Looking for a good abstract book

In summary, the conversation is about a person asking for book recommendations to learn abstract algebra with real-world applications. Suggestions include AndrewJacobsen's Algebra, Representations and Characters of Groups by Liebeck and James, Applied Abstract Algebra by Rudolf Lil, Rudolf Lidl and Gunter Pilz, and Adventures in Group Theory by David Joyner. Other recommendations include Applied Modern Algebra by Larry Dornhoff and Franz Hohn, Gallian's Contemporary Abstract Algebra, and Michael Artin's Algebra.
  • #1
AndyCiep
5
0
Hi, I was just hoping for some suggestions for a good book to learn abstract algebra with. Specifically, I'd like a book with a lot of real-world references, or practical application problems. Consider me a beginner. I've actually already taken abstract (just finished it this past semester) but, unlike calculus, statistics, and physics.. I had a difficult time grasping "how any of this matters" (so to speak :wink: ). For me, it all seemed like a jumble of new definitions and concepts without any allusion as to why I should want to know any of it. As a result, I think it became a tad difficult for me to follow and I didn't do as well as I'd have liked.

Any suggestions for a good book(s) that might nurture my somewhat stubborn "tell me why I should care" attitude?

thanks everybody
_Andrew
 
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  • #2
Jacobsen's Algebra is good but expensive, Representations and Characters of Groups by Liebeck and James.

If you want applications then the standard ones are:

without ring theory you wouldn't have the encryption techniques on the internet. indeed cryptography is a generally useful example, currently I believe that the security services think that elliptic curves may offer more codes.

then we can use it in chemistry, where the normal modes of vibration of atoms in molecules can be found using representations of the symmetry group.

advanced particle physics basically IS the study of lie algebras; and don't forget gauge groups, and category theory, and such seemiingly bizarre statements as fermions correspond to tracial elements in the infinite tensor algebra of [tex]M_2\otimes M_2\otimes M_2\ldots[/tex]
 
  • #3
It depends a bit on what you mean by "real world applications".

If you like Computer Science applications then you might try supplementing your reading with:

Applied Abstract Algebra
by Rudolf Lil, Rudolf Lidl and Gunter Pilz

It assumes you have already studies a first abstract algebra course, but it is nice because it shows applications of many branches of algebra. Most other books at this level only look at the applications of groups. Speaking of which, if you want to learn how to solve puzzles then try:

Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
by David Joyner

This one develops the theory from first principles.

If you prefer the hard sciences then you might try picking up a book on crystalography, which makes a lot of use of finite group theory.

The main physics applications use Lie groups, so you will have to get through a topology course as well before you can study them rigorously. Before then, you could look at:

Groups, Representations and Physics
by H. F. Jones

but it is liable to give serious mathematicians a heart attack due to its rather informal presentation.
 
  • #4
Another good applied text is Applied Modern Algebra, by Larry Dornhoff and Franz Hohn. It's currently out of print but you can get used copies at abebooks on the web.

This book is geared toward advanced undergrads in Electrical and Computer Engineering as well as Computer Science. This book contains a wealth of applied material on Finite State Machines, Lattices, Graph Theory, Coding Theory, as well as the usual Group Theory, Ring Theory, etc.

I completely understand the frustration of getting hold of the wrong book in studying these abstract algebraic structures. Without some appreciation for how this can be applied in the real world, it just seems rather pointless.
 
  • #5
The best book for algebra hands down is Gallian's Contemporary Abstract algebra, it is very clear and concise. It also has applications to real world problems.
 
  • #6
You might look at Michael Artin's Algebra.
 
  • #7
I took the course from a book by a guy named Fraleigh (A First Course in Abstract Algebra, I think it was). I really liked it, and still refer to it.
 
  • #8
i recommend the two a.a. books by herstein.

topics in algebra (advanced): 0471010901
abstract algebra (Beginner): 0471368792

and a site to find used books is here:
http://used.addall.com/
 

1. What is an abstract book?

An abstract book is a compilation of short summaries or abstracts of research papers or presentations. It typically includes a wide range of topics and serves as a reference for researchers and students.

2. How do I know if an abstract book is good?

A good abstract book should have a clear and organized structure, with well-written and concise abstracts that accurately reflect the content of the papers or presentations. It should also cover a diverse range of topics and be relevant to your field of study or research interests.

3. Can I access abstract books for free?

It depends on the source of the abstract book. Some abstract books may be available for free through online databases or open access publishing. However, others may require a subscription or purchase to access the full contents.

4. How can I find a good abstract book for my research topic?

You can start by searching for keywords related to your research topic in online databases or academic search engines. You can also ask for recommendations from your colleagues or consult with a librarian for assistance in finding relevant abstract books.

5. Are abstract books useful for my research?

Yes, abstract books can be a valuable resource for your research. They provide a quick overview of current research in your field and can help you identify relevant papers to further explore. They can also serve as a reference for citations in your own research papers.

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