Exercise books in abstract algebra and number theory

Question

I'm studying Herstein's Topics in algebra and Hardy&Wright's An introduction to the theory of numbers, and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as companions.

The books I am searching for should be:

full of hard, non-obvious, non-common, and thought-provoking problems;
rich of complete, step by step, rigorous, and enlightening solutions.

Roughly speaking, something similar (in some sense) to George Pólya and Gabor Szegő's Problems and Theorems in Analysis.

Update: I would appreciate some suggestions in reference to the answers given to these questions too: 1 & 2

@Hakim Thanks for your comment, but I'm lookinf for more suggestions. Do you have any other piece of advice? — Dal, Sep 30 '14 at 19:37
Like what? The answers in the two questions I referenced are already sufficient. — Hakim, Sep 30 '14 at 21:18
@Hakim Thinking better about it, I admit you are right. Thank you again very much. — Dal, Sep 30 '14 at 21:23
I would just get the solutions manual to Dummit & Foote's Algebra book. There is no shortage of difficult problems in that book — Patrick Shambayati, Apr 03 '15 at 15:05

score 1 · Accepted Answer · answered Apr 01 '15 at 19:08

You could try 'The Red Book of Mathematical Problems' and 'The Green Book of Mathematical Problems' by Kenneth Hardy and Kenneth S. Williams.

These contain numerous problems, with hints and solutions.

Available directly from Dover Publications.

An on-line selection of problems by Yang Wang is here, but no hints or solutions.

score 0 · Answer 2 · answered Apr 02 '15 at 22:35

0

There is a booklet floating around the internet titled " Problems in Elementary Number Theory".

Be warned, the problems in that booklet are VERY hard. Though it should supplement Hardy's book well if you are able to work through the problems.

answered Apr 02 '15 at 22:35

J.Gudal

1,313

score 0 · Answer 3 · answered Apr 03 '15 at 02:30

0

Abstract Algebra - Dummit and Foote is a good book to study and solve abstract algebra.

answered Apr 03 '15 at 02:30

Ritu

1,663

score 0 · Answer 4 · answered Jan 22 '24 at 05:55

I recommend checking David. M Burton's Elementary number theory book for exercises. He has great exercises to build up your foundation. As for abstract algebra, I'm currently studying it from Fraleigh, A First course in Abstract Algebra. He has great exercises which range from computational to theoretical.

Exercise books in abstract algebra and number theory

4 Answers4