I am an undergraduate student and i have completed courses like data structures and algorithms , discrete mathematics , elementary number theory (i have studied Burton's book completely), abstract algebra, topology.
I am mainly interested in computational (algorithmic) number theory because i have deep interest in algorithms and i didn't like abstract algebra course much but i enjoy computational number theory. Where should i head next now ?
I mean which are suggested books (note that i have read Burton's Number Theory) and what topic i can try to do research as an undergraduate.
I would suggest the following three books. The first one titled Computational Excursions in Analysis and Number Theory and authored by Peter Borwein is a collection of research problems and contains discussion and a comprehensive bibliography.
The second one is Computational Number Theory authored by Abhijit Das for a comprehensive study on computational number theory.
The third book is an encyclopaedia for algorithms and computational aspects of algebraic number theory. The name of the book is A Course in Computational Algebraic Number Theory authored by Henri Cohen.
Hope these will be of some help.