Where do I start with self learning linear algebra

Headacheguy

Hi. Im a physics major and Id probably go with mathematical/theoretical physics path.

Where do I start with self learning linear algebra? I'm good with proofs but I'm not comfortable with learning math without intuition or motivation behind the axioms. Still, I hate math without rigor (cookbook engineer math).

I'm looking for an intro book for linear algebra. Thanks. May be my first exposure to pure math excluding intro to proofs.

micromass

Try to get "linear algebra" by Serge Lang. It's an excellent book to study from.

Another good book is "linear algebra" by Friedberg, Insel and Spence.

camillio

Very nice intuitive approach to algebra provides Meyer's Matrix Analysis and Applied Linear Algebra. It is great for intuition but as the title indicates, it is far from being a rigorous mathematical text.

Headacheguy

Hi micromass. Which edition should I get?

micromass

Doesn't matter. If you can find a cheap old edition, then it'll probably be fine.

Headacheguy

Thanks!! As I've said, this is my first exposure to pure math. Is it okay if I can't at first answer the exercises? That is, can I skip the hard exercises? This happened a lot in Spivak and I just gave up on the book. Kind of a downer.

some_letters

I'm no expert but... If I were to buy a textbook to self-study from, I would check a homework-help site like Cramster and see whether that book is covered. Since you won't have anyone to really help you with the problems, having Cramster go over problems step-by-step can help a lot.

micromass

Was Spivak your first encounter to calculus?? It really shouldn't be the first calc book you study. It's more something like a second exposure to calculus/intro real analysis book.

It's ok to skip the hard exercises, but you should try them nevertheless. Ask for help if you really can't do them. This forum has a lot of opportunities for help.

Headacheguy

Yes it was. I hope Lang's would be different. And its been a year since my first dreadful take on Spivak.

micromass

I take it, that it's your first encounter with linear algebra as well?? That is: do you know something about matrices, determinants and linear systems?? If you don't know anything about them, then perhaps another book would be good. Meyers book, mentioned earlier here, would be a nice first book.

Headacheguy

Hey micro, since I've got your attention, I'd like to ask some more. I'm trying to get as good an education in math as I can cause its fun and exciting and I need it. I wouldn't be able to take any course in math (besides math methods, which isn't really math).

I've taken pre calc and methods single variable calculus. I'll be taking a course on DE on November. The class will consist only of physics majors - so It would probably be non-mathy.

Right now my plan is to learn linear algebra and will relearn calculus with Spivak and then use Fleming of Spivak on Manifolds for several variable calculus. Would this be okay for a physics major self-learning math?

Might be the case that all this math theory would be useless in physics. Still, I get the feeling that if I'd be using math, then, at least I should use it properly.

micromass

Whether it is enough highly depends on what kind of physics you want to do. For example, if you want to study general relativity, then courses on topology and differential geometry would also help. If you want to study quantum mechanics rigorously, then courses on functional analysis would be good.

So if you know what kind of physics you want to do, only then can we say what math you need.

Headacheguy

Ugh, yes. I don't know anything about matrices and stuff. What a waste.. I found Lang to be quite entertaining. And the Mayer book is large.

micromass

You can always get Schaum's outline on linear algebra. It's usually easy with lots of nice exercises. I think that would be a nice first exposure.

Headacheguy

I mean, for now as an undergraduate, without any particular field in mind, i.e. the maths that all physics majors (who will probably go with theory) should know.

micromass

Calculus (single-variable and multi-variable), ODE's, PDE's and linear algebra. That seems to be the bare minimum.

Try to get hold of Boas "mathematics mathods in the physical sciences". It might be nonrigorous but it's an excellent book and contains everything a physics major should know.

Headacheguy

Okay, thanks, micromass. Guess I'll first study the Boas book to get a feel for the maths.