# Number Theory, Linear & Abstract Algebra

1. Aug 6, 2011

### BloodyFrozen

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

2. Aug 6, 2011

### micromass

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.

3. Aug 6, 2011

### BloodyFrozen

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

4. Aug 6, 2011

### micromass

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 eachother. Things done in abstract algebra will increase understanding of linear algebra and vice versa. So it's probably best to study them simultaneously.

5. Aug 6, 2011

### 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)

Last edited: Aug 6, 2011
6. Aug 6, 2011

### micromass

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

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...

Last edited by a moderator: May 5, 2017
7. Aug 6, 2011

### BloodyFrozen

Ok, thanks for all your help:)

8. Aug 7, 2011

### BloodyFrozen

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

9. Aug 7, 2011

### micromass

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

10. Aug 7, 2011

### 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?

11. Aug 7, 2011

### micromass

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...

12. Aug 7, 2011

### BloodyFrozen

Ok, Second version it is!

13. Aug 7, 2011

### 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.

14. Aug 7, 2011

### BloodyFrozen

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