Other great books like Mathematical Transition by Chartrand

[medwatt]

Hello,
I was an electrical engineering student and knew how to utilize the necessary mathematical tools to solve anything that came my way.
I always had a deep latent predilection for mathematics but due to some constraints I was unable to spare much time on improving my knowledge of the subject on more advanced matters like topology and abstract algebra. There was a bridge that I couldn't see to make the leap to advanced mathematics, hence my vicissitude in reading books on analysis and topology. I end up every time perusing the preface, authors note, table of contents and the first 15 pages before closing the book and forgetting about it.
I found a book called A Mathematical Transition to Advanced Mathematics by Gary Chartrand. It is so far the best book I have read on mathematics which maybe due to its edifying effects of my long struggles with advanced math textbooks.
I am now looking forward for a book in Number Theory, Abstract Algebra and Topology to deepen my knowledge. I don't want a book too concise as to get one frustrated or full of prolixity as to make one lose his interest.
Thank You

 

[A David]

For Algebra, Gallian's "Contemporary Abstract Algebra" is very readable and has a ton of exercises. Wade is a good introduction for Analysis, and Munkrees is the standard for Topology. Do Gallian and Wade before Munkres.