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/sci/ - Science & Math

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[ERROR] No.1377887 [Reply] [Original]

My math education consists of what I learned at high school in New Zealand. However, recently, I have been watching videos on Linear Algebra on Khan Academy and have been learning a lot.

My questions are:

How full of an understanding will I get after I complete this course (I am so far up to video 71) and what could it mean for my education should I go on to university?

What math do I need to be able to grasp physics at a high level?

What should I study next? What resources should I use other than Khan Academy for my education?

Thank you, wonderful /sci/entologists.

>> No.1377910

Linear algebra, vector calculus, and differential equations will get you pretty far in physics.

>> No.1378042

>>1377910
Thanks. Anyone able to answer anything else?

>> No.1378048

>>1377887

Vector space Theory. It helps a lot with vector calculus. Especially with a math major where you work vector equations in more than 3 dimensions. VST helps you understand "dimensions" without using geometry and physical relations. It is purely mathematical. It is also confusing as hell but it is really helpful especially when you go into your third and fourth calculus classes.

Look up on you tube a professor from MIT with the last name Strang He has a whole semester of lectures on there and he is amazing at explaining VST.

>> No.1378070
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[ERROR]

>Implying dogs can read

>> No.1378089

>>1377910
They'll give you a good grounding for computer graphics as well.

>> No.1378166

>>1377887
Linear algebra is a good start.
Study vector calculus, multilinear algebra & advanced linear algebra (might require abstract algebra), differential equations (ODE and PDE), and extend towards tensor calculus and differential geometry.

>> No.1378173

>>1378166
Complex/holomorphic analysis is good for applications to circuits and other subjects in physics too.

>> No.1378187

Vector space theory is just that junk about how a vector space is just an additive group equipped with scalar multiplication from a field and linear functions are just special homomorphisms that preserve vector space addition and scalar multiplication, right?

>> No.1378224

>>1377887
>I have been watching videos on Linear Algebra on Khan Academy and have been learning a lot.
Ok then, I'll now ask you a few basic definitions.

0. Why does every finite dimensional vector space have a basis?
1. When is an endomorphism of a vector space V called diagonizable and how does the algorithm for finding the appropriate basis work?
2. What is the Caley-Hamilton theorem and why isn't it completely surprising?
3. What's the minimal polynomial and what connection is there between it and diagonizability of an endomorphism?

If you can't answer these questions you haven't learned squad.

>> No.1378403

>>1378224
Guy is just looking for directions on what to study.
No reason to attempt to show off by asking elementary questions cockyfag.

>> No.1378452

>>1378403
>No reason to attempt to show off by asking elementary questions cockyfag.
You're not getting me, I'm just trying to point out what a shitty resource Khan Academy is (if used without a good book/lecture for main learning). It's bits and pieces and you miss the big picture completely.

>> No.1378467

>>1378452

>What resources should I use other than Khan Academy for my education?

Then answer him that.

>> No.1378564

>>1378467
I strongly suspect you're actually the OP. But no matter, the answer to your question should be obvious: books, books and books. And none of that "for dummies" shit please, normal math books. Linear algebra isn't too hard, you can certainly learn it without a lecture (I did, in fact).
You have to do exercises, though. And it may take some time. You can of course watch Khan Academy stuff to aid your learning process, but don't think it can in any way substitute a book on the subject.
Now, I can't really recommend any good English linear algebra book, since I'm from Germany. If you were a German speaker I would strongly recommend Linear Algebra from Gerd Fischer. But since you aren't, I dunno. Perhaps look at lecture sites and the book recommendations and pick one which suits your learning style.

>> No.1379065

>>1378224