Introductory Group theory textbook
I am an Indian student currently in the eleventh grade.I haven’t yet learned calculus(I am learning it ) but I would also like to study a bit of Abstract Algebra by myself.Here is the context :
What I plan to do is to take the theorems for a particular chapter and then try to prove them myself.If I am unable to do so after trying for a long time or I have managed to prove them rigorously,only after that will I refer to the text.So, can someone please tell the name of a well-structured book which isn’t quite haphazard with good,tough problems.
If you want tough problems then I recommend
For reading I would recommend:
Fraleigh’s text might suit you.
I agree that Dummit and Foote is an awesome reference and a good book to learn, but since you are trying to learn on your own, Dummit and Foote might not give you enough examples and intuition as a course in Abstract Algebra would give you (i.e. with a teacher). I have an excellent reference which I used to learn Group Theory on my own too, it is my absolute favorite for learning group theory in solo. The reason why I like it is because they give you TONS of examples and intuition on group theory before going on the abstract theorems ; the main use of groups is because they are so broadly used in mathematics, thus intuition is very important. Looking at a problem in an abstract way might seem deadly, but seeing it as a generalization of a geometric or number-theoretic intuition might make it really easier, so getting examples from multiple branches of mathematics really helps. It is generally very user-friendly, so it’s perfect for starters. A must-read.
The name is Groups and Symmetry, written by M.A. Armstrong. If you can’t find the book online or at your library, I can send you a copy of the pdf’s I have so that you can read it.
Hope that helps,
This is likely not going to be a popular suggestion, since it’s relatively unknown, but I think the perfect book for you is Allan Clark’s Elements of Abstract Algebra.
It’s a unique book that covers the basics of group theory, ring theory, and even a tiny bit of Galois Theory, but it does it almost entirely through problems. Every chapter begins with a short section defining some terms and giving a few basic proofs, and then it leads the reader through the rest of the exposition in a series of problems, some difficult, some not. The end result is that if you actually do all the problems, you’ve written the book yourself. It’s impossible not to be comfortable with basic abstract algebra if you take this book seriously.
It’s also probably the cheapest book on this entire list 🙂