Books with a lot of problems but all with solutions

[Muhammad Ali]

Hi guys,
I am eagerly looking for books which contain a lot of problems with complete solutions. Please tell me the name of such books/resources for the following fields.
Number theory
Abstract Algebra
Geometry & Topology
Probability
I mean books like Calculus Problem Solver or Advanced Calculus Problem Solver published by REA or 3000 Solved Problems in Calculus from Schaum’s Series.
Please also advise me about studying mathematics because mathematics is not my major subject. I have BSc. degree in Electronic Engineering and recently I have got tremendous interest in mathematics (particularly pure mathematics) that now I want to study mathematics.

 

[clope023]

schaum's outlines

 

[deRham]

Good to know you have a newfound interest in mathematics.

I advise, however, that you not worry so much about solutions manuals. The classic books have solution to many problems floating around on the web anyway, and you should be able to use those as reference. Additionally, once you learn how to work with mathematics, you do exercises mainly to check whether you have a functioning understanding of the material - so you shouldn't need solutions, because these are proofs - you know it's true, but want to see if you can check why, so the steps you take help you exercise your understanding.

If you are truly new to mathematics, I would first get a good understanding of algebra and analysis. Books by Dummit + Foote in algebra and Rudin in basic analysis should introduce the fundamentals very well, plus provide more advanced reading.

 

[cwatki14]

I used a book called "Problems In Algebraic Number Theory", which is a graduate text. It has a lot of problems, and the second half of the book has all the solutions. Also, if you are not familiar with number theory it has a crash course in elementary number theory at the beginning.

 

[snipez90]

I mostly agree with deRham. I don't think the OP has any business touching an algebraic number theory text without first learning analysis and algebra (in particular algebra). The tools you learn in these two courses are fundamental, and there are many good concrete problems to work on. You can save the really abstract stuff for later, but I would recommend finding a good analysis text (deRham already mentioned Rudin, but there are many threads about good intro analysis texts), or an algebra text (I recommend Herstein, though our school uses Dummit Foote).