll need you to come in the next few Sundays, so that we can launch our product ahead of schedule and make our customers happy.

[Anonymous No.11411678]

>>11411670
lmao forgot the pic

[Anonymous No.11411689]

>>11401410
Boomer