Number Theory, Linear & Abstract Algebra

[BloodyFrozen]

Are there any basic prerequisites before learning about these branches of mathematics?

 

[micromass]

Are there any basic prerequisites before learning about these branches of mathematics?

For linear and abstract algebra: no. Although it kind of depends on the book. For example, if you use Hoffman & Kunze for linear algebra, then this will assume a knowledge of abstract algebra already. Conversely, there are some abstract algebra books which use matrices to a certain extent, so linear algebra could come in handy.

But in general, there are no prereqs before learning linear and abstract algebra. However, be sure that you're acquainted with proofs! (or at least be prepared to learn proofs along the way).

For number theory, a knowledge of abstract algebra comes in extremely handy. Again, it depends on the book. Sometimes, a knowledge of abstract algebra or a knowledge of calculus is required.

 

[BloodyFrozen]

How difficult are we speaking with matrices?
Normal det, or stuff like eigenvalues?

 

[micromass]

How difficult are we speaking with matrices?
Normal det, or stuff like eigenvalues?

We're talking about almost anything in linear algebra. Things like, determinants, eigenvalues, vector spaces, bilinear forms, Jordan normal forms, etc. can be (and mostly is) done without abstract algebra.

However, (and I highly recommend this:) linear algebra is best done when working with vector spaces over arbitrary fields. So knowing what a field and a group is (and some of their very basic properties) will be important. Of course, this doesn't mean that you should have taken an abstract algebra course before.

The way I see it, the abstract algebra and the linear algebra reinforce each other. Things done in abstract algebra will increase understanding of linear algebra and vice versa. So it's probably best to study them simultaneously.

 

[BloodyFrozen]

Great:)
Sorry for wasting your time, but are there any good linear and abstract algebra books that would go in harmony? (I new to the non-standard HS issued books)

 

[micromass]

Great:)
Sorry for wasting time, but are there any good linear and abstract algebra that would go in harmony? (I new to the non-standard HS issued books)

Check out my blog for a comprehensive answer: https://www.physicsforums.com/blog.php?b=3206

Basically, Friedberg is (what I feel) the best book out there to learn linear algebra. However, Friedberg lacks a bit of concrete exercises. That's why a Schaum's outline (or exercises online) should be a good supplement.

For abstract algebra, I still feel that Pinter's "a book on abstract algebra" is an excellent introdcution. It is quite elementary, but it also goes quite far! Fraleigh's book is a nice substitute though...

 

[BloodyFrozen]

Ok, thanks for all your help:)

 

[BloodyFrozen]

What edition do you suggest for Pinter? and for friedberg, is 4th edition ok?

 

[micromass]

What edition do you suggest for Pinter? and for friedberg, is 4th edition ok?

I don't think there is a remarkable difference between editions, really. The 4th edition will probably be ok.

 

[BloodyFrozen]

I was just wondering about Pinter because one is $115 and the other us $11. It's a large difference between the two. You have the second edition, right?

 

[micromass]

I was just wondering about Pinter because one is $115 and the other us $11. It's a large difference between the two. You have the second edition, right?

Oh, by all means, get the cheaper one. There's no need to pay $100 extra for virtually the same book!

I think I also bough the $11-version...

 

[BloodyFrozen]

Ok, Second version it is!

 

[Robert1986]

I haven't read nearly as many algebra books as say, micromass, has, but the best linear algebra book I have ever read is Finite Dimensional Vector Spaces by Paul Halmos. Yes, it looks like it was written on a typewriter (it was done WAY before LaTeX), but it is VERY good, IMHO.

 

[BloodyFrozen]

I haven't read nearly as many algebra books as say, micromass, has, but the best linear algebra book I have ever read is Finite Dimensional Vector Spaces by Paul Halmos. Yes, it looks like it was written on a typewriter (it was done WAY before LaTeX), but it is VERY good, IMHO.

Thanks for the suggestion, I'll go and check it out.