Should determinants be taught early or not?

determinants of matrices of order 2 and 3, yes.

File: inb4smartass.jpg (33KB, 500x301px) Image search: [Google]

33KB, 500x301px

>>8563632
Wrong. They should be taught right in the middle.

File: 1482192940409.jpg (46KB, 460x459px) Image search: [Google]

46KB, 460x459px

>>8563628
It depends on the goal of the course. If it's taken by pure math majors, then sure teach them later, but if the course is mostly engineers or cs majors then you're depriving the students of must have knowledge.

File: 1241427.jpg (130KB, 841x1200px) Image search: [Google]

130KB, 841x1200px

>>8563628
Yes.

>>8563628
Not too early. I learned determinants in 9th grade but I was like "wtf is this shit" and never used them again until Calc 3 and Differential Equations.

>>8564846
Edit: 9th grade being Algebra 2 for us Amerilards

No. Shouldn't be taught at all. There is no evidence that the universe or quantum physics is determinant.

>>8564846
You never computed the area od a paralepiped.

File: 1480218660452.jpg (25KB, 400x386px) Image search: [Google]

25KB, 400x386px

>>8564901
KEK

>>8564901
Go away.

>>8563628
>linear algebra
>a whole book about y=mx+b
Fucking mathematicians.

File: 1461471505448.jpg (51KB, 960x852px) Image search: [Google]

51KB, 960x852px

>>8564901
kill yourself

>>8565232
It's pretty much just y=mx

>>8565232

>y=mx+b
>linear

normies get out

>>8565232
>MUH PRACTICALITY
>MUH SALLARY
>MUH STRAIGHT FORWARD

Kys engineer brainlet

What is the best book to relearn linear algebra for a math major?

>>8565379
http://www.springer.com/us/book/9789400726352

>>8565400
>monic and epic instead of injective and surjective
dropped

>>8565422
Learn the lexicon, set theory fag!

TRUE mathematicians don't even learn LA, they learn abstract algebra and then are like: "the entirety of LA is just a specific instance of a field lolol 2ez4me get gud you fucking loser engineers :^)"

>>8565450
>the entirety of LA is just a specific instance of a field
but vector spaces arent fields...

>>8565364
Why do we need an entire branch of algebra to study one simplest equation possible?

File: 12353914_979001015519175_759668944_n.jpg (9KB, 320x320px) Image search: [Google]

9KB, 320x320px

>>8564901

Is there such a thing as nth order algebra, or whatever it may be called?
Like the study of equations and systems of nth order polynomials, or am I being retarded and that's just the whole of algebra

File: Manga_Guide_to_Linear_Algebra.png (514KB, 605x800px) Image search: [Google]

514KB, 605x800px

>>8565379

>>8563633
>specifically teaching determinants of order 3
Lol.

>>8565625
algebra; ring theory and algebraic geometry specifically

>>8563637
This is the correct answer; I think around the end of a first intro linear algebra course is the correct time to put them.

You need to put them in lin. alg. 1 because they're really quite important for applications and many non-mathematics students will not take a second algebra course.
But doing everything with determinant voodoo that babby students aren't equipped to understand is horrible pedagogy.

>>8565611
Have you studied it properly? It is a full generalization of that equation, with multiple variables and equations and how these systems interact, and their geometrical significance. The concepts of linear algebra eventually generalize to become pretty much the foundation (along with calc) of modern mathematics. So yeah, not just y=mx+c

>>8565625
Tensors maybe?

>>8565455
you're right, it's practically useless

I hate linear algebra because of my prof last semester

fuck that guy

GO /sci/ !


[math]

\det
\begin{pmatrix}
a_0 & a_1 & a_2 & \cdots & a_{n-2} & a_{n-1} \\
a_{n-1} & a_0 & a_1 & \cdots & a_{n-3} & a_{n-2} \\
\vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
a_1 & a_2 & a_3 & \cdots & a_{n-1} & a_0
\end{pmatrix}[/math]

Any good newbie books about linear algebra that have transition into more complex stuff later on ?

>>8565968
[math]\prod_{k=0}^{n-1}P(e^{2ik\pi/n})[/math], where [math]P = a_0X^n + a_1X^{n-1}+ \dots + a_{n-1}X[/math]

>>8563628

Jesus fucking Christ, no. You need linear first, most would just quit.

>>8565379
Hoffman and Kunze

>>8565232
Yeah, if b=0 you fucking brainlet

>>8565625
affine algebraic geometry

>>8565379
>>8566068
Seconding Hoffman and Kunze. Also if you know any abstract algebra Curtis's abstract LA is good.

>>8566377
>>>8565379
>>>8566068
Denouncing Hoffman and Kunze because the way it does inner products and spectral theorem is needlessly complicated; use Linear Algebra Done Right along with Hoffman and Kunze. Plus there's always old school Finite Dimensional Vector spaces which is good because it goes over the theory in a very elegant way. The only downside is the are no exercises.
the Schaum's Outline to linear algebra is great for learning how to solve lots of different problems. (Stay away from Friedberg, it's not that good).

There's also the book Linear Algebra by Steven Roman, of which I've heard good things but never looked at myself; although just a glance at the chapters will tell you that it requires a strong background in Abstract Algebra.

Determinants should be taught in the simple cases, then fully fleshed out when covering dual spaces along side wedge products

>>8565455
Every field is also a vector space over itself. But yes, "vector space" isn't a subtype of field

The algebraist line is something like "modules over principal ideal domains," since V is isomorphic to F^n or whatever.

Algebra is gay though